Hello! Welcome back to the third and final installment of the Hexcells trilogy: Hexcells Infinite. We've got 36 brand-new challenges ahead of us to complete the series. As a bonus, however, Hexcells Infinite includes a puzzle generator that creates a new puzzle based on an eight-digit number that you can either supply, or which can be randomly generated by the game. We'll spend some time with the puzzle generator after the main walkthrough and try out a few such levels.


As Hexcells Infinite builds upon the skills you have (hopefully) developed through the last two games, so will this guide assume you have at least some familiarity with Hexcells concepts and gameplay. What this means is that there will be a little less hand-holding than in the two previous guides. The greatest attention will be spent exploring the logic behind the most complicated puzzles, while still providing a complete walkthrough of the entire game. For example, I may not point out every single time there's a "1" in the center of a ring of five empty hexes and only one orange hex to mark; if you've played enough Hexcells puzzles, you should be able to see things like this with reasonable consistency.

That said, let's at least go through a brief primer. The idea is to use a series of restrictions on the game board to determine which of the orange hexes should be colored blue, and which should be eliminated. To mark a cell, left-click on it; to erase it, right-click on it. If you prefer, you can click on the mouse icon within the game to swap these controls.

The numbers within many of the empty (black) cells determine the number of its surrounding cells which should be colored. As in Hexcells Plus, you will also encounter empty cells with a "?" inside; there is no way to determine how many of their surrounding hexes must be colored. Instead, you must use other conditions of the puzzle to solve their surrounding cells.

You will also work with entire lines of cells, which are governed by a number. A normal integer, such as "3", simply determines how many cells along that line are colored blue. A negative integer, such as -3-, tells us that there are 3 blue cells in the line, but that they will not all be connected. That is, there will be at least one empty hex to split them up. That means you can have two blue hexes together, an empty cell, and a third blue hex; or, for example, you could have a blue hex, an empty cell, another blue hex, another empty cell, and a third blue hex. The conditions on the grid will help determine the sequence. Finally, an integer with braces, such as {3}, tells us that there are three hexes in the line, and that they will all be sequential within the line, without any empty hexes between them. These same basic rules apply to empty hexes with such notations, as well.

You can click on the line header to draw a line through all the cells within it. This is especially helpful in large puzzles, and in puzzles where there are several grids of cells; a line can extend through cells in multiple grids. Also remember that gaps within the same line do not count as line breaks! If you have a restriction that blue cells must be consecutive, a gap does not break that chain; only an empty hex does. Clicking on a line header a second time removes the line; right-clicking on the number dims it out if you are done with that line. If you do this by mistake, you can right-click a second time to embolden the number again.

Finally, you will also encounter blue hexes with a number inside. Clicking on such a cell extends a graphical overlay with a two-hex radius. The number inside the blue hex tells you the number of cells within that overlay which will be blue. You must use this information in conjunction with line and grid restrictions to determine which cells in the overlay will be marked. Similar to how blue hexes can be shared with multiple numbered empty cells, they can also be shared between multiple grid overlays. We'll discuss how to use these in great detail during the walkthrough as they introduce some of the toughest solutions the game has to offer. Once you have solved an overlay, you can right-click on that cell to dim the number. In fact, the actual control scheme is identical to that for line headers.

A nice addition to Hexcells Infinite is that your puzzle progress is now saved if you click on "Menu" and select "Exit." You may want to take a break from a particularly tough puzzle and return to it later, so this is a welcome change from the previous two games. You can also choose to restart the level from the menu, which is useful if you want to retry and see if you missed something earlier or just aren't happy with your current progress. These are nice tweaks to the game's basic presentation and can ease the frustration some players might experience on the toughest levels.

As always, you want to start with the most obvious moves you can find first; usually, doing so will eliminate a number of cells from the outset and potentially define obvious hexes which must be marked. Also, be sure to combine the use of line restrictions and grid overlays, in addition to the actual restrictions on the grid, to help with the solution. We'll spend a lot of time discussing individual situations as they arise.

Finally, if you need to go back over any concepts introduced in the previous two games, here are links to my other two walkthroughs. I highly recommend completing both before trying to complete Hexcells Infinite.

Hexcells: https://steamproxy.com/sharedfiles/filedetails/?id=320523083

Hexcells Plus: http://steamproxy.com/sharedfiles/filedetails/?id=368269515

With all of that said, let's begin our journey on the way to ultimate mastery of the puzzles of Hexcells Infinite!

SPECIAL NOTE: For some of the longest puzzles, I utilized the save feature myself in writing this guide. The save feature does not keep track of any line headers or hub numbers struck out by right-clicking on them; it only saves the actual progress of the puzzle itself. As a result, there are instances where screenshots may differ from one play session to the next as far as which such numbers I have dimmed out. This in no way affects the solution of a particular level, but I wanted to state this up front in the interest of full disclosure, and to prevent any possible confusion that may arise from this.

The first chapter of puzzles is designed primarily to review the basic concepts of puzzle-solving. We get an easy introduction to the game in Puzzle 1-1.




The opening puzzle is actually quite reminiscent of Puzzle 1-1 from the original Hexcells, except that we are given a third grid to work with instead of a column of cells extending downward from the "0" in the second grid. Our opening moves couldn't be easier. We get an empty hex with a "6" in the first grid, and one with a "0" in the center grid. Mark all the hexes around the "6" (by left-clicking), and erase all the hexes around the "0" (by right-clicking).

The final grid is only slightly more complicated. Start with the "3" at the bottom-center; it has only three orange hexes in a ring along its top edge, meaning they all must be marked. Notice that the "2" just up and to the left also receives two blue hexes from this. Since the "2" shares two blue hexes with the "3", clear the other four surrounding it. This leaves only two "active" cells on the far right side, adjacent to the "4." Since the "4" still needs two blue hexes, and there are no other active cells on the board, mark them both to solve the puzzle.



Special Notes: Remember that the term "active hexes" refers to both blue and orange hexes. Orange hexes are considered active because they're still in play; it's not yet known whether they should be marked or erased. Blue hexes are considered active because they are part of the pattern the puzzle represents and not eliminated from the game to become empty cells.

Also, concerning the concept of "shared hexes," this refers to any active hex that can be claimed by one or more empty hexes--for example, the two blue hexes positioned between the "1", "2", and "3" at the bottom of the third grid. This concept can also apply to hexes shared between empty hexes and a line header or, later, hexes covered by multiple Grid Overlays. Learning the concept of shared hexes is critical to solving virtually every puzzle we will encounter.

Hexes Earned for Completing This Puzzle: 3




The placement of the empty cells here is quite interesting. We get two zeroes in the top-right and bottom-left corners, and a "2" dead center. We can't possibly determine which cells it will claim yet, so go ahead and clear the cells bordering the zeroes. For that matter, go ahead and clear those around the "0" that we'll reveal on the left side from doing this.

The trio of empty "1" cells we uncover here can be a little tricky. Note that the one on the bottom has only one remaining orange hex bordering it. When it's marked, the "1" in the center of the trio shares it. This allows us to clear the other two hexes bordering the "1" in the center, and the "1" at the top-left will then claim the final hex in this cluster. Here's what it looks like:


Let's keep going to the right now. We want to clear the first orange hex in the narrow section extending towards the center; the "1" it borders already has a blue hex. We'll clear the next hex over, as well; the "1" we just revealed shares the same blue hex. Now we get a "0", so clear the next cell over, revealing a "1." Stop here; we can't completely solve it yet, though this does tell us that the "2" in the center will share one of its two blue hexes with this "1".

Let's move to the right side now. The "2" bordering the "0" only has two orange hexes to work with; when both are marked, one of them will also go to the adjacent empty "1" cell. Clear the orange hex below the "1". This reveals another "1", which shares the same blue hex. So clear the two remaining orange hexes around this "1". Guess what? We get a third "1" to share the same blue hex! So clear the orange hex on its top-left edge, which reveals a "2". Guess which cell gets eliminated next?

We're almost done. Clear the orange hex left of the "1" we revealed at the end of the last step, since it already has a blue hex. Another "0"; just clear the next hex over. We now get a "1" to the right of the "2" in the center. So we know from this that one cell to the left, and one cell to the right of the "2" must be marked; otherwise, the empty "1" cells cannot get the blue hexes they need. Go ahead and clear the two hexes above and below the "2". The "0" revealed below the "2" sets up the solution:



Hexes Earned for Completing This Puzzle: 4

The last two puzzles have done a good job of reacquainting us with the most basic logic of Hexcells. The difficulty starts going up just a little in this puzzle; we'll need to use logic similar to that of some of the early puzzles from Hexcells Plus.




So where do we even begin? We're given only an empty "1" and an empty "5". As you might expect, the maximum number of cells that can surround any one hex is 6. Both the "1" and "5" are placed to where they have the maximum number of surrounding hexes. In a situation like this, the idea is not so much to identify which potential cells will be marked, but instead to identify those which cannot be marked.

Notice that two of the orange hexes in question are shared between the "1" and the "5". We know that one of these cells--but not both--must be marked in order for the "5" to gain a complete set of blue hexes. We can decisively say, then, that the "1" must claim its blue hex from this pair, meaning that the other surrounding hexes will be erased. We can also decisively say that the remaining four hexes surrounding the "5" must be marked. That means our opening move is this:

Unfortunately, all of the empty "1" cells we just revealed are positioned to where we cannot logically determine any of the blue hexes they will gain just yet. The "2" we just revealed, however, can be solved; note that there are only two active hexes for it to work with, guaranteeing they will both be marked.

This opens up a path to solving the "5". Marking the last two hexes gave the "1" on the bottom-right edge of the "2" its lone blue hex; when we eliminate the three remaining hexes surrounding it, we'll actually eliminate one of the two hexes shared between the "5" and the "1" we started with. This also opens our path to solve the top-left corner; can you come up with the sequence?


We can work the top or the bottom from this. Let's just start at the top since we're there anyway. It may not look like we can solve the "3" yet, but notice that the "1" on its top-left edge has only one orange hex to work with. Once it's marked, it gives the "3" a third blue hex. Clearing the final orange hex from it gives us another "3". Well, this one can't be solved yet. Try the bottom?

Start with the "1" at the bottom-left edge of the grid. Notice that both it, as well as the "1" on its top-right edge, both have the blue hexes they need. This eliminates two orange hexes. We get another "1" and another "2" from this. The "1" has only one hex to work with, that being the very bottom-center cell. Once it's marked, the "2" gets a second blue hex, and the two on its right will be cleared. So now, we have this:

We want to continue along the bottom now. The "1" we just revealed will naturally share the blue hex we just marked below the "2", letting us clear the next cell to its right; doing so leaves only one remaining choice for the "3" we just revealed to get its third blue hex. This blue hex will be shared by the "1" just uncovered, so clear the next cell to its right going up the edge of the grid. Another "1"; you know what to do with its two remaining orange hexes.

We get yet another "1" right above the one we just worked. They both share the same blue hex, clearing two more cells. I'm sure you'll never guess what to do with the orange cell above the "3" that this reveals...





Almost finished. We opened up another "1" directly above the "3" we just uncovered. I'm sure you see the shared blue hex by now; go ahead and clear the three orange hexes still touching the "1". This puts the two empty "1" cells in the next-to-last column in position to claim the final orange hex on this side of the grid.

We only have two hexes left, one of which must be colored. Notice how the "3" we uncovered a moment ago, as well as the "1" on its top-right edge, have only the same orange hex they can possibly claim. Once that one is marked, we solve the "3" over to the left that we had to abandon earlier. Erase the final cell to solve the puzzle.



Hexes Earned for Completing This Puzzle: 5


The previous puzzle gave us a bit of a head-scratcher, but nothing we couldn't handle. In Puzzle 1-4, we revist the concept of sequential blue hexes with the notation of "{x}". The number inside the braces (brackets in-game) still tells us the number of blue hexes to be colored; the notation tells us that they also must be consecutive.



Let's just number the grids 1 through 3 in order from left to right and take them one at a time.

Grid 1: We get a {3} in an incomplete ring of only five hexes, with the top-left cell already blue. The notation tells us that the three blue hexes must be consecutive, without an empty hex between them. Since the existing blue hex is positioned at an endpoint, just start from there, mark the next two over, then clear the last two. Simple!

Grid 2: This is another situation where we want to determine which hexes cannot possibly be marked. We again have an incomplete ring of five hexes, this time surrounding a {2}. This time, our given blue hex is in the center of the ring. Since the next blue hex must be consecutive to this one, either the cell to the left or the cell to its right must be marked; the other two, on the bottom-left and bottom-right edges of the {2}, cannot possibly be connected to the blue hex. Erase them; the empty hexes revealed show us how to finish the grid.

Grid 3: We need to think this one through just a little bit more, since we are given both a {2} and a {3} in a larger grid. In Hexcells, always start with the simplest move you can make. The {2} only has three orange hexes surrounding it. Remember: We need two consecutive blue hexes here. There are only two possible ways to do that: either the first and second, or the second and third, cells will be marked. This means that the middle cell around the {2} must be marked.

Guess what? We fed a blue cell to the {3}, and it happens to be an endpoint in the incomplete ring surrounding it. So mark the next two consecutive cells around the {3} and clear the remaining two. We ultimately get a "0" from this; follow it back around to the {2}, and the solution will become clear.



Hexes Earned for Completing This Puzzle: 5

The puzzles start getting a little longer now. Puzzle 1-4 gave us a very basic reintroduction to the concept of marking consecutive hexes; that knowledge will be utilized in some fashion for the rest of the game.




So the opening gives us a rather interesting situation. We get a {2} on top, with a total of four hexes around it: Three on top, one underneath. We also get a "0" at the bottom. Start with the easiest move first; that means clearing cells from the "0". Hmm, a trio of empty "1" cells. Do you see any possible way of determining which cells they get yet? I sure don't.

Maybe we'll have better luck with the {2}. We know right away that the cell directly above it must be marked, and the cell directly below it eliminated. Why? Well, it should be pretty easy to see why we cannot mark the cell under the {2}; it doesn't have any adjacent hexes to mark! So naturally, our pair of consecutive blue hexes has to come from the three along its top rim; we have to mark the middle hex in the chain to attain this. Our opening looks like this:

We'll clear those cells from the "0" we just uncovered next; I only didn't from the last step to focus on the specific logic surrounding the {2}. After we do clear these hexes, we get a pair of empty "1" cells and a "2". We have to start with the "2"; it will guide us to solving the others. Notice how the "2" is positioned so that it has only two active hexes to work with. Mark both, thus giving a blue hex to the "1" in the center of this cluster. Clear the two hexes which remain under it, leaving only one hex for the "1" on the left to claim:

Here's where the puzzle gets a little more interesting. The "1" we revealed a moment ago shares the blue hex we just marked with the "1" directly above it; this clears two more hexes. I'll diagram this out in the next image; basically, we are looking for cells we can eliminate from the grid to lead us to the ones we need to mark.

We just revealed a "2" with the last elimination. It has three possible choices for blue hexes, two of which are shared with the "1" at the bottom-center. Since we know that one, but not both, of those cells must be marked, the "1" cannot possibly claim the orange hex on its upper-right edge. It also guarantees that the hex right below the "3" will be marked so that the "2" can get a pair of blue hexes. Mark this one, then erase the hex on the upper-right edge of the "1". This leaves only a single choice for the "1" at the bottom-right edge to claim its blue hex:

We have a somewhat similar situation with the "2" we revealed just now, and the "2" right in the center of the grid. The "2" in the middle has a string of only three remaining active hexes, with one of them already blue. Notice how its two remaining orange hexes are shared with the lower "2". So we know that whichever one it claims will also solve the lower "2", meaning that the hex on the upper-right edge of the lower "2" has to be eliminated.

We get a {3}, which couldn't be more helpful. Even though it has five total active hexes, we've already marked the first blue hex at an endpoint directly below it. Mark the next two in sequence and clear the two remaining orange cells. That leaves this:





The last sequence opened up the solution to the bottom section. The "2" in the center of the grid now has only two active hexes surrounding it; we need to mark the one directly below it now. This blue hex is shared with all of the nearby active hexes. So now, clear the hex directly below the "2" positioned on the lower-left edge of the central "2"; the "3" that this opens up has only one choice for a third blue hex:

Only the outer edge of the grid remains. You may have seen it earlier, but the "3" near the right-center of the grid already has three blue hexes; we'll now go ahead and eliminate its remaining orange hex (if you did so earlier, that's great!). The "2" this reveals shares two of those blue hexes; clear the one above it. A "1"; it shares one of those blue hexes, too. Continue clearing the next one; a "0". Follow it.

We can now solve the {2} at the top-center; the "1" we just revealed has only one possible blue hex to claim, which will also give the {2} its second blue hex. So now, clear the hex on its top-left edge. The "1" this reveals shares the hex we marked in the very first step! Clear the next one. Follow the "0" that appears, and you'll get to where the "2" ultimately revealed has only one choice for a second blue hex. Marking it completes the "3" we abandoned a minute ago. Erase its remaining orange hex, then mark the final cell to complete the puzzle.



Hexes Earned for Completing This Puzzle: 5

At this point, Chapter 2 will unlock. The first several puzzles have reintroduced us to the core puzzle-solving concepts in Hexcells, but there is still more to come. We've even had a few mind-benders thrown at us already; the game will only continue getting harder as we go.

Full disclosure: Some of the later puzzles are so long and intricate that they may require several sections to fully explain. As in the previous guides, I'll provide a screenshot of the current progress at the beginning of each new section for a puzzle.




We get nothing but a smattering of empty hexes to start this one. With puzzles such as this, even finding the opening move can be a bit of a challenge. We need to closely examine what we have. We can see pretty easily that we can't do much with the "1" on the left or the {2} on the right. It's so tempting to start marking hexes around that {5} at the bottom; after all, the odds are certainly in our favor! But we'll leave it for now.

The only hex that can get us started is the {2} at the top-center. With only a standard ring of three hexes around the bottom edge, we know for certain that the center one in that group will be marked. Once we do so, the puzzle opens up somewhat; the blue hex is shared with the "1" directly below it, and the remaining four hexes around the "1" can then be eliminated.

We got a "0" out of that batch of eliminations, so clear the two orange cells surrounding it. Notice that the "1" above that "0" shares the blue hex we just marked. After we clear the other two orange hexes around its top edge, we can also mark the remaining cell under the {2}. And guess what? The {2} we revealed a moment ago shares both of the blue hexes with the original {2}, and that clears two more hexes from the grid. So after all of that, we begin with this:

We're going to solve that {3} we just revealed next. As we have seen, the blue hex it owns is an endpoint in its ring of hexes, so we just need to mark the next two in sequence and clear what's left around the {3}. The "4" we then reveal has only four total active hexes surrounding it, so just mark the other three. We've now given a blue hex to the {2} on the right edge; we may not know which hex it will claim yet, but we do know that the hex directly below it cannot be marked since it cannot possibly link up to the blue one. Clearing it gives us another "0", which shows us how to solve the {2}:

We can continue working clockwise around the grid, or we can return to the top. Let's see what continuing clockwise gets us. We opened up a "2" on the bottom-left edge of the {2} we just solved. It shares two blue hexes with the "4" we solved a moment ago. Go ahead and clear the hex on its bottom-left edge.

Now, tackle the "1" directly below the "0" near the bottom-right corner; see how it only has one active hex to claim? Notice how this blue hex is shared with both the original "1", as well as the "1" directly above. We can clear the remaining hex from the bottom-left edge of this "1", uncovering another "2"; the "2" located above this one will then have only one possible hex to claim for its second blue hex.

The hex we just marked gave a second blue to the "2" we uncovered by that last erasure. Clear the two orange cells around the bottom rim of this "2". We might finally be able to solve that {5} at the bottom now. The "1" we just uncovered below the "2" already has a blue hex; clear the one on its bottom-left edge. Another "0"; clearing the orange hex on its top-left edge also removes one from the {5}. Color all five active hexes still surrounding it, thereby also solving both of the empty "2" cells along the top rim of the "0". Finally, to complete this section of the puzzle, the "1" right above the section we just worked has to claim the section's final hex:

There isn't much left to do now. If we continue circling around the puzzle, we see that the {2} just above and to the left of the {5} already has two blue hexes. We can go ahead and erase the remaining hex on its bottom-left edge, but we can't solve the "2" this reveals just yet.

So let's now return to the top. That empty "3" cell just left of the center has only three hexes it can claim. Marking them gives one to the "1" below it, clearing another hex.

Now this is an interesting dichotomy. We just revealed a "3" with four active cells around it; the one directly above it is already marked, so we need two more. Notice, however, that the next two cells in sequence from the blue hex are both shared with the "1" over on the left edge. Go ahead and mark the cell directly below the "3"; there's no choice but for this one to be marked.

So we know that only one of the hexes between the "1" and the "3" can be marked, thus solving both cells. We also know by extension that the "1" cannot possibly claim either the cell above or the cell below it. Erase both.

Believe it or not, we have to now turn to the "2" located just down and to the right of the "3" to solve this section. Remember how we just marked the cell directly below the "3"? Well, that gave the "2" a second blue hex. So if we clear the two remaining hexes from the "2", we might be able to work our way back around. Here's where we're at:



Let's now start with the "2" we uncovered directly below the "2" we just solved; it is two columns straight to the left from the {5}. It shares two blue hexes with the {5}, so the two orange hexes still bordering it need to be cleared. We get a "0" out of this, which will let us solve the "2" directly above it. More importantly, however, is the fact that the cell the "0" leads us to eliminate gives us a "2" with only two possible choices for blue hexes. Each of these, in turn, is shared by that {2} on the edge, letting us clear an extremely important hex:

Only one hex remains to be marked, and one to be erased. The "3" we just revealed gives us the answer. It has only three active hexes to work with; marking the one directly above it will give it a complete set of blue hexes. The final hex of the puzzle can now be erased, and Chapter 1 of Hexcells Infinite is complete!



This puzzle introduces more complex relationships between hexes than we have seen so far in the game. It's important to be able to recognize and understand how to work through these types of situations early on. Otherwise, when you reach the most advanced puzzles that Hexcells Infinite has in store, your brain will be utterly destroyed trying to work through them.

Hexes Earned for Completing This Puzzle: 6

Puzzle 2-1 reintroduces us to the concept of marking blue hexes which are not all connected around a particular empty hex. For example, the notation of -2- means there are still two blue hexes around it, but there will be at least one empty hex separating them.


I'm going to both show you the layout and how to solve it in one image:



And here's how it actually looks in preparation to mark the final blue hex:



There's not much to say about this puzzle at all; it's all about understanding how to work the restrictions imposed by negative integers. It gives us a very simple layout in which to understand these mechanics in preparation for the real mind-benders later on. Next puzzle, please.

Hexes Earned for Completing This Puzzle: 6




One thing is obvious from the very beginning: We are not going to solve this one with one image. :-)

The most obvious move we can make concerns the blue hex bordering the -2-. We can eliminate the hexes on either side of it immediately, since the negative notation means the next blue hex cannot touch it. While this doesn't so much help us determine which of the remaining two hexes the -2- will claim, it does tell us that the "1" over to the left has to share one of these hexes. That clears four cells from around the "1":

Well, this opened up a slew of empty hexes, with no obvious choices as to which ones we can mark to solve them. This is one of those situations where we have to try and find new hexes to eliminate (Pro-Tip: Get used to this.). Let's take the "3" that we opened up earlier. It has only four active hexes surrounding it; one is already blue. The two hexes on its left edge are both shared by one of the empty "1" cells. Since only one of these cells can be marked, we know that the hex above the "3" is safe to mark. We also know that the orange hex on the top-left edge of the "1" will have to be eliminated.

That erasure gives us a -2-, with only a standard ring of three active hexes around it. Don't worry about the empty hexes surrounding it; since they don't break up the chain of orange hexes around the -2-, we can still solve it as we did in the last puzzle. So mark the two endpoints and clear the center hex from the cluster. Now, just fill in all of the remaining active hexes around that "5" we just revealed.

That last sequence gave a blue hex to the "1" positioned below the -2- we just solved, so we can now just clear the next hex below that blue one. This opens up a "2", with only one choice for a second blue hex. Naturally, this blue hex will be shared with the "1" on the bottom-right edge of the "2", eliminating the cell directly below the "1".

When we eliminated that last cell, we solved the nearby -2-. Notice that with this erasure, the -2- now has the same standard ring of three orange hexes to be solved as we have been. Once we do so, we can solve the "3" that we abandoned earlier. The "1" located above the -2- now has a blue cell, clearing the next orange hex up the column. The final orange hex at the top will then be marked to solve the "3" and the "1" across from it:

Does anyone else find it odd that with all of those active cells remaining on the grid, only two of them get to be marked? Let's return to the bottom of the grid; that "2" at the bottom-center already has two blue hexes. Clear the hex on its bottom-right edge to continue. Well, here's one of the remaining blue hexes; that "1" we just opened only has a single choice for its blue hex. This also solves the "2" right above the hex we just marked; clear the one on its bottom-right edge.

The "1" that we opened here shares the blue hex we just marked, so clear its two remaining orange cells. We get another "1", which also shares that blue hex, and also a "0". The next two hexes we clear are obvious. And there is now only one hex remaining to be colored; using the positions of the empty "1" cells we just revealed, can you figure out which hex to mark?



Hexes Earned for Completing This Puzzle: 8

Puzzle 2-3 simply builds upon the skills we've been relearning for the last couple of puzzles.




Out of all the empty hexes we're given, we can't do anything with them except for the "0" at the top. So go ahead and clear those hexes to start out. Now this is an interesting setup: all of those newly-revealed empty "2" cells have only two obvious choices for blue hexes. Go ahead and mark them all.

While it looks like we can solve the {5} to the left, we actually can't with 100% certainty; there's still no way to know which of the remaining hexes will be excluded from its chain of blue hexes. So start with the {3} on the right instead; since it has two blue hexes, we can eliminate the two orange hexes which fall outside of the chain of three that it needs. The "2" opened up below the {3} shows us what to do. Mark the only two hexes it can claim, then clear the remaining orange hex on the upper-right edge of the {3}.

The -2- here has four active hexes this time, but that's okay; clear the hex below its existing blue cell to continue. The "2" revealed will have only one choice for a second blue cell, which will also solve the -2-. We now get a -3- with a ring of four continuous active hexes. With a -3- in this configuration, there are only two possible combinations that yield a series of three disjointed blue hexes: Cells 1, 2, and 4, and Cells 1, 3, and 4. This means that both endpoints in such a setup will always be marked.

With one of this -3- cell's endpoints already marked, go ahead and mark the other. Notice that this actually gives a second blue hex to the "2" in the center of the grid. We now can solve the {5}; clearing the final orange hex from the "2" eliminates a hex in the ring around the {5}, letting us mark all of its remaining cells.



We want to go back to the -3- now. Notice how its two remaining orange hexes are shared with the "1" at the bottom-center. Since one of these has to be marked, the cell on the upper-left edge of the "1" can't be. Erase it. Great, another "2" with multiple possible hexes to claim.

We have to apply the same type of logic again to progress. There are six orange hexes on the grid; three of those rim the "2" we just opened. Since this particular "2" has no blue hexes yet, the puzzle's remaining blue hexes have to come from this chain, which eliminates the other three from the puzzle. When this is done, the empty "1" cells at the bottom-center and bottom-left will only have obvious choices for their blue hexes. Clear the final cell to complete the puzzle.



Hexes Earned for Completing This Puzzle: 8

The last couple of puzzles gave us some more complicated logic to work through in their solutions. The skills that you learn from solving these puzzles will serve you well as you progress onward to still more challenging scenarios. Remember: We haven't even been reintroduced to all of the puzzle-solving mechanics yet!

Chapter 3 is now unlocked if you wish to preview some of the upcoming challenges.




So any time we have rows or columns of hexes which are marked by a number of some sort, it's a good idea to look for two things: A "0", which clears every hex in that line, or to see if the number of blue hexes in that line happens to equal the total number of active hexes in that line. A quick look at the puzzle tells us that we actually have both! The second column is governed by a "0"; the third is governed by a "5". Each of these columns has only five hexes apiece. So erase every cell in the second column (I like to refer to such columns as "empty columns," since they have no active hexes), and mark every cell in the third.

Note that I'm using the line-marking mechanic here. If you want to highlight a line of cells, just click on the line header; to clear the highlight, click the line header again. If you're done with a particular line, right-click on the line header to dim it. If you make a mistake and accidentally dim a line header prematurely, you can right-click it again to bring it back.

Moving forward now, we can actually clear the two diagonals marked along the top row of the grid. It doesn't actually matter which one we start with, so let's just take the "3" positioned outside of the "empty column" from before. Highlighting the diagonal shows that we have only three remaining active cells within it; we erased one in the beginning. Mark the last two that the row needs.

Now take the "1" positioned outside the next-to-last column of the puzzle. Highlighting this line shows that we've already marked the lone blue hex it needs. Clear the others.

It may take you a minute to recognize it, but the puzzle is now solved. The very first column, headed by a "2", has only three total cells. We just erased one. Color the two remaining active cells to solve it. Now check the "REMAINING" counter; there are no blue hexes left to mark! Erase all of the remaining orange cells to clear the puzzle!



Hexes Earned for Completing This Puzzle: 9


This one is not as straightforward. We can see pretty readily that we won't be able to outright solve any lines immediately like we did in Puzzle 2-4. Interestingly, we get a free blue hex right above the "2" at the bottom-right, which is the only empty hex we get.



What's interesting about the placement, however, is that the only two orange hexes around the "2" happen to be positioned in a column headed by a "1". Naturally, one of these two hexes will be marked to complete the "2", so this means that everything above this pair can be erased:




We can now solve the final column in the puzzle. It's governed by a "4"; the last series of eliminations cleared a hex from that column, leaving only four total active hexes within it. Color the other three (Remember, the freebie given to us earlier still counts!). Marking these actually gives the empty hexes we uncovered in the next column to the left all of the blue hexes they need. So we can now eliminate the top three cells of the column to their left.

So what do you think about that central column headed by the {5}? Can we solve it now? The answer is, "Yes."

We may not have much to work with, but if we analyze the information, we can determine where the chain of blue hexes starts. We cleared the top cell from the column by virtue of the "0" that we revealed next to it. The next two cells down are both adjacent to an empty "1" cell in the next column. Only one of these two cells can be marked, and they happen to be the only remaining active cells from which the "1" can claim its blue hex. Naturally, if we mark the cell on its top-left edge, the only way to make a continuous chain of five blue hexes is to also mark its second orange hex--a clear violation of its rules. The orange hex on the bottom-left edge of the "1", then, becomes the endpoint in this chain. Mark this one and the next four down, then clear what's left in the column.

We also have enough information to solve the next column to the right now. The "2" four spaces up from the bottom has now been given two blue hexes. The orange hex below it now has to be cleared, leaving only the column's final cell to be marked.

Just a little cleanup work now remains on this half of the grid. The "2" that we just revealed a second ago already has two blue hexes; when we clear the hex on its bottom-right edge, we leave only the last hex in that cell's respective column to be marked for its lone blue hex. Now, since the "2" located right below the chain of five hexes we just marked already has two blue hexes, we need to clear the one to its left, which opens up a "0". Go ahead and clear the hex to the left of it.



So any time you make substantial progress on a puzzle like this, it's always good to recheck the line headers to see if there are any entire lines of hexes that can be completed. We still have several diagonals left to process. Let's check them. Start from the right side. We have two diagonals, each headed by a "2". If we highlight them, we can see that we indeed have given each line two blue hexes. This will eliminate five hexes from the grid.

Now let's check the diagonals pointing from the upper-left of the grid to the lower-right. The first is headed by a "1"; the second, by a "4". The first one has its lone blue hex, which eliminates two more cells. Now, if you had started with the diagonal governed by the "4" before completing the previous series, you wouldn't have been able to do this. But now, this line has only four total active hexes, with two still needing to be marked:

We can now immediately solve the first two columns. For the first one, headed by a "3", we now have only three active cells total, with one marked. Just mark the column's remaining two orange hexes. For the second one, headed by a "1", we see that we have already given it a lone blue hex, so just erase the other three cells.

Finally, to complete the last string of orange hexes: For the one on top, it's the only active hex remaining for the "2" and the "1" between which it sits. So that one will be marked. The middle one in the column will be erased; all of its adjacent empty hexes have complete sets of blue hexes. The last orange hex will then be marked to complete the puzzle, as it is the only choice remaining for both the "3" above it and the "2" to its left to gain their final blue hex.



This puzzle is a bit more involved than what we've seen so far. It teaches us to use both the conditions on and outside of the grid to determine which cells to mark or to erase. It also teaches us just how much the completion of one or more lines of cells can contribute to the puzzle solution. Sometimes, we can almost ignore the empty hexes on the grid!

Hexes Earned for Completing This Puzzle: 10

Only one puzzle remains to complete Chapter 2, which will put us 1/3 of the way through the game. This next one will really put your line-solving skills to the test.




So we get absolutely nothing on the grid to start this one. All the information we're given comes from the various column and line headers. How do we even begin?

When we have line headers with a braced integer, such as the {5} heading the middle column, it's sometimes possible to find guaranteed blue hexes. If the total number of hexes isn't much bigger than the number governing the line, we can identify guaranteed blue hexes in the center of the line which will exist in any possible chain of consecutive blue hexes it requires.

This basic logic can be applied to the columns headed with the {3}, {5}, and {4}. Number the cells within each column; we'll continue the explanation in the following image:



So our opening move is to mark all of the cells we identified in that previous graphic. Here's what it looks like in-game:







Those last steps are going to let us eliminate a few cells from the puzzle, as well as solve one of the diagonals. Notice that on the right side of the grid, we have a diagonal governed by a {3}; if we mark the line, we can see that there are already two blue hexes, but they aren't connected. So all we have to do is fill in the one between them, then the whole rest of that line is erased!

One last thing we can do. On the left side, almost directly opposite the diagonal we just worked, is another one governed by a -2-. We've given that line a blue hex, as well; go ahead and clear the orange hexes on either side of it since we know the other blue hex won't be connected to this one.




Unfortunately, all of the empty cells we've revealed still have multiple choices for completing their sets of blue hexes. So we need to try to eliminate more cells from their respective clusters to narrow down which ones to mark. Our best option is the "2" in the bottom-left corner, right next to the "1"; it has only three active hexes surrounding it. Most helpful, however, is that two of these hexes are shared with the "1". That means only one of them can be marked, which also guarantees that the one on its bottom-right edge will be marked.

Marking this hex gives us an important new clue, since it also feeds a second blue hex to the "2" on the upper-right edge of the first "2". The two remaining hexes around this "2" now need to be erased. The "2" that comes up on its bottom-right edge--within the {5} column, no less--will also have the blue hexes it needs. That clears three more hexes. But just as importantly, it gives us a boundary for the central column's chain of five blue hexes and tells us how to solve it:

There are a few moves we can make now. We can actually complete several empty hexes on the grid. Returning to the bottom of the {5} column, we revealed a "3" a few moments ago. It has a blue hex and only two remaining active hexes around it to mark. Similarly, the "3" on its upper-right edge only has three active hexes to deal with, as well. Marking them does two things: It completes the "4" right above it, and it gives the last two hexes needed to the column governed by a {4}, which means we can clear the hexes at the top of the column.

There's another "4" to the left of the center of the puzzle that we should solve now, too. It has only four active hexes, with two already marked. Mark the others. We can also solve the diagonal from the left side, which is governed by a "5". We've left only five active hexes, with three now marked. Mark the remaining two. When we do so, we give a second blue hex to the "2" on the far left edge, so we can now erase the cell directly below it.

Now we get a "1", and its position tells us how to solve the chain of three hexes in the second column. Since the "1" has a blue hex, we need to clear the one on its bottom-right edge, then mark the remaining hex at the top of the column. Next, the "1" at the bottom of this column now only has a single choice for its blue hex. Once it's marked, the third column, which is governed by a "2", gains its second blue hex. Erase the column's remaining hexes.



We opened up a "5" a moment ago; the hex above it has already been eliminated, and there's only one hex around it left to mark. Doing so also gives the "2" above it the second blue hex it needs, so go ahead and erase the lone remaining hex in the section.

There are only three blue hexes left to mark, but most of the remaining orange cells surround a trio of empty "2" cells, with no obvious choices as to which ones to mark. As always, try to find the simplest move we can make. The "2" at the top of this trio has only three active hexes around it, whereas the others each have four.

This particular "2" has one hex on its right, and two on its left. Naturally, at least one of the cells on its left will have to be marked to give it a complete pair of blue hexes. However, note that they also fall into a column headed by a "3"--and two cells in the column are already marked blue. We know from this that the hex to the right of the "2" will have to be marked. All of this also rules out the third orange hex down the column headed by a "3" as being selectable; erase it. This gives us a "4" in the center of a ring of five active hexes, four of which are already marked. The cell above the "4" is cleared, and the top cell of the column is marked.

Only a few hexes left. The "2" farthest to the right now has the two blue hexes it needs, which clears two of these cells immediately. That "1" on the edge tells us which remaining hex needs to be marked. Mark the one beneath it and clear the final cell to solve the puzzle and clear Chapter 2!



Hexes Earned for Completing This Puzzle: 10

We don't begin to relearn Grid Overlays at all in Chapter 3. However, we do begin to encounter much longer puzzles, and it will remain this way for many of the game's remaining challenges. Just take each one as it comes, and remember the skills you've been learning.




This is another puzzle that can be really hard to even get started. We can't do anything at all with either the -2- cells at the top, or with the "3" at the center of the grid. And if we look at the line headers, there are no lines we can complete right away.

While it may seem weird, we have to start with the "4" at the top-center. Why? It's actually because of the -2- cells. Four of the empty "4" cell's six orange hexes are shared by the -2- cells. Because their blue cells can't be consecutive, we know that only one hex in each pair can be marked. The other hex in each pair will be eliminated, which takes care of four of the hexes in the ring. The cells directly above and below the "4", then, have to be marked.

Now what? This may be the most vexing part of the puzzle. It would seem that there should be a way to determine at least one of the blue hexes to be colored around the -2- cells. But if you spend time going through the possibilities in your head as I did, you'll find that you can make a logical case for all of them, even if you take the line headers into consideration.

The line headers by the top-center cell of the grid, however, do give us a clue. Two of the hexes required by each -2- cell fall under one of these diagonals, each of which is governed by a "2". So if we run through the possible combinations, there isn't a single one which doesn't include a cell in one of these diagonals. Clearly, we've given each of them one blue hex already. I'll illustrate this point in the next image, but suffice it to say that we'll at least be able to clear some hexes from these lines. However, we'll have to come back and try to solve this section later.



Hopefully, that description makes sense. We now know that all remaining hexes within these two diagonals which are not connected to the -2- cells have to be erased, which will open up more of the puzzle for us. Our opening sequence becomes this:




We at least have the puzzle started now. Doesn't it figure that we can't do anything with all of those empty "1" cells on the far left side yet? We can, however, work with the empty hexes we just revealed on the right side. Both of those empty "2" cells are positioned to where they have only two hexes they can claim. When we mark them all (four hexes total), we also give the pair of empty "1" cells one blue hex apiece. So the center hex along that line will now be erased.

Notice how the blue hex directly below the "2" on the right end of that cluster falls into a diagonal governed by a "1". Well, now we can eliminate that whole remaining string of orange hexes! For good measure, let's also clear the remaining two orange hexes from around the "2" we revealed a moment ago, between all of those blue hexes we just marked.


Let's return to the cluster we were working with. We opened up two -2- cells a moment ago. The one positioned directly below the normal "2" has only two active hexes surrounding it, so mark the second one it needs. This gives a blue hex to the "3" directly below the -2-. This "3" is positioned to only have three total active hexes. Mark the remaining two, and we'll also give a third blue hex to the "3" on its upper-right edge. So now, we can erase the final hex on this side.

Look now at the second -2-; it already has two blue hexes, so clear the pair to its left. The -2- we open on its bottom-left edge is solved by solving the "4" we just opened up. When we mark the two hexes the "4" still needs, we'll give a shared blue hex to the -2-. So now, we clear two more cells. This leaves the "2" at the bottom-left edge of this section with only two active hexes to claim; mark them to finish off this entire section.

Let's try to link that cluster up to the rest of the puzzle now. The "2" on its far left edge has two blue hexes, so we can erase the first hex going into that narrow strip towards the central column. Wait, what? A "?" cell?

Empty hexes with a "?" were introduced in Hexcells Plus and need to be treated as a roadblock. There is no way to determine how many of their surrounding hexes will be blue without additional information. We'll have to return here later. You'll see such hexes in large quantities throughout the rest of the game.

So what next? Can we do anything with the bottom section?

We've got a diagonal leading into this section which is headed by a "4". Highlighting the line reveals that we have already given it three blue hexes. Also, two of the line's orange hexes are positioned above a -2- cell; in keeping with the rules of such a cell, we can immediately determine that one of those cells has to be marked. Of course, this will also solve the diagonal, meaning that the two endpoints in this segment of the line have to be erased.

This doesn't help as much as we might have hoped. However, look to the left side now. We've got another diagonal, this one governed by a "6". Highlight it; there are now exactly six active hexes in this line. Mark every one of them.

Let's work now with the pair of empty "1" cells embedded within that diagonal. Start with the "1" farthest left, which also marks the end of the diagonal headed by a "4" that we highlighted a moment ago. Clear the two remaining hexes from this "1". The "1" we reveal over top of this one will naturally share the same blue hex, eliminating the cell on its top-right edge.

Let's now solve the -2-; we know to clear the hex directly adjacent to the blue one below it. That will leave only the cell on top of it for its second blue hex. The "1" we just revealed naturally shares the blue hex directly below the -2-, eliminating the next cell up the line and leaving only one final hex in this diagonal to mark.

Go ahead now and erase the last cell in this section, two cells above the -2-. Great, another "?". We're done here for now!



What conclusions can we draw next? We still have very little to work with on the left side of the grid. This is a good time to examine the remaining line headers and see if we have any more information about them.

Let's start with the "4" at the top-left. Highlighting it reveals the line has three blue hexes already. We know that the fourth will come from solving the nearby -2- cell. We can safely erase the two cells falling beyond the pair of hexes bordering the -2-. Wow, a {2}, and it already has a blue hex! This is a rare case when a "?" actually helps us, because it erases a cell from the {2} that we otherwise would have to deal with. Since the blue hex on the {2} is now at an endpoint, we just need to mark the next cell to its left and clear the final cell in that ring.

We can now solve this -2- cell! Clear the cell above the blue hex we just gave it, then mark the only remaining cell it can claim.

We're about 2/3 of the way through this one now; here's where we left off:



The opposite side on top also still has a diagonal to solve, this one governed by a "2"; can we apply the same reasoning to this line?

So this line has only one blue hex, all the way at the bottom-left. We again have two hexes in the line which border the -2- on this side; we know one of them has to be marked. So again, we'll clear the hex which falls beyond this pattern. Another {2}. So now, we can solve the right side in exactly the same manner as the left. Once we're done, we'll go ahead and clear the remaining hexes along the diagonal--as well as a large number of cells from around the two zeroes that we'll reveal!

Naturally, we want to try to solve this section next. Let's actually start with the "2" positioned right above that chain of four blue hexes on the bottom-left edge. Since it gets two blue hexes from that line, eliminate the orange hex on its top-left edge. This now allows us to solve the corresponding diagonal, which itself is governed by a "2". Now that we've eliminated that particular hex, the line has only two active hexes remaining. So mark both of them.

The rest of the section will be solved by the existing relationships on the grid; can you solve the last few hexes in the cluster?







This is interesting; all links to the central section are blocked by "?" cells. How on Earth do we determine where to go next?

This is another time the "REMAINING" counter will come in handy; in fact, you will actually need to use it as a puzzle-solving technique in some of the later puzzles! Notice that there are only three blue hexes left to be colored; the central cell is a "3". Naturally, the three remaining hexes are going to surround that "3". So our next step? Get rid of everything except that cluster surrounding the "3".


One last step. Solving the hexes directly above and below the "3" is obvious. The "2" which is revealed from eliminating the hex above the "3" gives us the solution.



This puzzle is a bit of a marathon and introduces us to somewhat trickier types of logic than the previous puzzles have used. In particular, it forces us to combine several rulesets at a time in determining which hexes can be marked. It also makes us jump around a little bit. Sometimes, we have to isolate a particular pair or group from which we will mark a blue hex, obtain more information from elsewhere, and then return with the final solution to that group. This type of puzzle-solving will become more common in the more difficult puzzles to come.

As for the next puzzle? Well, it's no easier to get started than this one was...

Hexes Earned for Completing This Puzzle: 14

Unfortunately, the next puzzle is no easier to start than 3-1 was; in fact, we actually get less information to start us out.




This is an interesting layout. LIke similar puzzles in Hexcells Plus, we essentially get a giant hex made up of individual hexes. We're given only three empty hexes: a "2", a "1", and a "5", each surrounded by the maximum of six hexes. Of these, the "5" is the easiest one to start with; after all, we know that all of its surrounding hexes will be marked except for one. Maybe we can narrow that down.

Our biggest clue here is that two of its orange hexes fall into a diagonal which is governed by a "1", which immediately tells us two things. First, we know that it's impossible to give the "5" a complete set of blue hexes without at least one of those cells; secondly, we know that only one of these cells will be marked. So to start, then, we can mark the four orange hexes surrounding the "5" which are not included in this diagonal. Additionally, we can erase the entire diagonal except for the two hexes in question.

Notice that when we mark the cells around the "5", we give a blue hex to the empty "1" cell a couple of spaces above it. This alone erases five more hexes from the grid. The "2" uncovered on the bottom-right edge of the "1" already has its two blue hexes; erase the other two which remain. The {3} that is revealed on the bottom-left edge of the "1" just needs a third consecutive blue hex, then we can erase the one which remains. Our opening move, then, looks like this:

This now gives us enough information to solve the "5". The "2" which popped up right next to our pair of orange hexes within the diagonal has two blue hexes. Erasing its remaining orange hex also eliminates a hex from the "5", leaving only one left to mark.

We can now head up the bottom-right edge of the grid. The "1" which appeared on the bottom-right side of the "2" that we solved in the last sequence shares a blue hex with that "2", which clears its remaining orange hexes. The "0" we reveal gets rid of another couple of cells, but the "?" cells stop us for the moment.

Heading back up the bottom-left edge, then, we come to a "1" which has a blue hex shared with the {3}. Clear the orange hex on top of it. Wow, another "?". Okay, here's what we have, then:






We'll need to check the line headers for a clear indication of what to do next. On the right side just up from the bottom is a diagonal governed by a "1", which actually has the blue hex it requires. The rest of this line can now be erased.

Now, on the left side just up from the bottom is a diagonal governed by a "4", with three blue cells marked. The trick with this line is that its only three remaining orange hexes border a pair of empty "1" cells. This pattern dictates that the only viable option is the center hex of that chain; if we mark either endpoint, it becomes impossible for one of the empty "1" cells to get a blue hex. So we mark the center one in the chain and clear the final two cells of the row.

Interestingly, that one blue hex will be shared by the empty "1" cells that we just revealed; because of their positioning, all four remaining hexes in the next diagonal up the grid now have to be eliminated.





The relationships between lines of cells and other cells on the grid will again be put to the test with the next sequence. Let's start with the final column of the grid, which is governed by a "1". Our focus will be near the bottom, where there is an empty "2" cell with only three orange hexes--two of which fall into this column. Since we know that only one of those two hexes can be marked, we can both safely mark the hex on the upper-left edge of the "2" and erase everything within the final column except the two hexes bordering it.

Let's start with the "0" we just revealed at the top of the column and follow it. We get another pair of empty "1" cells in the next column over. This column is governed by a "2", and it has one blue hex. Well, we also revealed a pair of empty "1" cells in the final column, right below another "?".

The "1" located directly below this "?" is the one we need to focus on; its only two orange hexes are in the next-to-last column. We know for a fact that one of these cells must be marked to complete the "1". Since it will also give the column a second blue hex, we can clear the next cell down from this pair of orange hexes and also the one below the "3" at the bottom of the column.

This now lets us solve both the last column, as well as that bottom diagonal. We've left only one cell in the diagonal, so we just need to mark it. Naturally, that gives the final column the lone blue hex it needs, as well. So now, we just erase the final orange hex of the column.




This is quite a difficult sequence to work through; if your brain is frazzled after that, I would recommend taking a breather using the game's built-in save function. You can come back later and pick up from this exact spot.

We'll try to solve the next-to-last column now. We've left the empty "1" cell halfway up the final column only one remaining orange hex to work with. Marking it actually completes the requirements for all of the nearby empty hexes, which results in the erasures of several more cells and also completes the column.

We'll move to the "3" near the bottom of the same column next; it has been left with only three active cells, with one needing to be marked. Completing the "3" also gives a shared blue hex to the "1" next-door, so we'll now erase its remaining orange hex.




So what about the next column over, which is also governed by a "2"? We can apply a very similar logic to this column as we did with the two diagonals along the bottom-left edge a little while ago. We have a virtually identical pattern: Three orange hexes bordering a pair of empty "1" cells in the next column; as before, the line only needs one blue hex to complete it. So as before, we have to give a shared blue hex that completes both empty hexes; this will leave the rest of the column to be erased.

This last step almost completed the next column, governed by a "1", without doing anything. When we erase the orange hexes from around the empty "1" cells we just revealed--which share the blue hex we just marked--it leaves only three orange cells left in the column. Two border the "3" in the column we just completed; one of these has to be marked, and it will also give the column the blue hex it needs. So the cell above this pair has to be erased. That leaves the "2" positioned above the "3" with only one choice for its second blue hex. It will be shared with the "3", and the last cell of the column is erased.

We're about halfway finished now; here's where we left off in the first part:



We can continue our current chain of logic even into the next column to the left, which is also governed by a "2". In the column we just completed are a "2" and a "3"; they each need one blue hex apiece, with the only hexes they can claim existing in this column. We know that one cell will be marked to complete each of them; these cells will also complete the column requirements. So now, we can erase every cell in this column which does not border the "2" or the "3".

We'll have to approach this from a different perspective now. In the column we just completed, right below the "3", is a "2" with only one blue hex; it has only one choice for its second blue, which will be shared with the "3". So mark it, and then erase the final hex from the "3".

For right now, we don't have a way to solve the "2" further up the column; we'll have to revisit it later.








So we need now to work on the left half of the grid. The lowest diagonal to be solved is headed by a "4" and has five orange hexes. Three of these orange hexes are adjacent to a "2" and a "1" in the next row down. The "2" already has a blue hex; the "1", of course, still needs one.

Trying to isolate what to mark or erase just using the line information is a little bit of a guess. This is a situation where the only guaranteed way to arrive at the solution is just to run the possibilities and see what we can logically make work, and what we can't.

So let's take the last three orange hexes in this line and number them 1-3. What happens if Cell 1 is marked? Well, Cell 2 would be erased, since we can't have another blue hex for the "2", and Cell 3 would be marked. The first two hexes of the line would then be marked, and we satisfy all the requirements of the rows and the empty hexes. The same is true if we start with Cell 3; we just carry out this same sequence in reverse.

But what happens if we mark Cell 2? Cells 1 and 3 then both get eliminated, and it's impossible to give the row four blue hexes. That sets up our solution:






We can clear the two orange cells from the "2" we just now revealed, since the hexes we just marked gave it the ones it needs. More importantly, we can solve the second column of the grid. When we solved that last diagonal, we gave the column a second blue hex. Just erase those which remain.

So the "2" uncovered in the center of this column has the two blue hexes it needs. That will clear a total of three hexes on either side of it. In the very first column, governed by a "2", we revealed a "1" directly above a blue hex. When we clear the cell above the "1", we leave only the top cell of the column to color for its second blue hex.

One last step for this sequence. At the top of the second column is another empty "2" cell. We just now gave it a blue hex; its only possible choices for a second come from the third column, which is also governed by a "2". The column already has a blue hex; naturally, the second hex that the empty "2" cell receives will also complete the column. So the third orange cell down this column has to be erased. The "0" that this reveals ultimately leaves only the top cell to be marked.

We'll try to tackle the next column, governed by a "1", next. The empty "1" cell we revealed near the top of the third column has a blue hex, so we need to clear the one on its top-right edge. Also, halfway down the third column is a "2" with two blue cells; go ahead and clear its remaining orange hex, as well. Now about that "3" we revealed a second ago...

The next column over is governed by a "3", and it has two blue hexes already. The empty "3" cell we just revealed has only four total active cells around it, two of which fall into this column. So we're in a similar pattern here; since only one of these two cells can be marked, the cell above the "3" must be, which completes that column.

Special Note: Or, you could have just seen that this was the only cell left in the column to mark. Remember: Simplest is best! :-)

We now also know that since the third hex the "3" will claim will also complete its respective column, everything else outside of this pair must be erased. Once again, a helpful "0" will show us the way...





We can easily see that the top three cells in the next column have to be erased; the "2" and "1" in the previous column have their required hexes, so we need to erase the orange hexes still bordering them. The two empty "1" cells that this reveals share the same blue hex between that "2" and "1", erasing some cells in the central column, which is governed by a "5".

I'm actually going to show this off now; the end solution is a pretty tough brain-teaser. So we'll pick up again after the next image.







There's no real choice here; we have to solve the central column. The most important thing about it is that it is governed by a "5"; highlighting it shows it has six total active hexes. We also have an empty "2" cell in the middle.

With four orange hexes remaining in the column, and two of those surrounding the "2", we can easily see that it's impossible to give five blue hexes to the column without also giving one to the "2". But just as important is the "1" located just above and to the left of the "2"; two of its orange hexes fall into this same column. That means it's also impossible to complete the column without giving a blue hex to the "1".

What this means, then, is that there is no logical way to give the "1" a blue hex right below it. If that cell is marked, then two cells in the central column are erased, leaving it only four active hexes and making it impossible for it to gain five blue hexes. This is the cell we must erase next.

We get another empty "1" cell from this, which doesn't help as much as we might hope. It does, however, tell us two of the cells we must mark in the central column: The very top one, and the one directly below the "2". Only one of those two orange hexes above the "2" can possibly be marked now.



Our next clue: Both orange hexes connected to the "1" we just revealed are also connected to the "2"; so whichever hex it gets will also give the "2" a second blue hex. That eliminates both hexes to the right of the "2" as possible blue hexes. The "0" that we get is immensely useful:




Only two final hexes to mark. We get to clear three cells immediately; the "1" four spaces down the center column has a blue hex, so the two on its right are erased. Also, that lone orange hex just down to the left of the "2" we just solved can be erased, as it's not linked to anything that needs to be solved.



To determine the final cells to mark, start with the "1" three cells down the middle column; it now has only one choice for its blue hex. It will be shared with all of the adjacent empty "1" cells, letting us clear the top-most orange hex and the one three cells down the last active column. Mark the final hex to solve the puzzle.



Hexes Earned for Completing This Puzzle: 17

Puzzle 3-2 can be a real beast, especially near the end. Your ability to analyze the patterns on the grid and how they relate to line restrictions is really put to the test there. This skill will also be vital to solving the hardest challenges still to come.

Chapter 4 is now unlocked if you would like to preview more advanced puzzles.




The game hint given here is one I wish would have been provided at least in Hexcells Plus: "Column numbers ignore gaps."

To me, this puzzle seems a bit superfluous, since we're already fairly familiar with the mechanics and strategies of working lines of hexes. However, it does give us a respite from the fairly daunting challenges we had in solving the last two puzzes. In fact, this one is simple enough that I'm going to present its solution in three images, with the full descriptions in each:



And here's how it all looks in preparation to mark the puzzle's final blue hex:



There's not much to say about this one; the only thing I might point out is to treat negative and braced line headers exactly like their counterpart hexes on a particular grid.

Hexes Earned for Completing This Puzzle: 7


So this is why we had that particular hint in the last puzzle:



We get a central island with a whole bunch of tiny groups of hexes surrounding it. We are given no empty hexes at all, and there are many line and column headers to work with.

We'll need to scan the line headers carefully to find an opening move. In a puzzle like this, where there are gaps in almost everything, line-marking becomes critical. If you need to, spend some time marking and studying every single line and column header in this puzzle. Remember: There is no time limit whatsoever.

We'll ultimately find that we can solve two of the shorter diagonals right away. The left- and right-center edges each have a diagonal governed by a "3"; highlighting them shows that each line only has three orange hexes apiece, so we can mark all of them immediately.

One last thing we can do. Just left of the center is a column governed by a {3} with only five active cells in it. If we plot out the combinations of three continuous blue cells, we'll find that the center one in the line will be marked in each of them. Go ahead and do this now to complete our opening move.



Because this puzzle is so open, we'll need to recheck the line headers after every move or two, just to see if we can make any inroads towards the remaining lines. We can actually determine that four of the hexes we just marked feed into four specific marked columns. Three of these columns are governed by a -2-; one is governed by a {2}.

We'll take those headed by a -2- first; they will all be treated in the same manner, with the only difference being that the one furthest left will have two cells erased. For each of them, we know that their second blue hex cannot be linked to the first. So that means erasing the orange hexes which are connected to the blue ones.

Let's shift now to the column governed by the {2}; it lies several columns right of the center. The column as a whole has only four active hexes; we know that the next blue hex it receives has to be linked to the blue one we just marked. Only two hexes within the column can do this; the top cell, therefore, must be erased.

One last step here. In one of the columns, we revealed a "0" with one orange hex connected to it; go ahead and erase it. In another column, we revealed a "1" with only one active hex to work with; color this one. Finally, in the -2- column furthest left, we've now solved all but one of the cells; mark the top cell to complete it. So we now have this:


At the bottom of the -2- column that we just completed, we have a "1" with a blue hex above it; if we erase the one on its bottom-right edge, we'll reveal a "0". Following that will actually let us solve this diagonal line, which is governed by a "2".

Notice that now, we have given a third blue hex to the column governed by a {3} in which we marked the middle cell in the beginning. We can now clear the top two hexes from this column. Go ahead and eliminate the lone hex beside the "0" that comes up.

There's also a diagonal, which is governed by another {3}, which crosses the column we just completed. There's enough information here to eliminate a couple more cells. We know that we need a continuous chain of three blue hexes here; if we treat the existing blue hex as an endpoint, we can determine the maximum reach of this chain and then eliminate those which fall outside of its range.

On the opposite side of the diagonal we completed at the beginning of the last sequence is a second diagonal, which is also governed by a "2". As before, the empty "1" cell at the end has a blue hex above it; if we clear the next hex in the line, we reveal another "0". Following the "0" shows us that the line is solved identically to the first one.

Helpfully, we eliminated a cell from the column governed by a {2} which we worked on earlier. With three of its four hexes now solved, just mark the last one. That gives the "1" at the top of the column a lone blue hex, so go ahead and erase the one on its left. The "1" this reveals tells us that the last hex in the cluster needs to be marked.

The hex we mark lies at an endpoint in another column headed by a {2}. So now, just mark the next hex down and erase everything else within the column below it.






The easiest move we have now comes from a diagonal at the right-center, which is governed by a "1". Highlighting it reveals that we have already given it a blue hex; just erase everything else in the line.

Now, in the cluster of five hexes to the left of where we began the previous step is a "1" with only one choice for a blue hex. Go ahead and mark it while we're here. Also, in the group of five hexes to the left of this group is another "1" with only one choice for a blue hex; mark it, as well.

Move now to the left side, to the diagonal headed by a "5" which criss-crosses the diagonal we completed a moment ago. We've now erased a hex from this line, leaving only five active cells. We can safely mark those which still remain unsolved.





Extending to the right of the center along the top are three column headers of -2-, "2", and "2", respectively. The third column in the trio has its two blue hexes, so erase the final two. The "0" revealed at the top lets us easily solve its respective cluster.

In doing this, we give a second blue hex to the column headed by the -2-. This lets us ultimately erase a number of cells in the central island; by extension, we'll leave the center column in the trio with only one final hex to mark.

We're trying to solve the central island next. Here's where we left off after the last sequence:



The "2" at the top-right corner of the island, as well as the "1" at the bottom-right corner, have only obvious blue hexes to claim. Marking them also solves this column, which is headed by a "3"; erase its lone remaining hex positioned right above the island.

Now, to solve the left side of the island, we have to look to the fact that its hexes fall into a column governed by a -2-, which has a blue hex farther down. The only way to give the pair of empty "2" cells in the next column their second blue hexes, while also maintaining two non-consecutive blue hexes in this column, is to share a hex between them. Erase the remaining hexes in this column.

We can solve several more lines now. Let's stay on top, where we have the two clusters of three cells apiece in the top-center. The cluster on the left has a "1" with only one choice for a blue hex. Marking that cell gives its respective column, governed by a "1", the lone blue hex it needs. So now, clear the rest of the column.

Over on the top-right edge of the board are a pair of diagonals headed by a "3" and a -3-. The line headed by a normal "3" has three blue hexes; erase those which remain. The -3- line, however, needs two more blue hexes. The line has now been reduced to only three active hexes, so now, mark the ones which remain.

Now, on the top-left edge, we can solve that diagonal governed by a {3} that we started a long time ago. The line now contains two consecutive blue hexes, with everything beyond them already erased. This tells us which hex to mark to complete the chain, and the first hex in the line is now erased.

Two lines up from this one is a diagonal governed by a "4", which now contains only four active hexes. Go ahead and mark the final two orange hexes.



This solved a large chunk of the puzzle. The only other row we can solve right now, however, is that other diagonal headed by a "4" which lies right in between the lines we just completed. It has now also been reduced to four total active hexes, with two still needing to be marked.

We now need to look on the board itself and solve some empty hexes:

• In the cluster on the bottom-left is a "2" with only an obvious choice for a second blue hex.
  
• In the cluster at the bottom-right, we just gave the "1" a blue hex; erase the one to its left. The "1" that this reveals is solved by marking the final hex in the cluster.
  
• In the cluster at the top-right, the "1" already has a blue hex; the cell to its left needs to be erased. Solve the "1" that this reveals by marking the cell to its left.
  
• In the cluster to the left of the central island, the "1" on the bottom has only an obvious blue hex to color.

The column governed by a "2" towards the left side of the puzzle can now be solved by eliminating its two remaining hexes. We've finally given it the two blue ones it needs. Doing this also lets us solve one of the remaining diagonals. The cell farthest right in the cluster on the top-left side of the board has two line headers: A column, governed by a -3-, and a diagonal, governed by a "2". The diagonal can be solved by just marking this specific hex; the line has only two active cells.

We can now solve the column, as well! Notice that two cells down, we have another blue hex. So we cannot mark the hex in between them, or else we would have three continuous blue hexes. The column requires three disjointed blue hexes. So now, erase the second hex down, and mark the last one on the bottom.



Of the remaining active hexes on the board, only one remains to be colored. That hex lies in the diagonal headed by a "2" which extends from the top-left cluster. In fact, we have an empty "1" cell in the next cluster southeast of this one; we just need to mark the only hex it can claim and erase everything else to solve the puzzle.



Truth be told, there is nothing especially difficult about this puzzle; it's just lengthy. The line-marking mechanic is absolutely vital just due to the massive amount of open space between clusters of cells. Because of its openness, it's also essential to continuously refer to the line and column headers; in fact, we didn't even do very much regarding the empty hexes themselves. There are a few places where it is necessary to solve empty hexes, but they primarily serve to either mark or eliminate cells within the lines in which they fall; the overall strategy for this puzzle is to solve the entire lines of cells as opposed to the individual cells on the board. The relationships themselves, however, are not terribly tricky. It just takes some time to think everything through before making a move in haste.

Hexes Earned for Completing This Puzzle: 19

Puzzle 3-5 reintroduces us to another concept governing lines of hexes which was originally introduced in Hexcells Plus: embedded lines.




Let's start with the center column as a place to reintroduce the concept. If we highlight the line by clicking on the "7" above it, we can see that as we get close to the bottom, the line breaks. And then, heading the segment after the break is a "1".

The part of the column headed by the "1" is an embedded line--literally, a "line within a line." But what does this mean exactly? The number at the very beginning of the line--the "7" in this case--is the Primary Line Header; the number governing the embedded line is the Secondary Line Header. The Primary Line Header defines the overall governing condition of the entire line; the Secondary Line Header defines the conditions under which the embedded line will contribute to the line as a whole. (We're going to throw another monkey wrench into this shortly. You may already have seen it; don't get ahead of me.)

So let's take this specific column. The Primary Line Header here says that the line as a whole must have a total of seven blue hexes; the Secondary Line Header says that one of those seven hexes must come from the embedded line.

I chose to point out this column because it's reasonably easy to work with. We can't solve the entire line immediately, but we will get close. And it's our opening move, as well. We actually only have six total active hexes from the Primary Line Header down to the embedded line; since we need one, and only one, blue hex to come from the embedded line, we can go ahead and mark all six.

When we do this, we give two blue hexes to the "2" located at the very top of the next column. So we continue by erasing the hex to its right. To finish our opening sequence, go ahead and mark the hex beside the "1" we just revealed, and then clear the next hex down that column; it's governed by a -2-, so the two blue hexes naturally cannot be linked.


I want to shift focus now to the next-to-last column, which has a particularly interesting implementation of the embedded lines concept.

The Primary Line Header is a {3}; the Secondary Line Header is a "2". So we're supposed to give the column as a whole three consecutive blue hexes but give the embedded line two total hexes by itself? How on Earth do we do that?

Treat the embedded line here as if it were just a normal gap. We already know that only empty hexes constitute breaks where a string of continuous blue hexes is either required or disallowed. What we're being told here is to continue our chain of consecutive blue hexes after the break signaling the beginning of the embedded line. So we have to mark the final hex before the "2", as well as the first two hexes after the "2". And voila! We have a string of three consecutive blue hexes to satisfy the Primary Line Header, with two of them falling beneath the Secondary Line Header to satisfy its requirements, as well.

Okay. Remember that monkey wrench I said we were going to throw into the whole "embedded lines" concept? I'm going to show this to you now. Highlight the second column to the left of the central column; We actually get two embedded lines with this one.

The Primary Line Header is the "2" on top, so we're still saying that the column as a whole will contain two blue hexes. The Secondary Line Header is the "1" in the middle of the line, meaning that one of the blue hexes has to come from below it. However, we now get a Tertiary Line Header, which defines how the second embedded line feeds into the requirements of the first embedded line. At least in this case, the Tertiary Line Header is a "0".

Does your brain hurt yet?

Basically, we're taking one long line and sub-dividing it so that it has two secondary lines, each with their own requirements. The Tertiary Line Header creates a secondary embedded line within that created by the Secondary Line Header. Whatever cells are included or excluded by the Tertiary Line Header are also considered included or excluded by the Secondary Line Header. Of course, we've already determined that everything governed by the Secondary Line Header feeds back into Primary Line Header.

This idea will become a lot more clear as we actually solve a few of them. We're going to do a little bit of work here. The Tertiary Line Header of "0" tells us that the column's bottom hex has to be eliminated. We'll go ahead and do this now.

At the top of the line, we can see that two of the orange hexes are adjacent to an empty "3" cell which already has two blue hexes. These are the only remaining active hexes from which the "3" can claim its third blue one. So since we also know that only one of the column's two blue hexes can come from this segment, we can actually erase the bottom two hexes between our Primary and Secondary Line Headers:

If your brain is totally fried after all of that, don't worry; we'll revisit these concepts as they appear in later puzzles. I have every intention of making sure everything is fully fleshed out before we reach the game's hardest puzzles.

We've spent a lot of time on analysis and not much time on solving this puzzle. We'll shift attention to the -2- that we revealed in our opening sequence, two cells down the column governed by a -2- right of center. We have two pairs of orange hexes on either side of it. The cells on its right fall into a column governed by a "3", with an embedded line below them governed by a "2". So only one hex above the Secondary Line Header can be marked, and due to the rules governing a -2- cell, we know that it's going to be one of the cells in that pair. We can thus immediately exclude the top cell of the column and erase it.

Erasing it reveals a "1", which already has a blue hex; continue to the right and erase the next one over. This reveals a "0" to follow; we reveal a "1" to its right with only one hex it can capture. Marking it shares a blue hex with the "1" to its right, and the final hex in this section can be erased.

The "0" we just revealed falls into a column governed by a "3", which now has only three active hexes. So for our last move in this series, go ahead and mark the remaining hexes in the column.

We haven't cracked much of this puzzle yet because of the complications thrown at us with the embedded lines. Here's where we're at:



In the next-to-last column, we've now given that "2" near the top a second blue hex, which erases the two orange hexes on its left. The "1" that we reveal has only one possible hex to claim, which will also give the "2" that popped up below it a second blue hex. When we erase the hex below the "2", the "1" that is uncovered also shares a blue hex with it. We clear the cells below the "1"; in doing so, the -2- that appears directly below it will now have a standard ring of three active hexes and will be solved just like any such -2- cell.

Solving the -2- gives the required blue hexes both to the "1" on its top-left edge and the "2" that appeared below it, erasing two more orange hexes. The "2" which appears on the bottom-left edge of the first "2" has only one choice for a second blue hex. Marking it gives a second blue hex to the "2" which appeared on the bottom-left edge of the "1". When we clear the next two orange hexes, we reveal a pair of empty "1" cells.

The bottom "1" here already has a blue hex; the upper "1" has only one choice for a blue hex. Go ahead and deal with them accordingly.

Now, continuing along the lower route, we'll get another "0" to follow, making the next couple of blue hexes fairly obvious. We can't quite finish out this particular grid just yet, but we've now completed a large chunk of it.





In that same grid, we've got a column governed by a {2}, which we can now solve. We have a blue hex directly below an empty hex; now, just mark the next hex down the column and erase what's left.

This gives us another empty "1" cell along the bottom. We can try to work our way along this section from the "1" near the right edge, which already has a blue hex. Erase the hex to the left of the "1"; a "0" to follow, so let's go ahead and do this now. It actually solves a big chunk of the section. The blue hex we mark to the left of the "1" we just uncovered falls into that embedded line from before, which now has only two active cells. Go ahead and mark the next one up the column to solve the embedded line.

We can now solve the column governed by the -2-; we've now given it two blue hexes, so erase the two which remain in the bottom section of the puzzle. The empty "2" cells in this pairing each have only one choice for a second blue hex, so go ahead and mark it.

This gives us another clue for the column in which this blue hex lies. The column is governed by a "3", and that was its second blue hex. So now, since we know the column's final blue hex will come from one of the two hexes beside the -2- near the top, the cell lying below them has to be erased. The "2" this reveals shows us exactly how to complete this column.

Now, let's complete the -2- cell itself. To its right is a "2", which has only one choice for its second blue hex--which will be shared with the -2-. Now, we can erase the orange hex which remains. Of course, this also solves its respective column, as well.




We'll solve the diagonal governed by a "3" from the right side of the puzzle. It's just been given a third blue hex, so we can erase its final one along the bottom row. The {2} that is revealed is easily solved. We'll then reveal a -3- at the bottom of the center column. We can't solve it immediately, but with only a standard ring of four active hexes around it, we know that the endpoints have to be marked.

The next step is a bit trickier, taking us back to the top of the puzzle, where there isn't as much information. We need to focus in the area around the empty "3" cell that we started earlier but have not yet been able to complete. We still have two hexes on its left to solve, which fall into a column governed by a "2". The next column to the left is governed by a "3". Both columns have embedded lines.

The embedded lines dictate that for both of these columns, only one blue hex can be marked above the Secondary Line Headers. Our best clue comes from the chain of four orange hexes within the column governed by a "3"; the bottom two hexes of this chain are adjacent to an empty "1" cell, and they happen to be the only hexes it can claim for a blue one. That means the top two hexes of the column have to be eliminated next.

That empty "3" we just uncovered solves this entire section. There are only three active hexes around it; when we mark all of them, we give the necessary blue hexes to all of these nearby empty cells! Once we eliminate the orange hexes around them, we'll eventually uncover another "0" to follow, and another -2- that will be solved like so many others:


To solve the "4" we just revealed, look to the blue hex on its upper-right edge. It falls into an embedded column governed by a -2-, which immediately tells us that the next hex down has to be erased. That leaves only two unsolved active hexes for the "4" to claim, and they will be marked next.

The next column over has an embedded line governed by a "1" with only two orange hexes remaining, and no blue hex yet. These hexes also happen to border the "3" we just revealed, which already has two blue hexes. Since one of the hexes within the embedded line must be marked, the hex below the "3" is eliminated as being a candidate. Erase it to open the solution:



The column in which the "4" lies is governed by a "3", and it has just one active hex remaining. Since the column has two blue cells already, we just need to mark this one at the bottom.

Now, for the empty "2" cell at the bottom, we have another important clue. The two orange hexes on its left fall into the embedded line governed by a -2- and are also the only orange hexes left in the column. We know for a fact that one of them has to be marked, which means the orange hex on the upper-right edge of the "2" can now be erased. That leaves only one hex for the -3- to claim, which lets us now solve the embedded line within the central column:

Towards the left side now, we can solve the column governed by a -3-. Yes, it still has five active hexes, but the two blue ones fall in the middle of the column, with orange hexes both above and below them. The orange hexes connected to them have to be erased, which will leave only one hex at the bottom to mark for its third blue one.

The "1" revealed at the top of the column is in an interesting position. The orange hexes on its left fall into a column governed by a {2} and are the only ones the "1" can work with for a blue hex. Can you figure out how to solve the column?

We're almost finished with Puzzle 3-5 now. Here's the last sequence we completed:



We only have a few remaining blue hexes to mark now. Starting at the top, we can easily solve the {2} we just revealed. Doing so gives us a small chain that sees us marking the top hex of the first column.

At the bottom of this same grid is a "1" with a blue hex. Clear the two orange hexes to its left. The "1" that appears shares the same blue hex; the "0" is of no real consequence here.

The "1" which appears on the top-left edge of the "0", however, lets us solve the first column, which is governed by a "2". Mark the only hex that the "1" can claim, then erase the rest of the first column:





The two empty "1" cells at the left side of the bottom row are pretty obvious to solve now. When we do so, we can solve the column governed by a -2- near the left edge; it starts from the grid above. The line has only three active hexes, and we just marked one. Solve it like we would a -2- cell with only three continuous active hexes: By marking the endpoints and erasing the center one.

Speaking of empty -2- cells, we just got one, and guess what? A chain of only three active hexes surrounds it! How did I just say to solve such a cell?

This completes the puzzle. The diagonal governed by a -2- now has a second blue hex; erase its remaining hex, then color the final cell to complete the puzzle!



On the whole, there is nothing extraordinarily difficult about this puzzle. The trick is in understanding how to work with the embedded line segments. This will be a recurring theme throughout the rest of the game, and understanding how they relate to the rows in which they fall is crucial. But once you get to work on the relationships between hexes on the grid itself, there's nothing you haven't seen before.

Hexes Earned for Completing This Puzzle: 19


So in effect, we have a giant hex with a big hole punched in the center:



This is another puzzle where it's very important to scan the layout carefully before jumping into it. If we check the empty hexes and the line headers, there isn't very much that sticks out as an opening move.

In truth, the only place we can even get this puzzle started is with the -3- near the top-right corner. Since it has a standard ring of four consecutive orange hexes, we at least know to mark the endpoints here. Doing this will also give a blue hex to each of the nearby -2- cells along that same edge. We know to erase the next cell over from the blue ones in their respective clusters.

Let's start with {2} we revealed towards the top. It shares a blue hex from the -2-; because the blue hex lies at an endpoint in its ring of active hexes, we know which cell it will capture next, letting us erase three more hexes. Once we do so, it becomes clear which hex the -2- will capture, as well.

The "2" that appeared on the bottom-left edge of the -2- we just solved naturally shares one of its blue hexes but has only one obvious choice for a second blue hex. It will be shared with the "1" we just uncovered, erasing two more cells. So we'll start with this:




If we stay in the same region, we can eliminate the next cell in line from the blue one we marked around the -2- at the top of the central column. The "1" we reveal shares that same blue hex, erasing four more. Interestingly, that leaves the -2- in the center column with only one unsolved active hex to mark.

Now, we have a {2} along its bottom-right edge, and a second -2- on its bottom-left edge. Each has only three active hexes to work with, and they each share a blue hex at an endpoint in their respective clusters. Can you solve them?





We can see that the "1" at the top of the column just to the left of the center column already has its blue hex, so the cell above it should be erased. That leaves the "1" on the bottom left edge of the "0" this reveals with only one choice for a blue hex, and it is shared with the "1" below it. So erase the cell below the one we just marked, revealing a "2". Stop here, though; we can't proceed any farther along this track yet.

You probably saw a long time ago that we gave the -3- along the grid's upper-right edge a third blue hex. If you've already erased its final orange hex, good; if not, that's fine, too. We'll do this next. The next step is more complicated, so let's stop for a second. Here's what we've got now:




The next step is a little more interesting. See that "1" on the top-left edge of the puzzle? It falls into a diagonal governed by a "2", which already has a blue hex. Notice that the line's only remaining orange hexes happen to be connected to the "1"; since we naturally must mark one of them to complete the line requirements, we can automatically erase its two orange hexes in the next line down.

The "1" and the "3" revealed here are a little bit vexing to work through. The "3" is probably a little more obvious because of its position relative to the "2" further up the line we're trying to solve. Since the hexes along the top and top-right edges of the "3" are each shared with this "2", we know only one of them can possibly be marked. After all, the "2" already has a blue hex. This means the hexes on the bottom-right and bottom edges of the "3" have to be marked.

Notice that we also just gave a blue hex to the "1" on the bottom-left edge of the "3". That clears the two orange hexes from this corner. The "1" left on the upper-right edge of the "0" that this reveals now has only one choice for its blue hex, which lets us solve the cluster:




We can erase a few more cells now. Notice along the upper-left edge that we also have a column governed by a "3", which also has an embedded line that itself is governed by a "1". Recall that the embedded line itself imposes conditions on how the main line has to be solved. This particular pairing means that while the column as a whole must contain three blue hexes, one must come from the embedded line. The top segment now has two blue hexes; the three orange cells which remain in the segment can now be erased.

Interestingly, the -2- that we reveal will let us solve the "3" just up and to its right, which we had to abandon earlier. The -2- has three active hexes, but they aren't consecutive; there are two on its left and one on its right. Naturally, the one on the right has to be marked, which will give the "3" a third blue hex. We can now erase the remaining hex on its bottom-right edge:

We've got a fairly intricate puzzle going on here; here's where we left off:



So we can work a little bit with the -2- we revealed near the top-left corner. It has a blue hex, so we'll erase the cell below the blue one. Interesting: A -4-. It actually helps us somewhat, despite the fact it has five active hexes. Two of those active hexes are shared by the -2- to the right. We've already established that only one of them is getting marked; this lets us mark the other two orange hexes around the -4-.

When we do this, we give a second blue hex to the -2- from which the -4- was derived. When we erase its remaining orange hex, we get another -2-. Again, clear the next hex in line from the blue hex it already owns. Another -2-?! Well, do the same thing again. This time, we get a -3- with two consecutive blue hexes; this means we again erase the next hex in line. And yet another -2-; do the same thing again. Since this is getting a bit convoluted, I'll stop here to show it to you graphically; it may make it a bit easier to keep up if you're playing along with me:

At last! We just revealed a "3" by the center gap which lets us actually mark a few cells this time. The "3" has only two hexes it can claim to complete its set of blue ones. Marking them solves it; the -2- on its bottom-left edge; the -4-; and the other -2- to the right of the -4-. With all of them getting complete sets of blue hexes from this, erase the orange ones which remain around them:


We'll continue working our way to the left from here; the -3- to the left of the "3" we just solved now has only one choice for a third blue hex. Marking it lets us continue to the left edge and back up to solve the negative cells we revealed earlier.

Now, we've reached a diagonal governed by a "3" that extends from the left edge of the grid. Along this line near the central gap is another -2- with a blue hex at an endpoint. Once again, we'll erase the next cell in its ring; this reveals a "2" that we can't immediately solve. So our last move in this section for now lies with the "2" at the beginning of this line; it has only one choice for its second blue hex, so we can mark it now.

We need to return our attention to the top-right quadrant now, to the column governed by a "5". This line contains an embedded line headed by a -2-; we know, then, that the top segment of the line can contain only three of the column's five blue hexes. It already has two.

In the next column to the left, near the central gap, we have a "3" with only one blue hex and four total active cells. The two on its right, of course, fall into the column we're working with; we can't give the "3" a complete set of blue hexes without including one of these cells. However, we know that only one of them can be marked without violating the column restriction. We can immediately mark the hex below the "3". We also can erase the two hexes nearest the central gap in the column we're working.

The "4" that we uncover from this is in a great position; it has only four active hexes, and when we mark the rest of them, we'll give that "3" the final one it needs, and this segment of the column is thus completed:





The "2" we revealed on the upper-right of the "3" we just solved already has its two blue hexes, so the orange cell on its bottom-right edge must now be cleared. The "2" that this reveals shares two blue hexes with the "4"; erasing the next hex from the "2" gives us a "3". More important, however, is that this lets us solve the "2" directly above the "3". It now has only two active hexes, and marking the second one gives a shared blue hex to the -2- on the edge. Now, just erase the last cell from the -2-. We still can't solve the "3", though.

One last step for this sequence, then. Focus on the diagonal governed by the "4" a few rows up from here; highlighting it shows us that it now contains only four active cells. Mark the two that remain unsolved on the far left side of the grid.





We've been given a little more information along the left side of the grid now; specifically, the "2" near the end of the line we just completed has been given a second blue hex. When we erase the orange hex under it, we leave the -2- on its bottom-right edge with only one remaining hex to claim for a second blue one. Mark it next before turning attention to the -2- just uncovered.

Now, the blue hex we just marked gives complete sets of blue hexes both to the -2- we just uncovered, and the "2" right by the central gap. We can erase four more cells from this. The "1" we reveal under the "2" shares a blue hex with it, erasing three more cells on top of this.




Now we really have to think to find another move. If we examine all of the empty hexes we just revealed, there is absolutely nothing which shows us what else we can mark or eliminate on this side. The same goes for the top-right section we abandoned earlier. How on Earh can we progress this puzzle??

Highlight the line governed by a "3" from the left side near where we left off. At the end of the line, on the bottom-right edge, we see a "3". That "3" is the secret.

The two hexes along the left edge of the "3" fall into the embedded line governed by a -2- that we abandoned earlier. What do we know about negative integers? This is the trick: Since the two blue hexes in this column cannot be consecutive, only one of these two hexes can be marked; and one of them must be marked since there are only four active hexes around the "3" to start with. That means that the two hexes around the "3" which fall into the diagonal are both guaranteed blue hexes. Marking them also gives the diagonal itself the three blue hexes it requires. We mark these two and erase the line's remaining hexes:

So we've given the -2- along the bottom-right edge of the grid a blue hex now, and again, it lies at an endpoint. Again, let's erase the next hex in the chain. The "2" that we reveal is actually very helpful, since it shares the two blue hexes we just marked. Erase its remaining orange hexes, then fill in the last remaining hex for the -2- to claim.

The "1" that we revealed on top of the -2- shares the blue hex we just marked. We can go ahead and erase the cell above the "1" but can go no further yet.

Instead, let's examine the empty hexes we revealed a few moments ago. Near the central gap are a "2" and a "1". The "2" has three active hexes; the "1" has four. The "2" and "1" share two orange hexes between them, which means only one of them can be marked. We also know that one of them has to be marked just to give the "2" a complete set of blue hexes. This tells us two things: First, that the hex on the bottom-left of the "2" has to be marked; and secondly, that the "1" cannot claim either of the hexes on its top-right or bottom-center edges. Those two will be erased:

We've made significant progress now but still have a decent chunk of the puzzle to go. Here's our most recent sequence:



The "1" that we revealed within the embedded -2- column, right above the "?", is in a helpful position. Two of its active hexes fall within a diagonal governed by a "2", which happen to be the only active hexes left in that line. The line itself has a blue hex, but we know that whichever hex is marked will also solve this particular empty "1" cell. That means the cell on the upper-left edge of the "1" cannot possibly be marked. When we erase it, we leave the "2" on its bottom-left edge with only one choice for a second blue hex.

We now know which cell that the diagonal will receive; the "1" we just revealed has only one choice for a blue hex. So mark it, then erase the last cell in that line. The "2" that is revealed can be solved by realizing that the "1" on its bottom-right edge also has only one choice for a blue hex. Marking that cell gives the "2" a second blue hex, and the orange cell above it can now be cleared.


Let's briefly turn attention to the embedded -2- column, which has now been given a blue hex. Clear the hex above the blue one; well, the "?" does nothing for us, but it still needed to be revealed.

Our next step will be more productive, however. Let's check the next column, which is governed by a "6". If we highlight it, we find it now has only six total active hexes. Now, mark the three orange cells in the center of the column.

Guess what? We just gave a third blue hex to the "3" on the bottom-right of the "?" we just revealed. Erasing the orange hex on the upper-right edge of the "3" is going to let us solve almost the entire right side of the puzzle using just the relationships on the grid:




This last sequence solved a massive chunk of what was left. Let's try to finish the upper-right quadrant now. We actually have two diagonals, each governed by a "3". Take the one starting from the indentation in the puzzle's edge. We've got two orange hexes bordering an empty "3" cell; these happen to be the cell's only unsolved hexes. The "3" already has two blue hexes; naturally, one of these must be marked to complete it.

Interestingly, these two hexes also border an empty "1" cell just down and to the right. Naturally, then, whichever hex gets marked also solves the "1". This also means the orange hex on the upper-right edge of the "1" cannot be marked. Erasing it gives us a "0"; you know what to do from here:




We now have just the few isolated hexes in the central gap and the bottom-left quadrant to go. We can solve one more diagonal now; look to the line governed by a "1" extending from the bottom of the right edge. We gave it a blue hex awhile ago; just erase the line's remaining orange hexes. For that matter, follow the "0" revealed in doing so.

These eliminations give us the information we need to solve the bottom-right edge now. The "3" closest to the bottom-center now has only three possible hexes to claim. When we mark them, we give the "3" farther up that side a third blue hex. Erase its final orange hex to also solve the embedded -2- column.



We want to focus now on the "2" that we uncovered above the "0" in that last sequence. It pops up with two blue cells bordering it, so let's erase the orange cell on its upper-left edge. The "3" that this reveals cannot immediately be solved...

We do, however, have enough information to solve the central column, which is governed by a "6". At this point, we've solved enough of its hexes that there are only six active hexes within it. Mark those which remain unsolved.

This actually gives us an important new move. Remember the diagonal governed by a "3" that we focused on a little bit ago to solve the upper-right quadrant? Well, now we can solve that line completely, as we just gave it a third blue hex. Let's erase its remaining orange hexes next.

For that matter, we have also given three blue hexes to the diagonal governed by a "3" extending from the upper-left quadrant, as well; this erases the two remaining orange hexes in the central gap.





We can solve some of the empty hexes over towards the left edge of the puzzle now. We have a pair of empty "2" cells near the far left edge, in the puzzle's third and fourth columns, which each now have only one choice apiece for their second blue hexes. Mark those next. Doing so gives a third blue hex to the "3" in the second column along the left-central edge. When we clear its last orange hex, another "3" is revealed, with only an obvious choice for a third blue hex.

We now must turn attention to the "2" near the bottom-center; two of its active hexes border an adjacent "1". This "2" has only three total active hexes to work with. We know that only one of the hexes shared with the "1" can be marked, meaning the hex on its upper-left edge is guaranteed to be marked. That hex falls into the embedded line governed by a "1". Once we mark it, the rest of the column is erased.

We can immediately mark two more hexes. The "1" we just revealed near the top of the embedded line has only one obvious hex to mark, as does the "2" along the bottom-left edge of the "1". Marking these also gives the "2" directly below the "1" the pair of blue hexes it needs, letting us clear the hex on its bottom-right edge:



We're almost finished now. The "3" that we just revealed has only two obvious hexes to claim for its complete set of blue hexes. Mark them next. Just marking them also completes the required blue hexes for several empty hexes in the vicinity, letting us erase several more. We'll find that the last orange hex at the bottom-center now has to be marked.

Only one last pair of empty "2" cells to solve. The one furthest down the bottom-left edge of the grid--that is, closest to the bottom-center--has only one choice for its second blue hex. To determine the puzzle's final blue hex, we have to solve one more logic puzzle.

Two of the final orange hexes bordering the "2" we must yet solve fall into that final diagonal from the upper-right quadrant, which is governed by a "3". That line still needs a third blue hex; of course, these are the last two unsolved active hexes within the line. Knowing that one of these two cells must be marked eliminates the orange hex on the upper-right edge of the "2". The "3" that this reveals already has three blue hexes. Erase the last orange hex from the "3" and mark the final cell to complete this massive puzzle and Chapter 3.



This puzzle is both tricky and a marathon. You have to be able to move back and forth between different sections of the puzzle and recognize how moves in one section feed into other parts of the grid. It's also very important to be able to analyze the positions of orange hexes relative to both empty hexes and line headers. We saw several instances where we had to use both in tandem to determine how to proceed. This skill will be vital in the hardest challenges.

Hexes Earned for Completing This Puzzle: 20

We've made it to the halfway point in Hexcells Infinite. Chapter 4 reintroduces us to quite possibly the trickiest puzzle mechanic that the series gives us: Grid Overlays.




We can identify Grid Overlays from numbered blue hexes. Clicking on such a cell extends a highlight across the grid over a two-cell radius; the number tells us how many hexes within the highlight will be marked blue.

That's simple enough, right? Well, in complicated puzzles, Grid Overlays can be red herrings; it can be easy to misread information from an overlay as to what needs to be marked or eliminated, leading to mistakes. We'll spend a lot of time on the hardest scenarios to outline just how to overcome any tricks they may present.

We're at least given a relatively easy introduction to the concept in Puzzle 4-1. We'll go ahead and start with that first grid. Click the Blue 18 to extend its overlay.

Notice that the entire grid is highlighted. The number, 18, tells us that 18 hexes within that highlight must be marked blue; the hub of the overlay itself--that is, the Blue 18 cell we started with--does not count towards this total! So we're saying that 18 total hexes surrounding the hub must be marked blue.

We can count all of the hexes here. If we count the total number of orange hexes within the grid, we see that there are exactly 18; we also see that this is the absolute maximum number of hexes which can be included within any such overlay. We can also clearly see from this that all of them here must be marked to complete the grid. Once you're done with an overlay, just right-click the hub to dim out the number like you would a line header.

The second grid is a little more interesting. Our hub in this one tells us that only one cell in this entire grid can be marked. At the top of the grid is an empty "1" cell.

If we click on the hub, we see again that it envelops the entire grid. In this case, we need to use that "1" at the top of the grid to guide us to the solution. Clearly, one of the three cells surrounding the "1" has to be marked. Our first step here, then, is to erase everything except the ring of cells surrounding the "1":



We get another clue from that pair of {2} cells we just uncovered. Now, here's the other important property about blue hubs: They're still blue hexes! This means that when a hub lies adjacent to an empty hex, it counts towards its blue hex requirement. For example: Let's say we had an empty "1" cell in the middle of a grid, with a total of six hexes around it. Now, we'll say that five of the hexes are orange, and the sixth one is a blue hub containing a number. Well, guess what? The "1" in this scenario has its required blue hex! We would then erase the five orange hexes to complete the "1". As you might expect, then, blue hubs also contribute to the blue hex count for any defined lines or columns in which they lie. We'll spend plenty of time on these concepts in later puzzles, as well.

So with that in mind, we're going to apply just that very concept here. The hub counts as the first blue hex towards completion of those {2} cells we just uncovered, and it lies at an endpoint in their respective rings of hexes. So, following the same rules as always, we're going to mark the next hex in line from the blue one, also giving a shared blue hex to that empty "1" cell at the top. The grid's final two hexes will then be cleared:

One grid to go, and only one remaining blue hex to fill. However, in the final grid, we are given two overlays to deal with, each indicating that only one hex can be marked within them. It's possible--and sometimes necessary--to extend more than one overlay at a time. Let's go ahead and do this here; notice how the only hex that the two overlays have in common is the center hex of the grid. Hmm...



What we can do immediately, then, is eliminate the two orange hexes which fall outside the range of either grid. After all, we know that each overlay must contain a blue hex.

Well, the two "?" cells that we uncover from this tell us absolutely nothing. The solution to this puzzle expands upon our definition of a shared blue hex. Previously, we have known that hexes can be shared between multiple empty cells. We can even say that they can be shared between a row and column upon which restrictions have been placed, such as the hex's diagonal line being headed by a "1" and its associated column by a -2-; clearly, that blue hex would contribute towards both such restrictions.

With this, however, we're also going to say that multiple Grid Overlays can share blue hexes between them, and it is this concept which will tell us how to solve the puzzle. The fact that the overlays simultaneously highlight the center hex of the grid but not any other hex tells us that this is the one that must be marked; we can only mark one blue hex in the puzzle, and it's the only one that will allow each hub to claim a blue hex. We'll mark this cell and erase the rest of the grid to complete the puzzle.



This is a decent introduction in how blue hubs and Grid Overlays work. If you can at least grasp the principle early on, it will be easier to understand how best to use them in later puzzles.

Hexes Earned for Completing This Puzzle: 5

Even though the next puzzle is relatively small, it will really tax your skills, especially your ability to deal with multiple Grid Overlays and understand exactly how to extract a solution using both they and the other conditions on the grid. Take this one very slowly...




We're given three small grids here, with a few column headers and three blue hubs. We can't do anything at all with the center grid until the end; it does not matter which of the other two grids we work first.

Let's take the grid on the right first. Here, we find a Blue 3 just off of its right edge; the final column of this grid is governed by a {3}. The column has only four total active hexes to start with, so we know that the two center ones must be marked; they actually open up two additional overlays to contend with later.

As far as that column goes, however, the current overlay covers only the two hexes we just marked, so we get no additional guidance from it as to which cell will complete the chain of three consecutive blue hexes. However, the next column over, which is governed by a "1", is also partially enveloped by the overlay. The three cells from this column that it covers are the only ones from which it can claim its third blue hex; naturally, it will also give the column its required blue hex. Our next step, then, is to erase the cells from this column which are not enveloped by the overlay:

The -2- revealed at the bottom of the column helps to guide our next move. We see that it has three active hexes: Two on the left, one on the right. The one on the right is a guaranteed blue hex, and it will give the final column the third blue hex it needs. Erase the final orange hex at the top of the last column.

That elimination lets us solve the "2" we just revealed at the top of the next-to-last column, since it now has only two active hexes to claim. Marking both gives a second blue hex to the "2" located below the first one, which eliminates two more hexes. Would you believe we get another pair of empty "2" cells from this?



Our next step isn't even remotely obvious, and it may be a bit of a stretch to see this one. It concerns the positioning of the -4- and -2-, as well as their respective surrounding hexes. Analyzing the column restrictions, as well as the overlays, tells us nothing concrete. But what if we simply analyzed what would happen with the -2- and -4- if we ran through the possible blue hexes? We want to do this with the -2- since it has only two active hexes to work with. If we marked the hex on its bottom-left edge, the hex on its upper-left edge would then have to be erased. Guess what? That would leave the -4- with four consecutive blue hexes, completely breaking its rules. So we need to mark the hex on the upper-left edge of the -2-, then erase the one on its bottom-left edge. The "1" we uncover shares the blue hex we just marked with the -2-, erasing the two orange hexes to its left. We also reveal another hub to deal with, this time governed by a "4".

This next step may seem counterintuitive, but of all the new cells we have opened up, the Blue 4 that we just revealed is the one we need to examine next. There is one puzzle-solving trick that we utilized quite a bit in Hexcells Plus but haven't actually touched thus far in Hexcells Infinite. We already know how to count individual hexes within a line or group as single units with respect to the requirements of whatever it is we're trying to solve. But what if we counted multiple hexes as a single unit?

Go ahead and click on the Blue 4 to expand its overlay. Notice how it covers: 1) The -4- and all of its surrounding hexes; 2) The "2" we just opened up on its bottom-left edge, as well as all of its surrounding hexes; 3) Three additional orange hexes above these clusters; and 4) Two blue hexes we have already marked.

The fact that the overlay covers all of the possibilities that both the -4- and the "2" can claim lets us use a modified counting system to determine our next step. The hub already owns two blue hexes, meaning it needs two more. We know that one blue hex will come from the ring of hexes around the "2"; and another blue hex will come from the hexes surrounding the -4-. As the overlay covers all of these possibilities, this means that whichever hexes we end up marking will give complete sets of blue hexes to each of these. Our next step, then, is to eliminate the trio of outliers above these rings of hexes:



By itself, this does little to tell us which hexes to actually fill in. We need even more information since each empty hex still has multiple possibilities. Go ahead and retract the overlay we have open, then move back to the Blue 5 hub at the bottom of the {3} column. When we expand it, we now find that it covers the "2" positioned above the Blue 4 hub, as well as three of its orange hexes. The overlay already contains three blue hexes; the orange hexes surrounding the "2" are the only ones from which it can claim the two that it still needs. Interestingly, this alone means that the orange hex on top of the "2", as well as the one on its top-left edge, are guaranteed eliminations.

Ah-ha! Now we're getting somewhere. We now have a trio of empty "2" cells within the same column, all in a row, with the bottom one contained within the overlay. The middle "2" of this trio has only two obvious blue cells to claim. One of them gives the column governed by a "1" its lone blue hex. Now, using that hint and the relationships on the grid, see if you can complete this sequence:


We're almost done with this grid, but we have a few more cells to work out. The "2" positioned on the upper-left edge of the Blue 5 hub we've been dealing with now has only two hexes from which it can claim a second blue hex, both of which are shared with the "1" on its bottom-left edge. This means that whichever hex the "2" gets is also shared with the "1", so the hex directly below the "1" cannot possibly be marked. Erase it next.

Another "1" is opened from this. It is in an identical position to the first "1"; whichever blue hex is marked to complete the "2" on its bottom-right edge will be shared with it. That eliminates the cell on the bottom-left edge of this "1" from being marked.

The "2" that this reveals is in position to claim both the orange cells it borders as there are no other active hexes around it. When we mark those two cells, giving a shared blue hex to the "1" and "2" we just left, we have enough information to basically solve the rest of the grid:




Let's take the Blue 4 hub we just opened at the top-center of this grid; it's pretty easy to see that it already contains four blue hexes within its overlay, so that lone orange hex it envelops will be erased. We'll complete the "3" that this elimination reveals by marking the grid's final hex:




The narrow strips pointing to the center grid each contain additional overlays at the endpoints; don't try to do anything with them just yet. As we'll see, however, they give us a rather nifty closing sequence for this puzzle. :-)

We've completed the grid on the right side of this puzzle. Here's the closing sequence to that side:



We now want to tackle the left grid. Expand the Blue 2 hub's overlay; it encompasses two cells in a column governed by a "1", and three hexes in the column governed by a "6". It's easy to think that one of the two hexes covered in the first column has to be marked, but that's actually not correct.

The second column has a total of seven orange hexes; we clearly need six of them to be marked blue, and the overlay contains the column's three middle hexes. Examining the column itself, we can determine that it's impossible to give it six blue hexes without including two of the three hexes included in the overlay. Go ahead and try; we can mark the two hexes at the top and the two hexes at the bottom, and we still need two of the middle hexes. So our opening move for this grid is to mark the four hexes at the top and bottom of this column, then erase the two hexes from the overlay which fall into the first column:



The column requirements dictate which hex we have to mark next. The first column now contains a pair of empty "2" cells. We know that one of them will get its second blue hex from the first column, and the second will get it from the second column. Which means that of the three remaining orange hexes in the second column, either the top or the bottom orange hex will be marked, but not both. The center hex of the column is marked next.

The Blue 4 hub that this opens up may seem useless, but it's actually an incredibly important clue. Go ahead and expand it; do you see how it encompasses three of the four blue hexes it needs? It also covers the only two remaining orange hexes within the column, meaning that whichever hex we mark for the hub will also complete the column. So now, every orange hex covered by this overlay except the two from this column has to be erased:

The "2" positioned on the bottom-right edge of the Blue 4 hub is now our focus; it has only one hex it can claim for its second blue. Mark it, then use the existing relationships to complete the first two columns:





We actually have another empty "2" cell with only obvious hexes to claim, as well. It's in the fourth column directly above the "1" that we revealed a little bit ago. Mark both of those hexes to give a shared blue hex to the "1", then erase the latter's two remaining orange hexes. Then, if you haven't already done so yourself, erase the orange hex below the "2" three cells up from the bottom of the third column, as it already has two blue hexes.

We can go ahead and erase the hex below the "1" we just revealed on the right edge of the grid next. But we'll then need to return to the existing overlays to make our next move. Start with the Blue 3 at the bottom of the second column; expanding it shows that it covers two blue hexes, as well as all active hexes surrounding the adjacent "3". We know that marking one of its two orange hexes will also give the Blue 3 a third blue hex, so we need to erase the lone orange hex not connected to the "3".

That gives us a {2} in a particularly interesting position. As the {2} has only its standard ring of three consecutive orange hexes around it, we can mark its center orange hex. This gives both the "3" and our hub the third blue hex they need; now, erase the hex to the left of the blue one, and then mark the one to its right to solve all of these markers at once!


To solve the rest of this cluster, then, erase the orange hex on the bottom-right edge of the "2" we revealed at the start of the last sequence. Now, just mark the final hex along the strip to complete the "2" revealed from this erasure.

Solving the top of this grid is much trickier. We have overlays governed by a "3" and a "4" to contend with. When expanded, the Blue 3 overlay encompasses five orange hexes; the Blue 4 encompasses only four. However, those four particular orange hexes are covered by both overlays.

The lone hex that is not shared between the overlays is the basis for our next move. For the sake of argument, mentally mark that hex; now, everything else within the Blue 3 overlay has to be erased, simultaneously erasing all remaining orange hexes from the Blue 4 overlay. Well, we can't mark that hex, then! Erase it next.

The -2- that this opens is immensely useful. As it also is surrounded by just a standard ring of three consecutive orange hexes, we can solve it easily. Doing this gives both of the overlays the last blue hex they need, and the final two orange hexes within them are now erased.




Now, just use the existing relationships on the grid to solve its last few cells:








And now we've come to the center grid. We need only four of its hexes to be marked. So now, go ahead and expand all of the remaining overlays.

Each of the overlays positioned in the corners of the two outer grids needs one blue hex apiece. Notice how only the cells in the corners of the central grid coincide with its center overlay. We need four blue hexes to solve the puzzle; four blue hexes to solve the center overlay; and one hex apiece to solve the four corner overlays.

This setup means that in order to complete the puzzle, the hexes we mark have to be shared between the central overlay and each corner overlay. The result is that every orange hex which is not shared between the central overlay and at least one corner overlay is immediately eliminated:




The "0" we just uncovered dictates the solution to the top half of the grid:








The final sequence will be determined by the "2" in the left-center of the grid, and the "1" at the right-center. The "2" has only one obvious hex to claim; the "1" already has its blue hex. Use this information to complete the puzzle.



This puzzle can be a relative nightmare in places, especially on the right side, where it's necessary to switch back and forth between different overlays and gradually erase more and more hexes to determine which ones to mark. The left grid is a little more straightforward but still difficult in spots. The final sequence is interesting in its use of five different overlays to determine which cells in the central grid to work with. This type of puzzle just requires a lot of analysis of the various rules governing any given cell or group of cells. Being able to count entire groups of cells as one or more units towards the requirements of an overlay or a line is essential to progressing the puzzle, and it can be a marathon of a puzzle to solve.

Hexes Earned for Completing This Puzzle: 10

So with the next puzzle, we gets lots of gaps, lots of line headers, and overlays to contend with.




This puzzle is going to require us to not only take care in using the overlays, but to also constantly monitor the line headers. The good news is that we can complete a column from the get-go. The very first column, governed by a "4", has only four total hexes to work with, with one already blue. So to start, we'll mark the rest.

Now, the top-center hex is a Blue 3 hub. Expanding the overlay reveals that only three hexes are covered by this overlay; naturally, we'll mark these next.






That starts us off with six blue hexes, but have you noticed that so far, all of them are hubs to additional overlays? That's going to be the theme with this level; don't worry, we'll get through it.

In the first column, we revealed another Blue 2 above the Blue 2 at the bottom. If we examine the overlay, we find that it already covers two blue hexes. So next, erase any orange hex within it.

When we do this, we can now solve the column into which those hexes fall; we've reduced it to just three active hexes, meaning we should now mark them all.






The first and second hexes in the first column are each Blue 3 hubs; expand the second one, and we'll find that another hex can be erased. The overlay contains three blue hexes already; erase the orange hex within it, which falls into a diagonal governed by a "7".

At the top of the puzzle, it doesn't actually matter which of the two Blue 4 overlays we expand; each contains three blue hexes, and the only orange hex they each envelop is shared by each. Go ahead and mark this cell next.





In a puzzle like this, with multiple overlays, it's a good idea to check them periodically, and dim out those which are completely solved. Expand them and first check that they have their required blue hexes. If they do, then next see if they cover any additional orange hexes, and erase any you find.

Screenshots going forward will illustrate this principle. Continuing now, we have a trio of Blue 5 hubs in a line. Start with the one within the diagonal governed by a "7"; expanding it shows that it covers four blue hexes, but there is no clear direction as to which of the two orange hexes within that line it will claim.

So let's look now at the Blue 5 in the column headed by the "4". Expanding it shows that it covers those same two orange hexes, plus one other; it also contains four blue hexes. Since we know that one of the two orange hexes within the diagonal governed by the "7" has to be marked, we can eliminate the extra orange hex within this overlay:


Now we can tackle the Blue 5 hub directly over the hex we just eliminated; its overlay now contains only five total active hexes, meaning we simply need to mark the last one.

We reveal another Blue 3; expand the Blue 3 above this one, and we'll find it covers three blue hexes. Erase the orange hex it envelops, which happens to be the top hex in a column governed by a "2".





Open the Blue 3 overlay in between those two zeroes now; we're going to use our modified counting system again. We've got another diagonal governed by a "7", this one extending from the right side. The row itself contains a total of nine active hexes. Well, the overlay contains two blue hexes already; the only three orange hexes it covers all fall within this diagonal. We know for a fact that the hub's final orange hex will come from one of those three hexes, which will contribute one and only one blue hex to the diagonal, giving it two in total to this point. This means all of the orange hexes within the line falling outside of the overlay are now guaranteed blue hexes:

Of course, we reveal a slew of new overlays with that step, including a Blue 1 at the beginning of the line. Let's expand it, and we easily see it covers a blue hex. We'll erase the two orange hexes within it, including one from the diagonal.

Let's now expand the Blue 2 overlay right next to the Blue 1; the eliminations we just made now leave it with only two total active hexes. When we mark the second one, we also give the line its seventh blue hex and can erase the last one within it.




Continuing down this line, we'll next expand the Blue 4 we just marked. It covers only four total active cells now; again, we'll just mark the last one it needs.

In the bottom-left corner now is another Blue 2 overlay; expanding it shows it covers three total active hexes, with one already marked. The two orange hexes it covers, however, each fall into a column governed by a "4", which already has three blue hexes. Whichever hex we mark to complete the hub also completes the column. We have another orange hex further up that column; it is now eliminated.

Open up the Blue 5 overlay right above the hex we just erased; it now contains only five total active hexes. Mark the final one.







The Blue 3 overlay on the upper-left edge of the "?" we revealed a second ago only contains three active hexes; again, just mark the last one it needs. Over on the bottom-right now, expand the Blue 2 overlay. It covers three orange hexes, but two of them fall into the column governed by a "2". This column already has one blue hex, meaning we can only give the hub one from this column. That means the orange hex above the hub is a guaranteed blue hex:

We're almost done. The Blue 3 overlay we just uncovered only contains three active hexes, so we'll again mark its final unsolved hex. This gives the column governed by a "2" its second blue hex, erasing the last one in the column. At the same time, we'll give the second diagonal governed by a "7" its final blue hex, letting us erase the last one in this line, as well.

Work now with the Blue 4 hub just to the right of the center hex--which, coincidentally, is another Blue 4 hub. Expand it to find that it has only four active hexes, then mark the last one it needs.






The Blue 4 overlay at the very center now contains four blue hexes; erase the one orange hex it covers. Incidentally, the Blue 4 directly below the center one is in the exact same situation, which lets us erase the next hex down the column. We'll get another erasure from the Blue 3 to the left; it covers three blue hexes, so the orange hex below this hub also has to be erased. This erasure leaves the column with only one final hex to mark in its completion:

Five hexes remain; only four can be marked. We can immediately see that two of them have to come from the central column, which is governed by a "6"; since the column contains three orange hexes, the other two orange hexes in the next column are now guaranteed blue hexes.

The Blue 2 overlay revealed from this gives us the solution; it contains two blue hexes already. When we erase its orange hex, the final two hexes are then marked to complete the puzzle.



Hexes Earned for Completing This Puzzle: 14

Puzzle 4-3 can be overwhelming just in the sheer number of Grid Overlays it tries to drown you in. You really have to be on your toes to get through it without making a mistake without any type of assistance. We'll continue seeing overlays spring up from the blue cells we mark for the rest of the game.

If you would like to take a look at some of the final challenges we will face, Chapter 5 is now open.




So we're given a more or less circular grid with several line headers and three overlays dead in the middle. We are not given any empty hexes to start with.

I worked through this puzzle again in a practice run before trying to write out the solution. This is not an easy puzzle. The solution is actually quite intricate and requires expanding even upon the relatively complicated logic we have been using in this chapter. Take your time if you're trying to do this one on your own; I'll try to present the solution in great detail to help you as much as possible if you get stuck. For those of you playing along with this walkthrough, enjoy the read.

This puzzle has a very peculiar opening sequence, and it does have to do with those Blue 2 hubs in the middle. What we'll find with each of them is that when we expand them, they encompass the other two hubs and only one other empty hex on the grid. In other words, each of the overlays already contains the two blue hexes they each need; whichever orange hex on the main grid that they cover will be erased, giving us our first three empty hexes: A -2-, a "0", and a {2}.

Solve the -2- at the top the way we would any such hex with just three continuous active hexes. Clear the cells from the "0", then mark the center hex in the ring around the {2}. Our opening move looks like this:





Interestingly, we can now immediately solve the central column. Go ahead and highlight it; we've already reduced it to six active hexes (Remember to count the hub in the middle!). We can mark the remaining orange hexes, which will also give a third blue hex to the "3" we revealed on top of the -2-. This erases the two remaining orange hexes from the "3".

Now, expand the Blue 3 overlay on the upper-right edge of the -2-; notice how it covers the "3" right above it, as well as all of its active hexes, plus two of the three blue hexes it needs. We know that this "3" needs a third blue hex and that the hex we mark will also thus complete the trio of blue hexes that the hub needs. Our next step is now to erase every orange hex contained in the overlay except those surrounding the "3":

We can use the relationships on the grid to progress further, but they're a little tougher here. Start with the "1" that we revealed on the bottom-right edge of the Blue 3; the hub clearly makes its blue hex, so erase the cell on top of it. What we'll find is that both the newly-revealed "2", as well as the "2" on its bottom-right edge, will have only obvious blue hexes we now need to mark.

In the previous sequence, we revealed another "1" on the bottom-right edge of the "1" we just solved; this one gains its blue hex from those we just marked. So go ahead and erase its remaining two orange hexes. The "1" that we reveal below this one will have only one obvious blue hex to claim, which will give a second blue hex to the "2" we just revealed. So clear the two remaining hexes along the right edge of the "2".

There's no obvious guidance for us to continue clockwise around the grid, so we'll need to move back to the top-center of the puzzle. You may have already erased the hex on the bottom-right edge of the Blue 3 up here; if not, go ahead and do it with me here. Now, go ahead and expand the overlay; it covers two blue hexes, the empty "3" cell just down and to the left, and three of its five active hexes.

This is a little bit tricky, and it requires you to analyze the area outside of the overlay, as well as what is covered by it. The "3" clearly needs one more blue hex, but only two of the three orange hexes are covered by the overlay. We have to mark one of those in order to give the hub the last blue hex it needs. This means that the empty "3" cell will get its third blue hex from completion of the overlay, and vice-versa. So the orange hex on the bottom-left edge of the "3" now has to be erased; there is no logical scenario in which it can be marked given these restrictions.

We get another "3" from this elimination, and it also has five active hexes surrounding it. Our goal is to try and isolate at least one cell that is a guanteed blue hex or a guaranteed erasure. We actually need the Blue 4 overlay on the upper-left edge of the -2- for this one.

This particular overlay encompasses both the "3" we're trying to solve, as well as the "3" we just revealed. It also encompasses all of their active hexes, two of the four blue hexes it needs, plus one additional orange hex. We've already established that one of the two hexes on top of the first "3" has to be marked; this will give the overlay a third blue hex. Additionally, since the second "3" has only one blue hex to start with, we have no choice but to mark at least one of its orange hexes, also giving the overlay its fourth. As a result, the orange hex that does not border either "3" is a guaranteed elimination:

We can also deduce our next guaranteed blue hex from this overlay, as well. If we were to complete the original "3" without sharing a blue hex with the one on its bottom-left edge, we would have to mark two additional hexes around the second "3", thereby giving the overlay five total blue hexes. As a result, the hex above the first "3" has to be erased, and the one on its top-left edge now has to be marked, and that will give a shared blue hex to the second "3":

So now, we have to shift overlays again; expand the Blue 4 we just revealed. It covers three blue hexes, but guess what? It also covers all of the hexes around the second "3" that we have yet to solve, just like the overlay we just left. We already know one of them is going to be marked; let's now erase the lone orange hex covered by the overlay that does not border the "3", at the top of the column governed by a "1".

This is where the logic gets a little more convoluted. We have many different restrictions to juggle here. We want to focus on the empty "3" cell nearest the central gap, to the right of the column headed by the "1". This particular "3" has two orange hexes to its left, which fall into that column; one orange hex under it; and two orange hexes, on its upper rim, which fall within range of the Blue 4 overlays we've been dealing with.

From these restrictions, we can determine the following: 1) Only one of the hexes to the left of the "3" can be marked; 2) Only one of its two orange hexes falling into the overlay can be marked; and 3) Because of 1 and 2 above, the hex below the "3" is a guaranteed blue hex. Mark that one next.

We also get one more elimination here; as a result of all of the restrictions governing the third "3", we can erase the hex on the top-left edge of the second "3". There's no possible way for this one to be marked while maintaining the rules of everything else in this region of the grid.

We've only scratched the surface of potentially the most intricate solution we've encountered so far. Here's where we left off:



That empty "2" cell we just revealed is our best friend right now. It has only an obvious second blue hex to claim, which is going to give the second "3" the third blue hex it needs, as well as giving the Blue 4 hubs their fourth blue hex. Erasing the last hex from under the "3" solves all of them. And now, concerning the column governed by a "1" now, we can go ahead and erase everything except the two cells which border the third "3"; we already know one of them has to be marked.

Now, we can use the Blue 2 overlay opened up below the third "3" to erase a few more cells. Expanded, it covers the "3" and all of its active hexes. Of course, we've already established that one of the two hexes immediately to the left of the "3" has to be marked; that lets us erase the three orange hexes at the far left edge of the overlay.

We can now solve the nearby diagonal governed by a "5". The last three eliminations cleared a hex from this row, and it now contains only five total active cells. Go ahead and mark the rest. Doing so also gives the column governed by a "1" the blue hex it needs, erasing the last one from the column. As a final step for this sequence, we can give the "3" that pops up from this the lone remaining hex it can claim as it is left with only three active hexes.

The next couple of moves can be made from just the cells on the grid. At the top of the column governed by a "4", the "2" has its two blue hexes, so erase the one on its bottom-left edge. Next, halfway down the column governed by a "1" that we just finished, the empty "1" cell has only one hex it can claim.

We get one more blue hex to mark, too. Two spaces below the "1" we just solved is another "1". Its only two active hexes are to its left, in the column governed by a "4". The column has five total active hexes, with two already marked; clearly, only one of these two particular hexes can be marked, making the final one at the bottom of the column a guaranteed blue hex.



The Blue 4 that we just uncovered is a lot more helpful than it may at first appear. When we expand the overlay, it covers only five total active cells, including the final two orange hexes of the column. We've already established that only one of these can be marked; therefore, the other three orange hexes covered by the overlay have to be marked.

One other step here: The diagonal governed by a "1" will lose the three hexes at its far end. The first two hexes of the line border an empty "1" cell and are the only ones from which it can claim its blue hex. Since marking one of them satisfies both conditions at once, the final hexes at the end of the line cannot possibly be marked.



So now, we have given the "2" positioned on the upper-right edge of the Blue 4 hub a second blue hex. This lets us complete the column governed by a "4" by erasing the remaining orange hex from the "2" and then marking the column's final hex. As a clean-up step, go ahead now and erase the orange hex from the "1" below the "0" we revealed at the puzzle's opening.

Our next step is fairly difficult to spot. Within the column that we just finished are Blue 5 and Blue 4 hubs. The Blue 4 overlay already has three blue hexes but covers four total orange hexes. When we expand the Blue 5, it contains only two blue hexes and covers six orange hexes--including the same ones covered by the Blue 4 overlay.

We need to use our modified counting scheme in conjunction with the Blue 5 overlay. We've already established that only one of the four orange hexes shared by both overlays can be marked, giving this hub a third blue hex; the fourth and fifth will come from the additional two orange hexes not shared by both overlays:



We can erase two more hexes now. We just gave the "1" at the top of the second column a blue hex, so now we can get rid of the first hex in the diagonal governed by a "1". Also, the same blue hex gave the "2" on its bottom-right edge a second blue one, letting us clear the cell directly below it. This uncovers a "4".

We can use either of the overlays we were just working with now; I'll stick with the Blue 5 since it was the last one I showed off. We know that whichever hex completes the empty "4" cell's blue hex requirement will also be the last blue hex for the overlay. So the lone orange hex not touching the "4" now has to be erased. Now, just solve that -2- to complete this section:


There's still a diagonal governed by a "5" on this side of the grid. We've reduced it to six active hexes, which helps us more than may be readily apparent. If we examine the unsolved end of the line, we find that its hexes run next to a "2" and a pair of empty "1" cells. This configuration means that it's impossible to complete the line without giving a blue hex to the "1" in the middle of that trio. This tells us two things. First, the hex on the bottom-left edge of the "2" is a guaranteed blue hex; and secondly, that the two hexes along the upper rim of the "1" cannot possibly be marked.

This now lets us solve the column governed by a "6" on this side. We've now reduced it to six active hexes; mark the last two to complete the column.







The next several moves can be made without the help of any overlays. Working with the trio of empty hexes we started with here, we've left the "2" with only one obvious choice for a second blue hex, and it will be shared with the "1" in the middle. The last hex of the diagonal is now erased, leaving the "1" on its top-right edge with a single obvious blue hex. Note that this gives a second blue hex to a column governed by a "2"; now, erase the rest of the column.

There isn't much left now. The diagonal governed by a "2" near the upper-right corner has the two blue hexes it needs, so clear its remaining orange hexes next. The "3" we uncover from this has only three obvious blue hexes to mark.

We now have two Blue 5 hubs bordering the "4" we uncovered a few moments ago. Expand the one directly under it. It covers a total of three blue hexes and three orange hexes, including all active hexes around the "4" itself. The "4" already has three blue hexes; naturally, we need one more from within the overlay. As we've seen before, then, the outlier has to be marked. But when we do so, we give the corresponding diagonal, governed by a "4", the final blue hex it needs; erase the rest of the line:

That last move left the "4" with only a final obvious blue hex to mark. We don't even need the overlays anymore; complete this next series using just the relationships between the cells:






To finish, use the "2" on the upper-left edge of the "1" near the bottom-center; it's left with only an obvious blue hex to claim, which is shared by the other empty hexes here. Erase the final hex in the cluster, then mark the final hex. Puzzle complete!



Hexes Earned for Completing This Puzzle: 15

What else can be said about Puzzle 4-4? It's brutal. We had to combine multiple rulesets in places to narrow down which hexes to mark or to eliminate, and it's this kind of logic that will be utilized throughout the final stages.


Grid overlays and lines with embedded Secondary and even Tertiary Line Headers. Oh, boy...



Be honest: How many of you saw that Blue 6 in the center and started trying to mark all six hexes around it? If only it worked that way! But it's an overlay, not an empty "6" cell. It just means that somewhere within its radius will be six blue hexes.

We actually do want to start with the Blue 6 hub, but we have to be very careful of the line headers here, as well. Go ahead and expand the overlay; it covers this whole central cluster of cells. Now, observe all of the line conditions. The first column of this grid has a Primary Line Header of "6"; a Secondary Line Header of "4"; and a Tertiary Line Header of "1". The middle column is simply governed by a "5". And the third column of the grid has a Primary Line Header of "7"; a Secondary Line Header of "5"; and a Tertiary Line Header of "2".

Notice how the grid itself can essentially be thought of as three clusters joined together by a single cell within the center column; that column's hexes are the only unbroken chain in the grid. The embedded lines start at the break points for the first and third columns of the grid.

Segmented columns like this are best interpreted from the Tertiary Line Header first, because it grants restrictions which then feed into the rest of the column as a whole. For the grid's first column, then, we need one blue hex in the bottom cluster; three blue hexes in the center cluster; and the final two blue hexes for the column as a whole need to come from the top cluster. Similarly, for the third column of the grid, we need two blue hexes in the bottom cluster; three blue hexes in the middle cluster; and two in the top cluster.

The Blue 6 overlay encompasses the entire center cluster of the grid, and we've just determined that its first and third columns each need three blue hexes to come from this cluster. Which means none of the hexes within the overlay from the center column can be marked. That's our first step: Erasing these four hexes.

Of the empty hexes revealed, the "5" is the most obvious one to solve as it has only five total active hexes surrounding it. Go ahead and mark all of them to complete our opening sequence:



Notice that every blue hex we marked revealed another hub. Being able to analyze each overlay is going to be critical to progressing beyond this point. The Blue 5 positioned on the bottom-right edge of the empty "5" cell is our best bet. Expanding it reveals that it covers four of the five active hexes around the empty "3" cell near the bottom of the cluster, as well as four of the five blue hexes it needs. The "3" itself already has one blue hex. What this says is that only one of its two remaining blue hexes can come from the three orange hexes inside the overlay. This means that its one orange hex outside the overlay--the one on its bottom-left edge--is now a guaranteed blue hex.

Marking this particular blue hex gives the first column the third and final blue hex it requires from the central cluster; now, erase the last orange hex from the line within this cluster.






We don't have quite enough information to solve those last two hexes in the cluster yet. Let's try to work our way back. At the top of the cluster, we've given the "2" both blue hexes it needs, so we can erase the hex above it to start working on the top cluster. Here, we uncover a -2- that can be solved in the usual manner. The "3" that pops up naturally shares the two blue hexes we mark for the -2-, but we can't immediately pick out which remaining hex it will claim yet.

So instead, let's now open the Blue 5 overlay positioned on the top-right edge of the center cluster. When we expand it now, we find that it covers five blue hexes. Erase the orange cells within its radius next. Doing this will now leave that empty "3" cell at the bottom of the cluster with only one obvious blue hex to claim, which also solves the Secondary Line Header within the third column. The "2" positioned below the "3" has now been given a second shared blue hex; erase the hex below it leading into the bottom cluster of the grid.

You'll find in the next screen that I've dimmed out some of the overlay hubs that have also now been solved as a result of that last sequence. I recommend doing this for more complicated puzzles to get rid of some of the clutter; it can only cause confusion later. That's not to say that if you accidentally forget to dim one or two that you'll run into problems; just try to do this with most of them as you go along to reduce that possibility.

Let's now open up the Blue 3 overlay on the bottom-right of the central cluster. It now covers the three blue hexes it requires, eliminating a few more. Now, we'll erase one more hex by expanding the Blue 5 overlay on the bottom-left edge of the empty "5" cell; it covers five blue hexes, so erase the lone orange hex it covers:



Now, we can solve the Blue 6 overlay at the top-left corner of the center cluster. When expanded, it only covers six total active hexes; mark the last unsolved one. That's naturally going to give the "1" we just uncovered a blue hex, so now, erase the two orange hexes to its left.

We'll want to go ahead and solve that {2} we just uncovered. The blue hex it shares with the "1" is at an endpoint, so just mark the next one in line and erase the other two orange hexes. Two more hexes we can mark: First, the -3 we just uncovered has only four consecutive active hexes around it, so mark the second endpoint in that ring; we'll give a shared blue hex to the "1" below the -3- with this, so erase the orange hex on the bottom-left edge of the "1". Secondly, the "1" positioned below the {2} has only an obvious blue hex to claim.

Moving back to the center grid now, expand the Blue 4 overlay on the upper-left edge of the -2- we solved earlier. It covers three blue hexes, but more importantly, it covers the "3" on its upper-right edge and all of its active hexes. We obviously know that one of the orange cells on the upper-rim of the "3" has to be marked to give it a complete set of blue hexes; that hex, as we have seen, will also complete the blue hex requirements for the overlay. Erase the orange hexes within the overlay that do not border the "3". Go ahead and also erase those from the "0" that this uncovers.

The "3" that we just revealed near the top of the first column of this grid is in a particularly interesting spot. It has only four active hexes around it, but two of those are also included within the Blue 4 overlay we're trying to solve. This additional restriction tells us a few things. First, that the "3" closer to the bottom of the cluster is going to get its third blue hex from the two orange hexes shared by the upper "3". Secondly, that the hex on the upper-right edge of the lower "3" can now be erased. And finally, that the two hexes along the upper rim of the upper "3" have to be marked:

We've only scratched the surface of this intricate solution; here's where we left off:



We can solve this pair of empty "3" cells by taking the line headers into account again. Remember what we said earlier about the first column: Two of its blue hexes have to come from the top cluster due to the embedded lines farther down. Well, we've just given the column a second blue hex from this cluster. So when we erase the last orange hex from this end of the line, we leave each "3" with only one hex to claim.

Marking this hex gives the "2" in the third column a second blue; erase the cell above it. The "3" that this reveals will then have only one obvious hex to claim. But what about the very top-center hex? Use the Blue 3 overlay on its bottom-left edge. When expanded, it covers the three blue hexes it requires, meaning this cell can now be erased:



Let's look at two other overlays now. If we expand both the Blue 4 at the top-right of the top cluster, as well as the Blue 5 at the bottom-right of the top cluster, we find that their respective overlays now encompass exactly the number of active hexes as blue hexes they need to capture. As a result, we'll end up marking the top three hexes of the first column in the grid on the right.

Back in the first grid of the puzzle, the "3" at the top of its next-to-last column has only two more obvious blue hexes to claim. One will also go to the -3- from before, giving it a third blue hex and letting us clear the orange hex on its top-left edge.





While we're in this section, go ahead and expand the Blue 6 overlay two spaces below the {2}. Those are six free blue hexes! The overlay covers several empty hexes and only six orange hexes; go ahead and mark that entire cluster.

We've now given a second blue hex to the "2" positioned at the top-left of the overlay. Erase the orange hex from its top-left edge. The "1" that this reveals naturally shares a blue hex with the "2", erasing three more.





Now, we can focus on the Blue 5 overlay on the bottom-left edge of the -3-. When expanded, it covers both three blue and three orange hexes. We obviously need to mark two of those three orange hexes, but they're adjacent to empty "1", "2", and "3" cells. The trick here is that the middle orange hex of the trio is shared by both the "2" and the "3"; marking it would actually force us to erase the other two, since it would complete both empty hexes. The proper sequence, then, is to mark the first and third orange hexes in the line, then erase the center one. Completing this cluster then just relies upon watching shared hexes and solving the empty hexes with the least number of active cells surrounding them first:

There's another Blue 6 hub to the left of the one we worked a couple of minutes ago. When we expand it, we find it has six blue hexes within its radius, letting us clear three more. The "1" which pops up in the center of that trio already has a blue hex, erasing two more yet. That will leave the "2" on the upper-left edge of that "1" with only an obvious second blue hex to claim.

Now, go ahead and expand the Blue 4 overlay overf the "2" we just solved. It now covers four blue hexes, giving us one more to erase:







Expand now the Blue 7 overlay on the upper-right edge of the "3" we revealed in solving the Blue 6 hub a moment ago. It covers six total blue hexes; it also covers the "3" itself and all of its active hexes. This is another situation where the hex that we end up marking will solve both of these. Since the seventh blue hex for the hub will also complete the empty "3" cell, erase those orange hexes within the overlay not adjacent to the "3".

We reveal a -2- / "2" couplet from this. Solving them will help us fill in this section. The "2" already has its two blue hexes, so we'll immediately erase the orange hex under it. For the -2-, it has a blue hex on top of it, so we need to erase the hex to the left of the blue one. That will leave only one obvious blue hex for both it and the "3" we're working on to claim. As a final step here, erase the orange hex below the "1" along the right edge since we gave it a shared blue hex a second ago; then, since the "3" uncovered has only three total active hexes, mark the two it still needs.

This grid is practically done now, but before we tackle that final diagonal, which is governed by a "6", let's move back to the central grid for a minute. Expand the Blue 4 overlay at the bottom-left of its center cluster; it covers four blue hexes and one orange hex from the bottom cluster. Erase this orange hex next.

Notice how we now have a trio of empty "1" cells here now. The center one is left with only one obvious hex to claim; marking it gives a shared blue hex to the others. So now, erase the hexes below each of the other empty "1" cells.

This is going to let us solve the Tertiary Line Header in the third column; we've now erased two of its four hexes, and we need two blue ones to satisfy the column's requirements. So next, mark these two hexes. This opens up the solution to this whole cluster; solve it by carefully observing the relationships between the cells, as well as the Tertiary Line Header ("1") in the first column of this cluster:

We have only the diagonal governed by a "6" to solve to complete both of these grids now. The problem here is that we have a continuous line of orange hexes adjacent to an equally long line of empty hexes, each of which has two possibilities for their remaining blue hexes. We need to study each empty hex individually to determine the way forward.

The "3" at the start of this line has only two choices for its third hex; the "2" a little farther down is in the same spot. These specific pairs of blue hexes will give us the diagonal's fourth and fifth blue hexes. Now, we focus on the "3" a few spaces down; its two orange hexes will give us the sixth blue one for the line.

What about the "2" in the middle of this section? We can't reliably use it because it shares an orange hex with the "2" on its upper-left edge, which introduces additional uncertainty. Which is why the orange hex below this "2" can now be safely erased:



Initially, it may look like the "2" we just opened up creates more problems than it solves. However, the "2" above it is now left with only one obvious choice for its second blue hex. And when we mark that one, we can complete the rest of the line:





Two-thirds of the puzzle is complete; now, we need to tackle the grid on the right. We can start with the remaining Blue 4 overlay on the right side of the bottom-center cluster. As it now covers four blue hexes, we can clear two from the left edge of the final grid. The "0" that we uncover gives us one more cell to clear, as well.

Note that the first column of this grid is governed by a "4"; we've left it with only four total active hexes, so just mark the one that remains. This will give a blue hex to the "1" above the "0", so clear the hex on its upper-right edge. Subsequently, we leave the "1" below the cell we just erased with only an obvious blue hex to mark.

We're nearing the end of the lengthiest puzzle Hexcells Infinite has thrown at us so far. Here's our current progress:



We're now left with a bit of a conundrum. We have no clear guidance as to which cells we need to mark or erase to progress the puzzle. In fact, the only information other than empty hexes is a couple of Blue 5 overlays at the top of the grid.

This is a situation where we have to use two overlays in tandem to make another move. We want to start with the one that covers the least number of active hexes, which is the Blue 5 at the top of the column. Expand it; it covers three blue hexes and three orange hexes. We need two of the three orange hexes within that triangle to be marked. Remember this and close the overlay.

Now, expand the Blue 5 overlay directly below the first. It also covers three blue hexes, but this one covers five orange hexes. This includes the three orange hexes from the first overlay, and that's the trick: Since the two hexes we mark for the upper overlay will also go to the lower overlay, we need to erase the two extra orange hexes covered by the second overlay:


Believe it or not, the -2- we just uncovered gives us our next blue hex; two of its orange hexes are covered by the overlays we're working with, and since its blue hexes cannot be consecutive, we know that only one of those two hexes can be marked. So the top hex within our triangle is now a guaranteed blue hex.

Marking this gives us a Blue 4 overlay, which is more helpful than it may appear. When expanded, it covers three blue and three orange hexes, but two of those orange hexes are shared by everything else we've been working with here. Since we have to mark one of those two, the extra orange hex becomes our next elimination:



The -2- we just revealed lets us begin filling this section in. Two of its orange hexes are along its bottom rim; only one lies along its top rim, and that one is a guaranteed blue. This gives us the second blue hex for our triangle; erase the third.

Now, the "3" below the "4" that we just revealed is left with only three active hexes. Mark the two blue ones it still needs. Just from this, we can fill in a huge chunk of the grid:






We want to shift now to the Blue 4 overlay in the center of the second column of the grid; expanding it shows that it covers three blue hexes, as well as the "1" just down and to the left and both of its active hexes. Clearly, the blue hex claimed by the "1" will give the overlay the last one it needs; erase the orange hexes inside its radius not connected to the "1".

Now, close this overlay, then open the Blue 5 overlay two columns to the right. It's in a similar situation; it covers four blue hexes but also the "2" under the hub and both of its remaining orange hexes. We can see that whichever hex goes to the "2" will also complete the hub's blue hex requirements. So here, clear the hexes not connected to the "2".


So we just left the "1" back to the left with only one obvious blue hex to claim; marking that gives a second blue hex to the "2" right below the "1", letting us clear another cell. See if you can carry out the next few steps:





We're left with only a few cells to solve, and with the relationships we've established from that last sequence, we should be able to complete the puzzle. Start with the "4" near the bottom-center of the grid and proceed out to the right edge:



This puzzle can be brutal in places. We not only have a large number of overlays to contend with, but right from the beginning, we're forced to deal with columns sub-divided into three miniature lines with their own restrictions. Additionally, we're forced in a few places to analyze the characteristics of multiple grid overlays at a time to determine our next step. If you can get through this one, however, you'll have a better chance at understanding the final challenges without additional assistance.

Hexes Earned for Completing This Puzzle: 18

We're at the end of Chapter 4. This last puzzle won't let it go down without a fight!




This is a very tricky puzzle, if for no other reason due to its disconnectedness. Dealing with multiple overlays and line restrictions is difficult under normal circumstances. In a puzzle where there are only small clusters scattered throughout, that challenge only grows.

Even in this puzzle, we have to deal with Secondary and Tertiary Line Headers, and those restrictions will become very important as we whittle down the overlays. There are only a couple of good places to start. We'll begin with the top-center cluster.

What's interesting about it is that the very top-center hex of the puzzle begins two criss-crossing diagonals that are each governed by a "2". These diagonals are sub-divided, with their respective embedded lines each governed by a "1". The segments at this end of each line have their only hexes in this cluster. We also have a Blue 1 hub to work with.

So if we highlight both Primary Line Headers here, we find that either the first or second hex in each has to be marked. The overlay covers every hex in this cluster and also the very top hex in the cluster below. Taken together, these restrictions rule out the hex directly above the hub, as well as the top-center hex of the cluster below, as being markable. So erase these two hexes first, then erase the hex below the "0" that appears.

The "2" that appeared on top isn't that helpful, but remember: We can only mark one hex in this whole cluster; additionally, we have to satisfy the requirements for the two diagonals. The fact that these lines are sub-divided so that they each can only have one hex marked from this section means the only possible way to fulfill all of these requirements is to mark the top-center hex and erase the others:

We can now look at the big Blue 7 hub in the middle. It covers the entire cluster except for the two free blue hexes at the left and right edges. Here, too, we're dealing with criss-crossing diagonals; however, these are subdivided twice. Looking at the line headers for each segment, they will claim two hexes apiece from this cluster.

Let's factor that into the overlay. Our two free blue hexes give each of the diagonals one blue hex apiece, meaning they each will get one more. So the two pairs of orange hexes within the overlay along each line will only contribute two of the blue hexes required by the hub. We have five orange hexes outside of the diagonals. Guess which ones are going to be marked next?


One thing that helps us now is that we gave a blue hex to a column governed by a "1" which passes through the central cluster. That gives us two more hexes to erase. The "3" that is uncovered from this lets us solve the first embedded line of one of the diagonals.

Our next step will factor into that same diagonal. At the bottom-right of the board is a Blue 5 overlay which encompasses six total active hexes; however, two of those fall under our Tertiary Line Header, which is a "1". We can't mark five blue hexes for the hub without marking one of these. And since only one of those two hexes can be marked, we'll mark the four in the lower line, erase the two within the embedded upper line falling outside the overlay, and let the empty hexes guide us:

Within that same general section is a Blue 2 hub. When expanded, it covers one blue hex already, as well as a "1" and both of its active hexes. It's another situation where giving a hex to the "1" will complete the blue hex requirements for the hub. As a result, the cells above and below the hub are erased, and again, the empty hexes guide us to solving the section. Consequently, we'll solve the embedded line governed by a "5" from this.

The blue hex we just marked falls into a column governed by a "2", so we can now erase the hex at the top of the column. Go ahead and erase the hex from the "0" that appears. Now, both the "0" and the "2" revealed here fall into our other sub-divided diagonal governed by a "5". The way it is sub-divided means that it needs two blue hexes from this cluster; there are now only two active hexes left. With these marked, the criss-crossing diagonal governed by a "1", as well as the Blue 2 overlay, dictate that all of this cluster's remaining hexes be erased:



Over on the left side now is a diagonal governed by a {2}, which contains a free blue hex. Only two hexes within the line can possibly marked to give it two consecutive blue hexes, so we can erase the other three. The empty hexes we reveal let us easily solve those two small clusters at the left- and bottom-center.


With this, we can solve the cluster at the right-center by using its associated diagonals, each governed by a "3". The top such diagonal has three active hexes and needs two marked; the lower diagonal has its three blue hexes and needs its final hex to be erased:




We so far haven't even touched the top-left cluster. Our only guidance here is a Blue 3 hub and some line headers. The overlay covers every single hex in the cluster except the first hex in a diagonal governed by an "11". The line already contains nine blue hexes; we need two of the three remaining to be marked.

The overlay also covers all of the remaining orange hexes in a line governed by a "5", which contains three blue hexes already. Right away, we know that two of the three blue hexes we mark for the hub will come from specifically from this line. The other thing we know? We can't complete the diagonal headed by the "11" without marking one of its hexes inside the overlay--and we know that only one of them can be marked without breaking the rules of the hub.

We've now just guaranteed that the first hex in the line headed by the "11" has to be marked. This hex also falls into a diagonal governed by a "1". So the rest of that line will be erased; we won't even need the overlays to finish the cluster:





We can now start the bottom-left cluster. We just gave another column governed by a "2" a second blue hex, allowing us to erase those at the bottom. This also lets us finish the diagonal governed by the {2} by erasing one of the two hexes it had left; mark the last one, which also falls into the embedded line governed by a "1". Naturally, we'll erase the rest of this line segment:


Now, that Blue 4 overlay at the bottom-left only covers four total active hexes; mark all of them next, contributing four of the five blue hexes this diagonal needs. The Blue 3 overlay just up the line then covers two blue and three orange hexes. We've also got a pair of empty "2" cells which each need a second blue hex, and even two diagonals headed by a "5" to complete. The only way we can satisfy all of these restrictions is to give everything a shared blue hex. This means the one at the far right end is the correct choice:

End of the line! The column near the middle governed by a "2" now has its two blue hexes. Erase the line's last orange hex and mark the final cell of the puzzle to complete Chapter 4!



Hexes Earned for Completing This Puzzle: 20

And with that, we end Chapter 4. We are approaching the end of our journeys through Hexcells. Only 12 puzzles remain, including the toughest of the tough. And so we begin Chapter 5 with...a car?




It kind of looks like a side view of a futuristic car with a bubble-covered cockpit to me. Almost all of our information is concentrated near the top-center; off to the sides, we're given a couple of hubs and column headers.

This is a fairly complicated puzzle; I did a practice run and really did get stumped a couple of times.

It's tempting to try and start with the Blue 9 hub over on the right, but if we examine it, we find that there's no way to isolate enough hexes to make any guaranteed moves. Where we do want to start, however, is the central column. It's governed by a {5}, but more importantly, we've been given a blue hex towards its chain of five continous blue hexes. The positioning is interesting; only one orange hex exists above it, meaning that only six possible hexes can be included. So if we assume the blue hex is an endpoint, we can determine the maximum reach of our chain and erase the cells below it:

Since we've reduced the column to only six active hexes, the next move we can make is ensure that the four in the middle of the chain are marked; we know that they will be included in either combination of five continuous blue hexes.

Here's where it gets tricky. See the positioning of the {2} at the bottom? There are only four active hexes around it, divided into two pairs on either side of it. This means we will mark either the pair on the left or the pair on the right; there's no split in the two blue hexes it will claim since they have to be connected.

That's going to play a huge role in what we do next. To start with, the requirements of the {2} will also ensure that the "1" directly above it will share a blue hex with it. That tells us the "1" will not be able to claim either orange hex on its upper corners; those two cells need to be erased next.




The problem now is in solving the "2" positioned above these other empty hexes. It now has only three active hexes around it, but we don't yet know if we'll be completing the {5} chain or not.

It takes some thinking out, and this is where I became stumped for quite awhile. The answer to this problem also lies with the {2} at the bottom. For the sake of argument, let's say that the two hexes on its left are marked. This feeds a shared blue hex both to the "1" above it and to the "1" on the upper-left edge of the first "1". That results in the clearing of three more hexes--including the one on the upper-left edge of the "2".

Notice how this entire section is perfectly symmetrical; this means that if we were to mark the two hexes on the right side of the {2}, we would have the exact same situation concerning the "1" on the upper-right edge of the first "1". That would also erase the hex on the top-right edge of the "2".

What this ultimately means is that there is no scenario in which both corner hexes on top of the "2" are marked. This guarantees that the cell directly above the "2" is marked--which also completes our chain of five blue hexes for the column, letting us eliminate its top hex.

I'm going to show the logic of this solution separately first, then show how the overall puzzle looks from this afterward.



Notice that we are not attempting to mark hexes around the {2} yet!!! We are only outlining how the possibilities play out with respect to the "2" we're trying to solve:






You've probably already guessed that we're going to mark the cells on either side of the "2" we just revealed; go ahead and do so next, then expand that Blue 3 overlay in the center of the ring. We've just completed its required set of three blue hexes; erase all of the remaining hexes in that ring:




We're about to solve that {2} at the bottom. First, give the "3" we revealed along the lower-right edge of the upper ring the two obvious blue hexes it needs for a complete set. This gives the "1" on its upper-right edge a shared blue hex, so erase the orange hex on the bottom-right edge of the "1". For that matter, erase the hexes along the bottom rim of the "1" that this step reveals, since it shares the same blue hex as the first "1".

We'll come back here in a minute, but for now, we can solve that {2}. How? Notice that the two orange hexes on its right fall into a column headed by a "3", which now has two blue hexes. Well, that automatically rules out these two hexes as being marked; if we did so, the column would end up with four blue hexes. So now, erase the two hexes on the right side of the {2}, mark the two on its left, and continue the sequence from there:

And now, the column headed by the "3" has its three blue hexes; erase the two orange hexes still in the middle. We reveal a "3" from this, and it pops up with three blue hexes already bordering it. So clear the two hexes on its right edge. Now, from the -2- just above here, erase the cell directly below the blue one it has claimed. Doing this allows that "2" we just revealed to claim the only remaining active hexes it has. This, in turn, allows us to erase the final orange hex on the bottom-right edge of the -2- and give the "1" on its upper-right edge the only blue hex it can claim:

We can expand the Blue 5 overlay located right below the -2- and -3- we just solved. The overlay covers four blue hexes already; a quick glance tells us that the "3" on the upper-right edge of the hub still needs a blue hex, as well. The overlay covers the "3" and all of its active hexes, so naturally, whichever hex the "3" gets will complete the hub's blue hex requirements. So we'll erase the string of three orange hexes within the overlay that are not attached to the "3".

The "1" that we uncover here will guide our next move. The two orange hexes still attached to that "3" are also shared by the "1". This means that the blue hex we ultimately give the "3" will also go to the "1". So the orange hexes not shared between them now become our next erasures:




The -2- that we just revealed under the "1" is extremely helpful here. It pops up with only three continuous active hexes on its underside, meaning we can solve it in the same manner as any such -2- cell. When we do so, we can fill in a decent chunk of this section:




We opened up two more Blue 3 hubs by solving the -2-; go ahead and expand the one on its bottom-left edge. It already covers two blue hexes, but its placement here means we can actually determine which blue hex to mark next.

The overlay covers both the "2" on its bottom-left edge and the "3" on its bottom-right edge, as well as all of their surrounding hexes! Both the "2" and the "3" need only a single blue hex to complete them, but we can only mark one hex out of all of these. There's only one choice, then: We have to share a blue hex between the "2" and the "3" as it's the only possible one that will satisfy every requirement at once:

We've cracked about 1/3 of Puzzle 5-1 now but still have a long way to go. Here's where we left off:



We'll be able to make several more moves just by examining the relationships on the grid now. Start with an empty "1" cell near a pair of "?" cells at the bottom; I'll mark it in the next image. Give that one the only possible blue hex it can claim, and see if you can get here on your own:




We need to tackle that second Blue 3 overlay now. It looks harder than it is, but that cluster of empty "2" cells immediately to the right of the hub can be confusing. The overlay itself contains two of the three blue hexes it needs. Focus only on the pair of empty "2" cells on the upper- and lower-right edges of the hub; they're the only ones relevant. They each need only one blue hex and have two active hexes to choose from. As only one of these hexes can be marked without giving the hub more blue hexes than it needs, our answer again is to share a hex between them and erase the other orange hexes within the overlay:

We revealed a Blue 5 hub from this. We can now solve a few more empty hexes in the same general area. In the column to the left of this hub are a "2" at the top, and a "1" near the bottom. Each have only obvious blue hexes to claim. At the top, the "2" on the upper-left edge of the first one will gain its second blue hex, as well, letting us erase the last orange hex up there.

Now, we'll actually need the overlay. Expand it now. The overlay covers three of the five blue hexes it needs. Again, the positioning is important; it covers the empty "3" cells above and below the hub, as well as all of their active hexes plus a few more beyond. Neither "3" shares any active hexes with each other, which makes this setup a bit "cleaner," if you will. We know that each "3" will get one blue hex apiece, also giving the hub the two blue hexes it still needs. We thus can erase the orange hexes within the overlay not connected to them:

That {2} we just revealed is in a really bad position here. Like the one from the beginning, it has two pairs of two orange hexes around it, one to the left and the other to the right. It can be more helpful, then, to refer to the "2" right above it. The two orange hexes to its left are shared with one of the empty "3" cells we're trying to solve; since the "3" already has two blue hexes, we know that only one of these can be marked. It also tells us that the hex on the bottom-right edge of the "2" is a guaranteed blue hex; guess what it's shared with?

We have now started making inroads into that ring of cells at the right side with the Blue 9 in the center. We're now able to complete the diagonal governed by a "6" which intersects the ring, as well. The line has been given the six blue hexes it needs; to begin this sequence, erase the two orange hexes at the end of the line.

You can now go ahead and mark the two obvious blue hexes that "2" on the right will claim, but I like to approach the ring in a different manner. Intersecting the top-right edge of the ring is another diagonal, this one governed by a "3". It contains only four active hexes, with one blue and the other three forming the top-right edge of the ring. So we know outright that two of the hub's nine blue hexes will come from this line. The hub already has one; these two will make three.

Outside of this line, there are exactly six additional orange hexes remaining in the ring. It doesn't matter which two in the upper line are marked; there is no valid scenario in which all six of these hexes are not marked. After marking them, complete the "2" on the edge by marking the cell above it. To derive the final hex to mark, realize that the column governed by a "2" within the ring will now have two blue hexes. Erase the hex at the top and mark the ring's final hex. Finally, to complete this side of the puzzle, erase the hex below the "3" positioned under the {2} we solved a few minutes ago, then the last hex of the section; you'll see why when you reveal the empty hex beneath it.

The only way forward now is the diagonal governed by an "8" extending from the left side of the top ring. We've filled in seven of the eight blue hexes it needs, but we can only mark one of the three hexes at the start of the line. In the line above are a "1" and a "2", each of which need a blue hex to complete their individual sets. Like we've seen before in this puzzle, our only choice is to share a hex between them. The line header alone prevents either of the other hexes from being viable without violating one of the rules governing this cluster.

So we mark the center orange hex in this string of three, then erase the other two. At the start of the line, we reveal another "1"; it naturally will share the hex we just marked, which lets us erase two more cells. We can use the {2} that is uncovered to progress further; when we give it a second consecutive blue hex, we also give the "4" that we just revealed the last blue hex it needs, which opens up some additional steps:

I could have carried that out even farther, but we don't want to rush and get too far ahead. From this sequence, the next move is to locate an empty "2" cell with only two possible hexes to mark; it is located below the "1" on the bottom-left of the {2} we solved a minute ago. Mark the two blue hexes it needs, then use that information to carry out the next series:


We need to deal with those new overlays we revealed to go any farther. Go ahead and expand the Blue 3 overlay; it covers one blue and four orange hexes. Helpfully, it encompasses a "3" and all of its active cells; the hub itself gives the "3" its first blue hex, and there are only three orange cells still surrounding it. So we know that two of them have to be marked and that they will also give the hub the two remaining blue hexes it needs. As a result, the lone orange hex inside the overlay not attached to the "3" has to be erased.

It may not seem like the "2" we just uncovered does very much, but it actually gives us our next two blue hexes. See the "2" on the upper-left edge of the one we just revealed? It's now left with only two active hexes; they are the next ones to mark:





Let's again look at the empty "3" cell and the "2" we just uncovered. The "2" just received its first blue hex from the adjacent "2" we just solved. It now has three possibilities for its second blue; however, two of those are shared with the "3". The "3", on the other hand, still needs two blue hexes; it also has three to choose from.

We can immediately see that it's impossible to give the "3" a complete set of blue hexes without marking at least one of the hexes shared between it and the "2". The fact that the "2" already has one blue hex further means only one of them can be marked. This, of course, means that the "3" and the "2" will also end up sharing a blue hex. So now, we can eliminate the hex directly below the "2", and we can mark the hex directly below the "3":

We're nearing the end of Puzzle 5-1. Here's the setup as it stands now:



The "1" that we just uncovered below the "2" sets us up to complete this cluster. Since it gains its blue hex from the "2", we can now erase four more hexes. That allows us to complete several additional moves:





So now, we want to open up the Blue 3 overlay on the far left side of the cluster we just completed. When opened, it covers the "2" below it and all of its active hexes. It also covers two blue hexes along its upper rim. It's easy to see that whichever hex we give to the "2" will also provide the third blue hex the hub needs. So now, we can erase the five orange hexes inside the overlay which are not connected to the "2":

We just uncovered another -2- with only three continuous active hexes around it. Solve it like all of those others, and we can use its shared blue hexes to solve this section, as well:






We now only have the final ring of cells to solve. We have to mark three more blue hexes; of course, they will all fall under the Blue 4 overlay in the center of the ring. The first one will be determined from the diagonal governed by a "6" from the top ring; the line has only six active hexes, with only the final one needing to be marked:


Two more blue hexes to mark. The most helpful hint we get is the fact that there are still two more diagonals to solve from the upper section of the grid. One is governed by a "2", the other by an "8". When highlighted, we can see that each of these lines still needs one blue hex apiece. That means we can erase the two orange hexes not embedded within these lines. The "0" that we reveal at the bottom-left corner tells us how to complete the diagonal governed by the "8":

To complete the puzzle, we need look no further than the column governed by a "2" here. The column only has three total hexes to begin with. The Blue 4 hub itself gives the column one blue hex, and we just erased another one. So the top hex of the column becomes our final blue hex. The final two hexes are now erased to solve this marathon of a puzzle.



Hexes Earned for Completing This Puzzle: 16

Puzzle 5-1 is a bit of a marathon. Strangely, it's harder in the beginning, because you have to stop and think about almost every move. Later on, lengthier sequences open up which allow the solution of long strings of cells. Puzzle 5-2, by contrast, is very small and compact.


It sort of looks like a ghost to me...



The difficulty with this puzzle lies in the fact that there are so many shared hexes. Almost every hex we mark will feed into the blue hex requirements of multiple empty hexes; the fact that several of them require continuous chains of blue hexes raises the difficulty somewhat.

The most obvious moves we can make involve the {3} cells at the top-right and bottom-left edges of the grid. They are each surrounded by a ring of five active hexes. In such a situation, the middle hex is a guaranteed blue hex; if we count out the possible combinations for three continous blue hexes, it will be a part of each. So that gives us two blue hexes to mark.

The hex we mark at the top feeds into an empty "5" cell with six total active hexes around it. At least for right now, we can't determine which hex will be eliminated. The Blue 5 overlay here adds another complexity. Clearly, when we expand it, we're going to mark four of the hexes surrounding the empty "5" cell. But how do we determine where the fifth comes from--or, perhaps more importantly, where it will not come from?

We can also see that it's impossible to give the "5" a complete set of blue hexes without giving at least one hex to the {4} further left. The question is how many blue hexes they will share. The overlay covers both the {3} and the "5", as well as all of their surrounding hexes; only three of the active hexes around the {4} are covered. We also have to ensure that the hexes we mark around the {4} and {3} are consecutive. The trick lies in that we can only mark five total hexes within the overlay; we have to distribute them in a manner that satisfies all of these requirements at once.

If we keep with our cardinal rule to work on the simplest moves first, we want to focus on the {3}; not only does it need fewer blue hexes, it also has only five active hexes around it, compared to six for the {4} and the "5". We have to work through at least one or two possibilities before doing anything. What happens if we mark the hex directly above the {3}? Well, we would have to mark the next hex over to complete the chain of three continuous blue hexes. This doesn't work; we've already established that four blue hexes need to go to the empty "5" cell, but we also can only mark five total hexes within the Blue 5 overlay. This gives us a hex to erase.

The "1" that appears tells us how to solve the {3}, so let's complete its chain and erase the last orange hex on its bottom-left edge. When we do this, we block off the chain of four hexes around the {4} from continuing counterclockwise; this defines an endpoint that lets us complete the {4}, as well:



Go ahead next and mark the center hex in the ring of three active cells surrounding the {2} in the top-left corner; it's guaranteed in either combination of two consecutive blue hexes. This uncovers a Blue 1 hub; expand the overlay. Only one of those three orange hexes covered by it can be marked, and we know it's going to go to the {2}, as well. This lets us erase the hex on the upper-left edge of the "3" below.

The "1" this reveals is important as it defines additional conditions for the "3". The "1" shares two orange hexes with the "3", so we know that only one of them can be marked. As the "3" is now surrounded by only four total active hexes now, this guarantees that the hex directly under it is marked. Do this now:



The second {4} near the center of the grid now has three continuous blue hexes; this lets us define a maximum reach for the chain. The cell directly below it cannot possibly be included now; erase it. That leaves the {2} on the bottom-right edge of the "?" we just uncovered with five total active hexes.

Now, this {2} and the "5" up near the center of the grid play off of each other. We cannot give the "5" a complete set of blue hexes without giving at least one to the {2}. Because of this, we can now define a maximum reach for its pair of blue hexes. Regardless of whether we share one or two blue hexes between the {2} and the "5", the one directly below the "5" is guaranteed to be marked. So now, either the cell on this one's upper-left edge, or the one below it, will give the {2} its second blue hex. This lets us erase two hexes from the {2}:

This leaves the "4" closer to the bottom-left corner with only four total active hexes. One is already marked, so mark the other three next. This gives a second blue hex to the {3} in the corner, again letting us define the maximum reach for this chain of blue hexes. The very bottom-left hex of the grid can now be erased. Unfortunately, this only gets us another "?".

Luckily, we also gave the {4} near the center the fourth blue hex it needs; when we erase the orange hex on its bottom-right edge, we erase one from the "5" and can solve both it and the nearby {2}:





Our next clue comes from that Blue 7 hub. Expand it; the overlay covers the "5" below it and all of its active hexes, plus one additional orange hex and five of the seven blue hexes it needs. The "5" needs two more blue hexes itself; naturally, they will also go towards the hub's blue hex requirements. So we can erase the orange hex not connected to the "5"; when we do so, we can finally give the "5" near the top-right corner the last blue hex it needs:

The "5" and the {2} in the bottom-right section are in much the same position as those we encountered earlier; we can't give the "5" a full set of blue hexes without giving at least one to the {2}. Here again, we can define a maximum reach for its pair of consecutive blue hexes; this means the puzzle's very bottom-right hex has to be erased. Here, we get a "0", letting us clear one more cell up the line.

The {2} is now left with three continuous active hexes; mark the center one as before. This gives the "2" on the bottom-left edge of this new blue hex the second one that it needs, letting us erase three more cells. That will give us enough information to solve the entire bottom half of the puzzle:



We're down to the final three orange hexes; two of them have to be marked. This is fairly easy. Both the {2} and the "1" in this corner need a blue hex apiece. If we were to mark the orange hex shared between them, it would fulfill the blue hex requirements of each, eliminating the other two cells. Since we have to mark two hexes, that won't work. So this hex is eliminated, then we'll mark the final two hexes to complete the puzzle.



Hexes Earned for Completing This Puzzle: 18

We get three reasonably large, disconnected grids in the next puzzle.




This is another of those puzzles that can be very hard just to get started. Except for a hub near the top-center, we're given only a smattering of empty hexes and quite a few line headers. Notice also that all of the empty hexes given to us at the beginning will require chains of continuous blue hexes.

It's tempting to try to start with that big Blue 15 hub near the top-center; technically, we can do so, but I like to start the puzzle a little differently. We can't do anything with the {5} cells; while we can guess with a high degree of probability one or two of the blue hexes they will capture, there's no way yet to know for certain which ones will be erased from their rings. And we certainly can't do much with the {2} and {3} cells yet.

So to start, near the left side of the main grid is a {3} cell in a column governed by a "1". Why is this important? Well, it's because there is no possible way to give this {3} a chain of three continuous blue hexes without one from this column. Try it; you simply can't do it. So while we don't know which cells to mark, we can determine which cells to erase from this column. So for our opening move, erase all cells within this column except for those tied to the {3}. In doing so, a "0" will let us eliminate five more hexes, leaving only the top hex of this column to be marked:

Great. Now what? Even finishing that whole column doesn't help us all that much because there is so much uncertainty as to which way the {3} cell's chain of blue hexes will extend, or which lone hex all of those empty "1" and "2" cells will capture. So now, we're going to see what we can do with the Blue 15.

Start with the very top-center hex. It marks the beginning of two criss-crossing diagonals, one governed by a "3" and one governed by a "4". However, each diagonal is sub-divided and contains an embedded line; the divisions dictate that only one hex per diagonal can come from the top cluster covered by the Blue 15 overlay. Process of elimination: What happens if we mark that top-center hex? Well, we would have to erase the four remaining hexes--two per diagonal--from those particular lines. This would allow the hub only 14 blue hexes. Our next step, then, should be to erase this cell.

That gives us a "3", and it only has three active hexes around it. So first, mark all of those. Secondly, erase the two remaining hexes from each diagonal. Finally, fill in all of the overlay's remaining hexes.

We've just given our {3} a second blue hex. We don't know what the third will be, but now, we can at least determine that the hex on its bottom-left edge can't possibly complete the chain. Erase this cell; it will leave the "1" directly above our "0" with only an obvious blue hex to claim, completing our chain for the {3}. We'll erase a few more cells from this relationship:



The "2" that we revealed at the top of the second column of the main grid has only one obvious second blue hex to claim; after marking it, we can complete most of the first two columns by just using the existing relationships. For the Blue 2 hub, expanding it will then show that it has two blue hexes within its radius, letting us erase two orange hexes from the first grid. Upon doing this, we'll be able to complete the {5} near that corner:

Let's finish the first column of the center grid now; it's governed by a "2" and has its two blue hexes. Erase the bottom hexes from the column. We can use the pair of empty "1" cells to solve the next column, which is also governed by a "2" but has only three active hexes remaining. They border the empty "1" cells, and since we have to mark two, sharing a hex between each "1" is impossible. So mark the first and third orange hexes, then erase the middle one.

Move now to the "1" at the bottom of the next column; carefully observe the relationships between the marked and empty hexes to make this series of steps:






We've solved a big chunk of the first grid, too; let's see if we can finish it. The top diagonal is our embedded line; it's governed by a "3" and has two blue hexes. The next line down actually contains a second {5} at the far end; clearly, we cannot give it five blue hexes without marking one within the embedded line. Since only one of those two can be marked, the other four surrounding the {5} are guaranteed blue hexes; similarly, we can also erase the cells within the embedded line that are not connected to the {5}. The "3" that we uncover shows us how to complete both the {5} and the embedded line.

Now, two of the blue hexes rimming the underside of the {5} fall into a diagonal governed by an "8", which now has its eight blue hexes. Erase the last hex in the line, then complete the "6" that appears.

We've just given two blue hexes to the {3} near the bottom of the grid. From this, we can eliminate the two hexes which cannot complete its chain of three consecutive blue hexes. We can then complete the grid except for one cell by using that "2" which appears; to solve that final orange hex, notice that it falls into a diagonal governed by a "4" which already contains four blue hexes. Erase the line's remaining cells.

We're back to the central grid, and there are a couple of places we can go. Let's start in the middle and see if we can progress towards the right edge. When we erased that last line, we uncovered a "3" with only three active hexes around it; it's in the center column about 3/4 of the way down. Fill in those three hexes. See how they're shared? Use that to get to this point:


So how do we solve those -2- cells? Refer to the diagonal governed by a "5" extending from the first grid through those bottom hexes. Two of those three orange hexes have to be marked; two of them border the left-most -2- and are the only ones left for it to claim a second blue hex. Since one of them will also make the line's fourth blue hex, the bottom-center hex is now a guaranteed blue hex. That gives the regular "2" we revealed a minute ago its second blue; this lets us solve the cluster:

We don't really have any additional guidance for the center of the grid now. We need to shift focus to the {2} near its top-right corner. You may already have seen this, but the {2} gets its first blue hex from the Blue 8 hub. We can immediately determine which three hexes to erase from the {2}, since only two hexes can possibly be connected to the Blue 8. But we'll need the overlay itself to make our next move.

When expanded, the overlay covers seven blue hexes already; it also covers the {2} and all of its surrounding hexes, so clearly, whichever hex we mark for the {2} will also give the hub its eighth blue hex. So the two orange hexes within the overlay not connected to the {2} are now erased.




The "2" we just revealed at the bottom-left corner of the highlight already owns two blue hexes, so we can clear its two orange ones. That leaves the {2} with only an obvious second blue hex to mark. We'll be able to use the existing relationships to solve the rest of this corner:

At roughly 2/3 of the way through this puzzle, here's where we left off:



We can finally make some inroads into the third grid now. We just completed the diagonal governed by a "5" from the upper-left edge of the central grid. As it contains the five blue hexes it needs, we can erase five more from the third grid.

This gives us an exceptionally interesting setup. The top diagonal of the third grid is our second embedded line, which needs two blue hexes. In the next line down are two {2} cells, from which we have just erased two orange hexes apiece. The arcs of their remaining orange hexes give them two orange hexes apiece in the embedded line, and two apiece within their own respective line.

It is 100% impossible to give the {2} cells a continuous pair of blue hexes without marking one hex apiece in the embedded line. So we can erase all hexes within this line which are not connected to either {2}:





I'm sure you'll never guess what our next move is, right?








We have a couple of empty "1" cells at the edges of this grid from which we can erase one orange hex apiece now. This almost gives us enough information to solve the {5}...

Go ahead and expand the Blue 4 overlay that we just revealed on the upper-left edge of the {5}. When we expand it, it will cover the {5} and all of its surrounding hexes. Remember: The hub itself gives the {5} one blue hex; we have already marked three more. This leaves both the hub and the {5} itself needing a final blue hex. The blue hex we use to complete the {5} will complete the blue hex requirements of both. So next, erase all orange hexes within the overlay not connected with the {5}:

This leaves the bottom diagonal governed by a "5" with only five active hexes; marking its last one gives the {5} its fifth blue hex, and we can then erase the final hex from this grid.

Now, expand the Blue 3 overlay near the top-left of this grid; it covers only three active hexes, so we just need to mark the third one. This also becomes the third blue hex for the "3" on the hub's upper-left edge; now, clear the hex directly below the "3".




We are now left with only one final cluster of orange hexes, of which only six will be marked. Let's start with the "2" we just now revealed; it shares its two blue hexes with the "3" above it, so clear the two orange hexes still bordering it. Let's now complete the last column of the grid; it has two blue hexes, so we need to erase its final hex at the bottom.

We are now faced with a scenario in the last two columns of the grid with a similar-but-different situation to the first two columns. Remember earlier, when we had three orange hexes beside of two empty "1" cells? We needed to mark two of the orange hexes; well, here, we can only mark one. So this time, the shared hex is the one we mark:


The hex we just marked falls into another diagonal governed by a "5" and becomes that line's fifth blue hex. When we erase the line's final orange hex, we leave the "2" on that cell's bottom-right edge with only one obvious choice for its second blue hex; see if you can get here using that information:



There are a couple of ways to approach these final hexes, but the most straightforward way is to begin with those final two diagonals from the upper-left section of the puzzle. The line governed by a "4" has been reduced to four active hexes and needs its final blue hex to be marked; the one governed by a "2" has two blue hexes and needs its remaining three orange hexes erased:


The final hex we mark comes from the diagonal governed by a "3" extending from the upper-right; reduced to only three active hexes, we just need to mark the final one and then erase the two remaining cells to complete the puzzle.



Overall, the hardest part of this puzzle is getting it started. It takes a little additional analysis of the cells on the grid compared to the line headers to really get it going. The bulk of the solution afterward is reasonably straightforward, with a couple of more complicated situations towards the end. There's very little work with Grid Overlays in this one, barring the Blue 15 at the very beginning. We do need to use them towards the end, but the logic involved is reasonably simple.

The puzzles will get substantially harder going forward. We are now down to the final nine puzzles of Hexcells Infinite. You won't believe what kind of behemoth awaits us at the end of the game...

Hexes Earned for Completing This Puzzle: 20

Yikes...




Orange, blue, orange, blue, orange, blue, orange, blue, orange.

This puzzle looks like it should be so simple, yet it's one of the most challenging in the game. I remember it giving me fits during my initial playthrough. It does unravel more towards the end, but meshing all of the overlays with the line restrictions is an incredibly difficult task.

One important note for this puzzle: I'm defining columns as only the ones with orange hexes to solve. Since technically, every other column in this puzzle contains only hubs to expand and contract, I feel this is a more prudent way of approaching the concept.

Getting started is by itself a relative nightmare. We have no empty hexes to guide us; the only information we get are line headers and overlays. In my practice run, I focused on the final column, which is governed by a "6". All of the actual columns have seven total hexes apiece; since all but one of the hexes in the final column are going to be marked, this should be the simplest place to start with, right?

Well, in running through the puzzle again for this guide, I found that this is not the case. Strangely, the Blue 7 hub between the third and fourth columns is where we need to start. First, expand it, then take note of the headers of the columns it envelops. The third column is governed by a "5"; the fourth, by a "2". The overlay covers two blue hexes--namely, the hubs above and below this one. So we need five of its six orange hexes to be marked. It's impossible to come up with that without marking three in one column, and two in the other. Clearly, the column headed by the "2" is not going to get three blue hexes. Not only does it tell us to mark the three hexes within the overlay in the third column, it tells us to erase all hexes in the fourth column resting outside the overlay:

Let's see what that does for us. If we check the overlays which influence these last three columns of the puzzle, we actually find that the Blue 5 overlay in between the last two now covers only five active hexes. So we can mark the four orange hexes still within its radius.




Now, expand the Blue 6 hub right below the Blue 5 we just solved. We can glean a little more information for it now. We know that we still need a blue hex in the fourth column to give the line its second one, which will also give the Blue 6 its fifth blue. The hub's sixth one will then come from one of the two orange hexes the overlay covers within the final column, which is headed by a "6". We've marked three hexes in the column already; whichever one we mark to solve the hub will make the fourth. So now, we need the column's bottom two hexes to come up with a count of six blue hexes for it:

We'll need to come back here in a little bit; there isn't quite enough information to solve those two columns yet. Let's go back to the third and fourth columns and the hubs between them. We need to use the Blue 4 hubs at the top and bottom to continue. The one at the top now covers three blue hexes; the only orange hexes it covers are in the third column, dictating that one of the top two will become the fourth blue hex for the column.

What that does, then, is tell us that one of the bottom two hexes of the column has to be marked, as well. This is where the bottom Blue 4 comes in; it covers those two orange hexes, but this one only covers two blue hexes. Its only other choice for a blue hex comes from the single cell it covers in the next column--which is now a guaranteed blue hex. When we mark it, we give that column its final blue hex and can erase the last one in the middle:

With this, we just gave the Blue 4 overlay between the final two columns the fourth blue hex it needs. That tells us which hex to erase in the final column, and we then color the one that's left:






This is where it really gets hard. We have to simultaneously use all three overlays between the second and third columns to progress.

The second column is governed by a "3". If we consider that the Blue 4 hubs at the top and bottom each have to get a blue hex from the third column, we can immediately establish that we will get one blue hex from the top three cells of the second column; one from the middle three; and one from the bottom three. Now, we have to reconcile the two hexes within this column which are shared between two overlays apiece.

The easiest way to tackle them is to plot out what would happen if we were to mark one of them. If we marked the third hex down the column--which is shared by the top Blue 4 overlay and the Blue 6 overlay in the middle--we would actually have to erase the two hexes above this one, and the two hexes below it. This would wipe out half of the column; because of the restrictions imposed by the Blue 4 hub at the bottom and by the third column, it would be impossible to give the column three blue hexes and satisfy the other criteria. We can apply the exact same logic in reverse if we were to mark the third hex from the bottom. As a result, the two orange hexes shared by the overlays here have to be erased:

And now, we have honest-to-goodness empty hexes to work with!! That "2" is easily solved; mark both of its obvious blue hexes. This whole column is solved just by dealing with that "1" and "2" we just uncovered, and then by remembering what we learned in the previous step:




We're just about at the point where the puzzle opens up. Our last sequence gave us a blue hex for the diagonal governed by a "1" extending from the left edge. When we erase the two orange hexes remaining in the line, we can immediately mark the bottom hex of the central column, since it will be the only one left for those nearby Blue 4 hubs to claim.

After marking this cell, go ahead and expand the Blue 4 between the first and second columns at the top; it now covers only four active hexes, so we can mark the two it still needs:






We'll use the remaining hubs between the first and second columns to complete the first column, governed by a "5". Expand the Blue 5 in the middle first; it covers four blue hexes and two orange hexes in the first column; so whichever one we mark here to complete the hub will give the first column its third blue hex. To make the fourth and fifth, we now need to mark the column's bottom two hexes. Now, expand the Blue 4 at the bottom; we just gave it a complete set of blue hexes. When we erase the final orange hex in its radius, we can then mark the first column's final hex:

The final blue hex is determined by the diagonal governed by a "3" off of the center column; the line has been reduced to three active hexes. Mark the first hex of the line, then erase the final hex to complete this confusing puzzle.



This puzzle demonstrates possibly the most challenging use of Grid Overlays we have seen in the entire series. But the hardest puzzles are yet to come...

Hexes Earned for Completing This Puzzle: 20

We've now unlocked Chapter 6. With that, only eight puzzles remain in all of Hexcells.




Wait, what? That's it?

This puzzle consists of only 18 total hexes, arranged in a hex-shaped, 5 x 5 grid, which is the exact size of a single Grid Overlay.

As far as information: We get five hubs and a "?". That's it. Also, we're only marking five total blue hexes for this puzzle.

The trick, then, is in checking the overlays to try and eliminate some of the orange hexes. To begin, we need to work with the Blue 7 at the bottom-center; expanding it shows that it covers all but the top three hexes, including two of the other hubs. Guess what? Those three hexes not covered by the overlay can immediately be eliminated! Since this hub needs five additional blue hexes, it's also going to claim all of the blue hexes for the puzzle!

What's most vexing is that we only get another trio of "?" cells from this. So now, we have to start examining the remaining overlays.

Each of the Blue 3 overlays covers one blue and four total orange hexes; they share the hex directly below the top-center "?". Each Blue 7 overlay at the upper-left and upper-right covers everything but four hexes along the outer edge; when both are expanded, they share three of the orange hexes. Maybe they're trying to tell us something?

Just to give you an idea of how confusing this puzzle can be, this is actually my second write-up of the solution. The solution I scrapped took me long enough to figure out and used some pretty complicated analysis that I have only just now figured out doesn't need to be conducted. I'm confident that this is the solution as intended by the developer.

Notice that both sides of the puzzle are mirror images of each other; as such, the logic that applies to the left half also applies to the right half. In other words, the puzzle is completely symmetrical.

In keeping with determining the simplest move possible, let's start with one of the Blue 3 overlays; each covers the fewest number of total hexes and requires the fewest number of blue hexes. We'll work the left side first for this walkthrough, but if you would rather work the right side first, that's fine. You'll simply see a horizontally flipped version of the screenshots compared to what you'll have within your own playthrough.

The Blue 7 hub on the bottom-right edge of the Blue 3 contributes its first necessary blue hex. Of the orange hexes the overlay covers, we only need to mark two more. This is important; make a note of the hexes this overlay covers.

Now, expand the Blue 7 overlay. It covers the same hexes that the Blue 3 overlay covers; it also covers three of the other hubs, plus two additional orange hexes. (You can expand both overlays at once, or you can retract the Blue 3 first; expanding both can be harder to work with, but it makes it easier to see which hexes the overlays share.) We know that only two of the hexes shared with the Blue 3 overlay will be marked. That will give the Blue 7 overlay five; the two extra orange hexes that this overlay covers are now guaranteed blue hexes:

We are now going to repeat this exact same step using the Blue 3 / Blue 7 couplet on the right side; the only difference is that we have an extra blue hex from the previous sequence:






This leaves us with only one final blue hex to mark, and five total orange hexes. Every single overlay still needs one blue hex to complete them. At this point, the final solution is pretty simple: We have to mark the hex at the top-center, which is the only one that is covered by all five overlays. All of the other hexes will be erased to complete the puzzle.



Only one puzzle to go before we reach the final chapter of Hexcells Infinite!

Hexes Earned for Completing This Puzzle: 22

We've arrived at the final puzzle of Chapter 5, which means there are only seven to go before we complete the game!


Wait, is this the central grid from Puzzle 6-4 of the original Hexcells??



I found some definite similarities in the layout of this grid compared to its predecessor, but it's definitely different, and the additional overlays certainly make it its own puzzle. Our only information is a series of hubs in indentations around the perimeter of the grid, and a number of line headers. We're again given no empty hexes to start us.

Getting the puzzle started is a bit tricky, but it's not exceptionally difficult. It does, however, take careful observance of the overlays and the column headers. Where we end up starting is with the Blue 5 hub at the top-left. When we expand it, it covers seven total active hexes. Three of those fall into a column governed by a "1". Subtracting those out tells us that the other four have to be marked. It also means that we cannot mark a fifth blue hex for the overlay without including one from this column. And since only one hex from this column can be marked, our opening move is to: 1) Mark the four hexes within the overlay not included within the column; and 2) To erase all of the hexes within the column that are not covered by the overlay. For good measure, I've also cleared that "0" revealed towards the bottom:

The trick with the {2} near the top of that line of erasures is that we don't know which second hex it will claim. However, we are able to eliminate the two hexes on its right edge since they fall outside the pair's maximum reach.

Below the {2}, we also have an interesting dichotomy with the "1", the -2-, and the second {2} all dictating terms to each other. Since the lower {2} has two active cells on either side of it, it's going to provide one blue hex to the -2- on either its bottom-left or bottom-right edge. Since we can't mark both of its bottom hexes, that automatically means one of its upper hexes will be marked. And that blue hex will be shared with the "1", so the "1" cannot possibly claim the other hex on its upper rim. And when we clear the one from its top-left edge, we leave the upper {2} with only one left to claim:

The hex we just marked gave the column its sole blue hex, so now, we can erase the two on top. We do uncover another "0" from this, which gets rid of a couple of cells in the next column. It also allows us to make a few moves using the existing relationships on the grid. From the {2} near the top, notice that the "1" on its top-right edge, as well as the regular "2" on its bottom-left edge, have their required blue hexes; see if you can continue from there:

There isn't much more we can do with this particular sequence, but we are going to finish up the relationships we've established; this time, focus more on the -2- at the top of the fifth column and the "1" on its bottom-right edge:





We're left with a problem here. There are numerous empty hexes to complete, but they all have multiple possibilities we could mark. We don't yet have enough guidance to make any guaranteed marks or erasures.

We need to use the Blue 5 hub we uncovered towards the left side of the puzzle to guide us next. When we expand the overlay, it covers three blue hexes already. It also covers the "4" above it, the "2" below it, and all of their surrounding hexes. Both the "4" and the "2" need one blue hex to obtain complete sets; since they do not share any orange hexes, we know that one will be marked for each, also giving the hub its final two blue hexes. As a result, we can erase all hexes within the overlay not connected to the "2" or the "4".

We're interested now in the first three columns, as well as the Blue 3 hub just sort of floating there. The requirements of the -2- cell we just uncovered dictate that it will claim one of its blue hexes from the first column, which is headed by a "2". That Blue 3 hub contributes one blue hex to the column already. As such, we can erase the hexes within it not tied to the -2-; we actually get two zeroes to clear out of this step.

This brings us to one of the toughest brain teasers in this puzzle. How on Earth do we fill in that third column? We need to start with the opposing empty "2" cells: The one in the middle of the second column, and the one directly across to its right, below the Blue 5 hub. They share two orange hexes between them; since the Blue 5 gives a blue hex to the one on the right, we know that the "2" on the left is only getting one blue hex from the pair between them. Therefore, the hex on the upper-left edge of the "2" in the second column is now a guaranteed blue. Since it becomes the second blue hex for the first column, its final hex can now be erased:

At the very least, we've left the "1" at the top of the first column with only one obvious hex to claim; mark this one now, giving a shared blue hex to the adjacent "2".

This is all the information we get to try to solve the third column, which is governed by a "5" and has one blue hex already. Somehow, we have to figure out which four additional cells to mark to come up with five, while honoring the restrictions of the empty cells in the surrounding columns and the two overlays we're trying to solve.

If we analyze the empty hexes, we can come up with four whose pairs of orange hexes will each give us one of the column's remaining blue hexes:

• The "4" near the top of the fourth column;
  
• The "2" directly below the Blue 5 hub;
  
• The "1" right below the gap within the second column;
  
• The "2" at the bottom of the second column.

That allows us to erase the center hex of the column, directly to the right of the Blue 3 hub:



We'll get two of the third column's blue hexes from the Blue 3 overlay now; we've left it with only three total active hexes. So now, just mark the other two. This gives us enough information to solve the column by just using the relationships these new blue hexes establish:

This is one of the hardest puzzles we've faced so far. Here's where we left off:



We're given another brain teaser as to how to proceed. We've done about everything in the center that we can until we get more information, and even in the section we just completed, there isn't much to help us. It's tempting to guess here, but there is one remaining move.

Expand the Blue 5 overlay at the bottom of the third column. It covers two blue hexes; the four orange hexes adjacent to the empty "3" cells above and below the hub; and three additional orange hexes. Those three hexes fall into a column governed by a "3". This column now contains only five total active hexes; we've marked one near the top, and there's one additional orange hex not covered by the overlay.

We can tell that both the "3" above and below the hub will each need a separate blue hex, because they don't share any of their remaining orange hexes. These will give the hub its third and fourth blue hexes. So the fifth has to come from the trio located in the next column over, which is headed by a "3"; however, we can only mark one, which will become the second blue hex for that column. The column's third blue hex will come from the one orange hex not covered by the overlay:

The cell we just marked goes to the "1" on its bottom-right edge, so we can erase the next hex down the column. Another "3"?

We get a similar setup to that of the opposing empty "2" cells up near the top from earlier. The "3" we just uncovered has three orange hexes from which to claim its other two, but two of those are shared with the "3" across to the left. That "3", of course, has two blue hexes already, so only one of those shared hexes can be marked. This means the next cell down from the "3" we just uncovered has to be marked, and it will be the third for the column. Erase the bottom hex from the column. And would you believe that we get yet another "3" from this??

We actually do establish enough new relationships from the last hexes we solved to fill in this section a little more. But for right now, there is absolutely nothing we can do to complete that fourth column. There's a diagonal governed by a "7" from the right side of the grid that passes through here, however; maybe we can complete this column when we solve the diagonal?


So now, we can focus on the other column headed by a "3" on this side, closer to the center. Expand the Blue 4 overlay about halfway down this section. First of all, the overlay already contains one blue hex; secondly, the hub itself is the sole blue hex needed by the "1" above it, so erase the orange hex from the "1". (You may have already done this earlier; if so, you're ahead!)

This erasure gives us a "2", which doesn't immediately seem helpful. However, consider that the Blue 4 hub contributes a blue hex to it. Secondly, notice that all of its other orange hexes are covered by the overlay; naturally, only one of those can be marked. Finally, notice that only two additional orange hexes are covered. Since we've just determined that only one of the hexes around the "2" can be marked, these other two are now guaranteed to be marked:

We don't quite have enough information to solve the column, but we're close. The column now has two blue hexes; we can easily see that its third will come from whichever hex we mark for a "1" near the top of the next column to the left. So now, erase the hexes within the column not connected to that "1":



Okay: Clear that "0"! Doing so opens a chain of additional moves we can make by following the established relationships:







We can continue our series into the Blue 4 overlay now. Start with the "1" positioned on the upper-right edge of the overlay, then mark the hex on its bottom-right edge; it's the only one left for it to claim. Clear the hex below the one we just marked since the "2" and "3" below the "1" now have their required blue hexes.

We've solved the upper Blue 4 overlay; now, we need the other one. It's pretty straightforward, however. It covers only two blue and three orange hexes. The orange hexes coincide with a "2" and a "3", each of which needs one blue hex for a complete set. Since we have to mark two here, do not mark the shared hex; mark the other two in that trio, then erase the center one:


We're getting ready to cut the rest of the puzzle in half, but first, one more move from near the bottom-center. At the top-left corner of the gap is a "2" with its two blue hexes. Clear the two on its right; in doing so, that Blue 3 hub on the left side of the gap is solved. The empty "1" cells uncovered each have their required blue hexes, as well, clearing three more from the section.

Now, we have a diagonal governed by a "3" extending from the top-left edge of the grid; it now contains three blue hexes. Erase everything else in that line:






About halfway up the same column as the "2" we just solved is a "3" with only one possible hex to claim for a third blue one. When we mark it, we also mark the third required blue hex for its respective column, as well as giving another "3" and another "2" their final blue hex. So when we clean them up, we're going to have this:



Solving the Blue 4 overlay we just uncovered is simple; it already covers four blue hexes. So just erase the two orange ones within its radius. We then leave the "1" at the very right-center tip of the highlight with only one blue hex to claim; mark it next:




The hex we just marked is also shared with the "1" on its top-left edge, so we can clear the two orange hexes still bordering it. It doesn't really do much, though; we only unveil a pair of "?" cells.

We need to work from the "2" below the hex we just marked. Naturally, that blue hex is the first one that this "2" needs. Notice, though, that both of its remaining orange hexes are also shared by the "1" on its bottom-right edge. So obviously, whichever hex we give the "2" will also go to that "1". That allows us to erase the orange hexes on the upper-right and bottom edges of the "1".

When we do this, we uncover a -3- with only four consecutive active hexes around it. Mark the endpoints as usual:







Let's clean up this cluster. The hexes we just marked are shared with several empty cells around the section. See if you can come up with this sequence next:






We can try to solve the Blue 5 on the upper-left edge of the -3- now. When we expand it, the overlay covers two blue hexes and four orange hexes. The tell-tale sign of how to solve it comes from the shared orange hex between the -3- and the "2" two columns to the left. We have to mark three hexes inside of the overlay, but if we mark the shared one, this becomes impossible since it would result in two additional erasures. So erase this cell, then mark the others inside the overlay:

At about 2/3 of the way through this monster of a solution, here's where we're at:



We can now solve the second Blue 3 overlay at the bottom-center; when we expand it, it covers three blue hexes, allowing us to erase the three orange hexes still in its radius. This gives us another "0" to clear; we can also mark the obvious blue hex the "1" below the "0" will then claim. This blue hex is shared with the "1" on the bottom-right edge of the "0", so we can clear the two remaining cells from this "1".

Now, move back up to the -3- we solved a minute ago. Start from the "1" on its upper-right edge, then move one space up to the next "1" up the column. This particular "1" has only one obvious blue hex to claim, as well. Mark it; it will be shared with two more empty "1" cells here. We can erase two more hexes from that; one of them becomes a "4" with only four total active cells surrounding it:


The hexes we mark for that empty "4" we just uncovered will fill in a few more blanks here. Primarily, they will let us work our way up the grid towards the top-center and top-right sections. You can execute this sequence just with the relationships on the grid, without overlays or line headers:



We're finally going to solve those four lone orange hexes on the left side!!!!! The diagonal governed by a "7" which passes through that section has now been reduced to exactly seven active hexes; mark the last one at the end, which happens to be the top orange hex in that chain. This completes the adjacent empty "3" cells, so erase the next orange hex they share. Let the "4" that appears guide the solution:

We want to solve next the Blue 4 overlay marking the start of that diagonal. The next cell down that line is an empty "2" cell which already has two blue hexes; erase the two orange hexes from around it, then expand the overlay. With these cells gone, the overlay now covers only four active hexes; mark the final two within its radius.

The hex we just marked in the upper-left corner of the overlay begins a column governed by a "3". The line now contains only three active hexes; now, mark its last hex near the bottom.






The next column to the right is also governed by a "3". This is a setup we've seen before. The line contains two blue hexes; at the bottom of the line, several of its remaining orange hexes are adjacent to a pair of empty "2" cells which each need a second blue hex. As we have seen, the orange hexes in this column are the only ones from which each "2" can claim a second blue hex. So as before, we will mark the shared hex; in this case, we'll also erase the rest of the column. While we're down here, erase the orange hex from above the "1" located on the upper-right edge of that "0" further left.

We've established some new relationships extending towards the bottom-right corner now. We'll ultimately be able to complete this section; can you follow these next couple of screens to do so? Use only the relationships on the grid; there are no special tricks or puzzles here:





Now, continue up the right edge, then back towards the left:








To complete the top-right edge of the puzzle, we need to utilize the Blue 4 hub we revealed awhile back. When we expand the overlay, it covers three blue hexes right away; it also covers the "2" on its upper-right edge and all of its surrounding hexes. The hub itself, of course, gives the "2" its first blue hex; we know that whichever hex we mark for its second will give the overlay its final blue hex, as well. So we can start by erasing the two orange hexes within its radius not connected to the "2":

This gets tricky. Two of the hexes covered by the overlay fall into a column headed by a "3", whose remaining orange hexes border a pair of empty "2" cells, including the one we're trying to solve. So we can do what we did before, right? Well, not so fast; the "2" we're trying to solve still has an orange hex under it. It's possible to mark that one, erase the other two within the overlay, and mark the final hex of the column to satisfy all of the requirements here.

So instead, we're going to deal with the upper "2". As its only two remaining orange hexes fall into the column headed by the "3", one of them is a guaranteed blue. So the bottom hex within this chain of three orange cells is going to be erased next.

What now? We have to analyze the additional "2" that we just opened. One thing that helps us is that the orange hexes on top of it and on its bottom-left edge fall inside our overlay, so we know one of them is going to be marked. The other two on its right fall into a column headed by a "2", which already has a blue hex. We know that one of these hexes also has to be marked. So now, erase the top two hexes of that column, since they aren't connected to the "2":

The -2- we just uncovered at the top-right is a gift. Its blue hex is in a pair of active hexes to its left, with only one additional active hex to the right. Erase the orange hex below its blue one, then mark the one on the right. The hex we erased uncovers a "3" with just one obvious blue hex to claim for its third, which also finishes off the column. It also provides our overlay with a fourth blue hex; erase the last orange one within it. That leaves the "1" on the bottom-right of the overlay with only one active hex to claim, which will also be fed to the "2" above the "1". It's possible to solve these last three orange hexes without using that Blue 3 overlay or the column headers; can you see how?

Only one final cluster remains. Go ahead and expand the Blue 3 overlay; it covers a blue hex and five orange hexes. The clue here is that two of those orange hexes fall into a column governed by a "3"; they are also the only remaining orange hexes within the column. Since the column only has one blue hex so far, we know that two of these three have to be marked. That eliminates the other two hexes inside the overlay.

We get another pair of empty "2" cells, but this is straightforward. As the orange hexes in question are the only ones from which they can claim a second blue hex, and we have to mark two of them, erase the shared hex between them. Then, mark the other two:

We've finally arrived at the end of this puzzle; here's the last section we completed:



Helpfully, the "2" we just revealed gets its two blue hexes from those we just marked; clear the two on its left. Another pair of empty "2" cells...

This is the final big brain teaser of the puzzle. We have four blue hexes to mark. Let's number the remaining columns from left to right, 1-3. The orange hexes in the first column need to solve both a "2" and a "1" in the next column to the left; they do not share any orange hexes. Thus, this column will get two blue hexes. The other two columns will each get one hex simply due to their column restrictions and the fact that they have all but one of the blue hexes they need.

The trick is that with respect to the second and third columns we can only solve one empty "2" cell per blue hex. We also are forced to solve one "2" per blue hex; if we mark the shared hex between them, then we would be forced to erase all other hexes in each column. This gives us two critical eliminations: The hex shared between each empty "2" cell, and the orange hex at the bottom of the cluster not connected to anything that we need to solve:

We have to bring that Blue 2 overlay in now. Expand it; it covers a blue hex and the three orange hexes along that upper diagonal. Clearly, only one of these can be marked; the trick is in isolating at least one that is impossible to mark. There's no real way to do this but to run the possibilities mentally, and predict what will happen:



We have our dud; erase the orange hex inside the overlay directly below the hub. That "3" is a welcome sight as it only has three active hexes. Mark the two it still needs, and that's going to set up the final solution to the puzzle:





And now, the final three hexes. The "3" right in the center of that cluster has only three total active hexes around it; mark the two that it still needs, then erase the final hex to solve this monster of a puzzle and complete Chapter 5.



This puzzle is a BEAR, certainly the hardest one that Hexcells Infinite has given us so far. The way that the empty hexes are scattered such that they don't give us all the information we need forces us to use not only line headers, but also, as we saw, overlays to fill in the missing pieces. The way that they combine, and the way that they force us to redirect our focus, is what makes it so challenging.

Think of this one as a prelude to the absolute hardest puzzle that we will encounter. Spoiler Alert: As we saw in the previous games, the next-to-last puzzle is the pinnacle. So in only four more puzzles, we will reach the absolute hardest puzzle in all of Hexcells.

Hexes Earned for Completing This Puzzle: 24

If you've managed to complete everything to this point without making a mistake, give yourself a round of applause, especially after making it through Puzzle 5-6. Welcome to Chapter 6, the final chapter of Hexcells Infinite and all of Hexcells. Some of these puzzles, especially 5-6, have been extremely lengthy and intricate. Thank you all for joining me in unraveling the final challenges of the Hexcells universe.




From a size perspective, this puzzle is enormous. We're given three very small grids along the top of the board, then one very large grid, with several sections joined by only a single hex. As far as information, we're given one blue hex, a -2- cell, and a slew of line headers.

In a twist from previous puzzles, this one isn't as hard to start as it is to keep going. After the first few sequences, we get a couple of mind-benders.

At the very least, we're given an obvious place to start: Right in the center. We're given a free blue hex for that -2-, so we can immediately erase the hexes on either side of the blue one. From there, we get a pair of empty "1" cells to share the blue hex, letting us clear six more hexes. From this, we'll leave only the hex under the -2- for it to claim, so mark that one next. Then, clear out the "0" just over to the right.

The "0" ends up with nothing but a ring of empty "1" cells. The "1" on its upper-right edge has only an obvious blue hex to claim; the one on the upper-left edge shares the freebie we were given above the -2-. So using this, see if you can complete the opening sequence:




With all of that completed, it can be easy to overlook the fact that we can complete the center column, which is headed by a "4". We've filled in four blue hexes for it now; go ahead and erase those which remain. After doing so, go ahead and mark the third hex that the "3" unveiled at the bottom of the central cluster needs.

Here's where everything starts getting trickier. First, expand the Blue 4 overlay positioned directly below the -2-. It covers three blue hexes already; we can easily see that the fourth will be whichever hex we mark to give the "2" on the hub's upper-left edge its second blue hex. So erase the two within the overlay not connected to that "2".

One of those eliminations reveals another "2" which pops up by the two blue hexes it needs. When we erase its two orange hexes, we leave just one left for the "2" inside the overlay to claim. So mark that one to complete the "2" and the hub. Then, erase the hex on the upper-left edge of the "1" positioned directly below the hex we just marked.


We can now examine the Blue 4 hub we just revealed to the left of the one we just solved. Expanding this one shows that it covers five active hexes, including a blue one. Its second will come from whichever blue hex is given to the "2" on its bottom-left edge. That accounts for two of the four orange hexes; the other two now have to be marked.

Now, retract the overlay, then expand the new Blue 4 overlay we just revealed from the last step. We have to use similar logic, but this time, we apply it to two empty "2" cells. The overlay covers the same hexes we're already trying to work but also covers the "2" on the hub's upper-right edge and its surrounding hexes. These empty "2" cells account for two of its blue hexes; the overlay already covers the other two it needs. So the one lone orange hex not connected to the empty "2" cells contained within this overlay has to be erased. The "2" that opens up from this gives us a few more moves:

We're left with the center section basically solved except for two final cells. Unfortunately, there's nothing we can do with them for right now; we'll have to come back to them. And the only other empty hexes we have to work with are those from the center column. We'll have to tackle them next; there just isn't enough information anywhere else.

At the top, we have a "3" and a -2-; at the bottom are a -2- and a "2". Their active hexes are all spread across the columns to their left and right, which respectively are headed by a "6" and a "7". One thing that helps is that each column needs exactly four blue hexes to complete them.

The specific pairings we are given at the top and bottom automatically dictate that each column will get two blue hexes from the top, and two from the bottom. The other problem we have to resolve is whether or not the "3" and -2- will share more than one blue hex; clearly, the -2- will get at least one blue hex from the "3".

It's actually easiest to start with the bottom grouping; in fact, we have to. For right now, trust me on this and follow along; I will explain the reasons later. It actually gets pretty interesting.

For now, though, we're focusing on the -2- / "2" pair at the bottom of the central column. The position of the -2-, situated between two pairs of orange hexes, dictates that it will claim a hex both to its left and to its right. But what about the regular "2"? The question is essentially whether or not the "2" and -2- will share any blue hexes between them.

We can run through a couple of combinations to see if they are viable. In theory, it should reasonably be possible to mark hexes along a diagonal line here, which would cause one blue hex to be shared between the "2" and -2-. But remember: We are also required to mark two hexes within these same columns at the top of the grid. So by just mentally attempting to share a hex between these two cells, we find that doing so would prevent us from marking two blue hexes at the bottom. This would necessitate marking three consecutive blue hexes within a column at the top--and with another -2- up there, this is impossible. The solution, then, is to mark the four corner hexes in this cluster, then erase the two which are shared between the "2" and -2-:

This opens up some additional moves at the bottom, to both the left and the right of this grouping:







One more task before we move up to the top cluster. When we marked our four hexes a couple of minutes ago, we gave the Blue 3 and Blue 4 hubs their required blue hexes. We can now erase those hexes which remain within their overlays:





Go ahead and erase the hexes by that "0" which appeared towards the left. We're now going to tackle that top-center cluster.

Remember how I said earlier that it was mandatory to solve that bottom cluster first? We're about to see why. The last sequences we completed laid the groundwork to complete another column. The top-center grid actually begins with two columns headed by a "6". We've just finished reducing the first one to six total active hexes. So next, mark those which remain.

And now we come to that "3" / -2- pairing. The -2- is quite obviously going to share one of its blue hexes with the "3"; but can it share both of them? This question will be answered shortly.

We already know that the column to the left of our pairing needs two more blue hexes. We can also see that for the -2-, only one of the hexes on its left can be marked. This guarantees that the top hex of the column will be marked. That same logic applies to the hexes to their right, as well. So next, mark the top hexes of both columns:

We're about to solve the top-center grid of this puzzle; here's where we're at so far:



The Blue 4 we just opened up on the upper-left edge of the "3" is actually critical. Expand that overlay next; it covers three blue hexes, but guess what? It only covers three of the four hexes surrounding the -2-. So only one of those hexes will be marked; this means the hex on its bottom-right edge is now a guaranteed blue hex.

So when we mark it, the hex directly above is automatically eliminated, leaving the "3" with only one obvious choice for its third blue hex. Additionally, we can immediately solve that "4" we just revealed. In fact, the only thing this doesn't tell us how to solve is the final orange hex on the bottom-right corner of this grid...



So why did we have to solve the bottom-center section first? In a practice run, I actually did try to solve the top-center first. What happens, though, is that if you don't work the bottom first, there's not enough information to work with on top. Let's say we didn't solve any of that bottom cluster first and tried to solve the "3" and -2- first. The positioning of their active hexes still lets us see that the top two hexes of the columns on either side of them have to be marked. But when we reveal the Blue 5 hub on the top-left corner of the "3", there isn't enough information to 100% guarantee which hexes are marked or eliminated from the overlay. You can make a very educated guess about it, but it's still guessing. The problem with the overlay is that you end up with an additional orange hex to work with. So the only way to narrow things down to where you can make a 100% logical decision is to solve the top-center grid's first column, and the only way to do that is to work the bottom-center section and then complete those overlays at the bottom of the central cluster. It's the only way to solve enough hexes that allow for a perfect solution to the Blue 4 overlay by the time we get to it.

All of that said, let's finish off those Blue 5 hubs at the upper-left corner of this grid. Start with the upper one; it covers only five active hexes, meaning we just need to mark the last one. When we do so, the Blue 5 below it will then cover five blue hexes, letting us erase the last orange hex within its radius:



You can probably see immediately that the {2} we just found is pretty easy to solve. Go ahead and do that next, reducing its column to six total active hexes. As this one is also headed by a "6", we can mark the rest of that column.

This lets us complete a few more small clusters. At the top, the "2" we opened up right below the {2} has only two active hexes to work with, and we just marked the first one. In the middle cluster, the "2" that we had to abandon a long time ago just obtained its second blue hex from completion of that column. Finally, closer to the bottom, the "1" on the bottom-left edge of the "0" we solved awhile ago still needs its obvious blue hex, which will give a second blue to the "2" right above it. Erase the final hex from that "2".

Continuing towards the left, the next-to-last column starting from the top-left grid can now be solved. This one is headed by a "3" and contains its three blue hexes, so erase those which remain. This opens up the bottom just a little bit more, as well:




The next column over, headed by a "4", doesn't have much to work with yet. However, we can at least get one more elimination from it. Expand the Blue 6 overlay about halfway down the column we solved a few minutes ago. It covers seven total active hexes, with the only two orange ones within the column we're trying to solve. The hex below that pair is blue; one of those two orange hexes will become the column's second blue. At the top, we have two pairs of orange hexes which each border a "3" that already owns two blue hexes. Since none of the orange hexes are shared by either "3", we know that one hex from each pair will be marked; these will become three and four for the column. Notice that within the cluster we just worked in the last step, we have another orange hex inside this column; this one can now be eliminated.

This elimination gives us another "2", but it more importantly leaves the "2" directly above this one with only one obvious choice for a second blue hex. Mark this one now, and the "2" we just uncovered will then share two blue hexes with the "2" above it, setting this up:




We're left with no real way to continue towards the left edge; there just isn't enough information yet. Even if we try to work with the line headers, there is no clear route to completing any additional lines.

What we can do, then, is go back to the Blue 5 hub in the top-center grid. We can use similar logic to the column we were just in to at least progress a little bit. When we expand the overlay, it covers six active hexes, including two at the top of a column headed by a "4" beginning in the top-right grid. The overlay has three blue hexes already; the column contains two. If we look farther down the column, two of its orange hexes border a "1" to their left; they are the only hexes from which the "1" can claim its blue hex. Naturally, one of them will become the third blue hex for the column. Which means that only one of those within the overlay at the top can be marked.

This lets us do two things. First, the final hex in the top-center grid will be marked, solving that grid completely. Secondly, within that next column, we can erase the three hexes not linked to either the overlay or the "1" farther down:





The "0" we just uncovered is very important and lets us solve several more hexes:








This gives us an interesting setup for the second column starting from the top-right grid. This one is headed by a "3"; we just gave it a blue hex. The second will come from what we mark to solve a "1" at the very bottom; again, its only possible blue hex comes from this column. The third will come from the very top, where we have another "1" which needs a blue hex from this column. So now, we want to erase the two hexes at the top of this column, since they are not linked to either "1":

The pair of empty "2" cells we just revealed add additional conditions to this section. The one on top has three active hexes from which to claim two blue hexes; however, we've already established that only one of the hexes to its left can be marked. So we now guarantee that the hex on its bottom-right edge has to be marked.

This shares a blue hex with the bottom "2" of the pair. Notice now that the "1" on the bottom-left edge of the lower "2" shares two orange hexes with it, and that they are the only ones left for it to claim. In other words, we can't give the "1" a blue hex without giving a shared blue hex to that "2". So now, we can erase the hex on the bottom-right edge of this "2":

We're still only about halfway through this puzzle!



Let's now take the diagonal headed by a "4", which extends from this general section. The line contains three blue hexes; however, it is impossible to complete the "4" we just uncovered without giving a fourth blue hex to this line. As a result, all of its remaining hexes at the other end can be erased.

We just uncovered a "2" and a trio of empty "1" cells. The "2" has only two obvious blue hexes to claim, which actually lets us complete this small cluster:






Let's solve the Blue 5 hub we just opened up; the overlay only covers five total active hexes, so we just need to mark the other three. This actually gives a third blue hex to one of the empty "3" cells we analyzed earlier; erase its final hex next.

The new "3" that this erasure uncovers pops up with three blue hexes already; this lets us ultimately solve the column headed by a "4" from this section--and almost this entire grid:






We're starting to open it up a lot more now. Let's go back towards the bottom, where we still have a pair of Blue 4 hubs to deal with. Expand the bottom one first; it covers only four active hexes. Mark the other two, which lets us solve another big chunk of this section:




The third column of the puzzle is headed by a -2-, and we've now given it a blue hex. Erase the one above it. This reveals a {3}; it already owns two blue hexes, including one at an endpoint in its ring. So we just need to mark the third one in sequence and erase its final two orange hexes.

We uncover a "1" directly above the {3}, which shares a blue hex with it. That erases three more cells. One of those erasures gives us a "0"; when we clear it, the "1" uncovered on its bottom-left edge has only one obvious blue hex to claim. So we now can solve this cluster, as well as our -2- column. After doing all of this, if we expand the Blue 5 overlay at the top, we get to mark the final hex on this side of the puzzle:

And just like that, we're nearing 3/4 of the puzzle solved! To make our re-entry into the right half of the puzzle, start with the diagonals headed by an "8" and a "7" from this section; both lines contain their necessary blue hexes, so erase all remaining orange hexes within each:




This leaves us a couple of paths we can follow; they'll eventually link back up together. We still have a Blue 3 hub in the bottom half not far right of the center. If we expand it, it covers several active hexes, including one blue. Well, the "3" on the upper-right edge of the hub still needs two more blue hexes. So clearly, they wil give the hub two more blue hexes, as well. That means we need to erase the one hex within the overlay not connected to that "3". After we do so, we can solve most, but not all, of the remaining hexes within that thin strip at the bottom:

The "1" that is positioned above the pair of zeroes down here is in an interesting position. We can't give the "3" on the upper-right edge of our Blue 3 a complete set without giving a blue hex to this "1". Which means that the hex on the upper-right edge of the "1" can now be cleared. This uncovers another "1", which isn't all that helpful.

We do, however, need to mark the hex on the upper-right edge of the "3"; it's the only hex remaining for the "2" on top of the "3" to claim for a second blue hex. This gives us a Blue 4 hub...






If we expand the Blue 4 overlay, it covers a slew of active hexes, including two blue ones. We can see from the array of orange hexes covered that the blue hexes we mark will definitely be shared by multiple empty hexes here. Is there anything we can erase?

I find it easier to work with the two empty "3" cells covered by the overlay here. If we divide the orange hex clusters inside the overlay into an "upper" and a "lower" cluster, we can see that each "3" will claim one hex from each. Since each "3" has two orange hexes to work with, the lone hex inside that is not connected to either--the one on the bottom-right edge of the hub--will now say, "Sayonara." Erase that one next.

We get a "2". Its positioning leaves both it and the "2" directly above with only obvious blue hexes to claim; marking both lets us solve everything within the overlay:






Let's continue up the same section; the "2" we just opened at the top-most extent of the overlay we just solved already has two blue hexes. So erase the three around its top rim. This gives us enough information to complete that cluster, too:





The Blue 1 hub we just revealed is in a great position, because we can immediately erase three more hexes. When expanded, the overlay covers the blue hex on the bottom-right edge of the hub, plus three more active hexes in the top-right grid. Erase those three.

The "2" we reveal at the upper-left edge of the overlay has only two obvious blue hexes to claim. Mark these next. Doing so will let us make some additional moves in this section; we'll expand upon this shortly, but I don't want to get too far ahead.





And from here, we can complete this entire grid; just work from left to right:








That leaves one reasonably large cluster at the right of the main grid to complete. Start with the puzzle's final diagonal, extending from the upper-left corner and which is headed by a "3". The line contains only three active hexes, giving us two important blue ones to mark.

The "3" right above the Blue 4 hub we just uncovered has only three total active hexes to work with; when we mark the other two, we also give a complete set of blue hexes to the "3" located above the Blue 5 we just revealed. This establishes enough relationships to solve several more hexes, as well:



We'll do two things here. First, the column governed by a "3" here now contains three blue hexes; erase the rest of the column. Then, if we expand the Blue 4 overlay near the bottom of this column, we find that it already covers four blue hexes; erase the last one. Now, we have enough information to complete that narrow strip at the bottom:


Only nine orange hexes remain. Both the "2" and "3" we uncovered when we erased the final hexes from the column headed by the "3" have only obvious blue hexes to claim, and we can also complete the column headed by the "6" from this.





And finally, completing the puzzle relies on nothing more than completing the remaining relationships on the grid:



Hexes Earned for Completing This Puzzle: 20

Puzzle 3-2 of Hexcells Plus gave us an array of bubbles to solve. Welcome to Bubbles 2.0:




This is a very interesting puzzle. It's not easy, but it's certainly not the hardest the game has to offer. For this puzzle, I'm going to label each row of bubbles from top to bottom as A, B, or C. Each individual bubble within a row will be numbered from left to right. So, for example, the fourth bubble in the top row will be Bubble A-4; the second bubble in the second row would be B-2; and so forth. This should help with identification.

This puzzle is big enough and has enough line headers that it's again very important to recheck everything periodically. We're going to focus on three primary areas for our opening move: The empty "6" in Bubble C-1; the column headed by a {7} starting at the right edge of Bubble A-2; and the column headed by a {8} starting at the left edge of Bubble A-3.

The "6" is completely obvious; no hex can ever have more than six cells surrounding it, so go ahead and mark everything around it. Now, the columns headed by the {7} and {8} are still short enough that we can determine quite a few obvious hexes to mark. The {7} column contains 10 total orange hexes. If we plot out its possible combinations for continuous blue hexes, we find that the fourth through seventh cells will be marked in all of them. Similarly, the {8} column also contains 10 total orange hexes. In this case, the third through eighth hexes are guaranteed to be marked. So our opening is this:



That leaves us with two Blue 12 hubs in the corners of Bubble B-3. Expand them one at a time; each one covers exactly 12 active hexes! So we can now mark every hex inside of their respective overlays:





Now, expand the Blue 9 overlays within the same bubble; here, we have the opposite situation. Each of these overlays covers nine blue hexes already; so now, we want to erase the orange hexes within their clusters:





Notice that this eliminated a hex from our column headed by a {7} from before, establishing an endpoint in its chain of blue hexes. We can now complete this column entirely:






We'll stay in Bubble A-2 for just a moment. The "2" we revealed along its right edge has only two possible blue hexes to claim. The two empty "1" cells positioned above and below the "2" each gain a shared blue hex from this, and we'll erase the last orange hex from the top of the column headed by a "6".

Let's move to Bubble C-3 now. First, if you didn't skip ahead and do so already, erase the hexes from the "0" we revealed earlier. Notice that the "2" revealed below the "0" has only two possible blue hexes to claim; marking them will give a shared blue hex to the "1" at the top-right edge of the bubble, letting us erase the last orange hex bordering it. The "2" revealed from that elimination will then itself have only two active hexes to work with:

This is where the puzzle starts to get tricky. In my practice run, it took me quite awhile to determine where to go next. It turns out we have only one way forward, and it involves the Blue 5 hub in Bubble C-2. When expanded, it covers three blue hexes and a large number of orange hexes. The most important aspects of the orange hexes it covers are the columns and column headers governing them.

The orange hexes directly adjacent to the hub on its left fall into a column headed by a "6", which already contains five blue hexes. So we know only one of these last three can be marked; it will become the fourth blue hex for the hub.

This leaves four more orange hexes to reconcile. The two farthest left fall into a column headed by a "5", which contains two blue hexes. There is no obvious guidance here; we simply haven't worked enough cells yet. The two farthest right fall into our column headed by a {8}. We still don't know which way our chain of eight consecutive hexes will go yet, or even if either of the column's hexes inside of this overlay will be marked.

One thing we can figure out, though, is this: If we were to mark the column's very bottom hex, the one immediately above it would be a required blue hex. This doesn't work; if we were to mark both of these hexes, the hub would actually end up with six blue hexes. As a result, we must erase this cell. This uncovers a "0"; now, we can solve this column:


Let's work on Bubble C-3 now; the "0" let us open up the bottom half quite a bit. Both empty "2" cells to the right of the "0" have only two active hexes apiece to worry about; marking them gives the "3" in the center of the bubble its third blue hex. Erasing the last orange hex from the "3" gives us a "4"; unfortunately, we cannot immediately solve it.

So let's return to the Blue 5 overlay. We've solved everything to its right, giving us only five remaining orange hexes from which to choose its two remaining blue ones. We've already established that the fourth will come from the vertical chain of three immediately to its left. This means that the last one will come from the column headed by a "5".

This line already has two blue hexes. Naturally, we'll pick the third from whichever one we give to the Blue 5 hub. But what about the fourth and fifth ones? Well, up at the top, in Bubble A-2, we still have a pair of empty "2" cells which need one blue hex apiece. It turns out that all of their remaining orange hexes are positioned within this column, and since none are shared between them, we know to mark one hex per "2". These will complete the column's blue hex requirements. So now, back in Bubble C-2, we have one orange hex not connected to any of these markers that can now be erased:



We've just uncovered a -4- with three blue and three orange hexes around it. Remember: We can't link all four of the blue hexes around it. If we were to mark the one on its bottom-right edge, we would do just that! So we have to erase this one. That gives us a normal "4" with four blue hexes already surrounding it. Let's erase the orange hex from below it, revealing another "4". This elimination leaves only one final hex to mark for this column to give it six blue hexes. That hex also completes the blue hex requirements for the "4" we just uncovered. Erasing its final orange hex gives us a "5" that we can instantly solve:

Okay, we still can't solve that -4- yet, but the Blue 8 hub within Bubble C-2 does give us a lot more information. The overlay already covers four blue hexes; we can see that the fifth will come from the last hex we give to the -4-. Only three orange hexes not connected to the -4- are covered by it; we want to mark these next.

We've just marked three blue hexes for this column, which is headed by a "4". Where will the last one come from? Well, in Bubble B-2 is an empty "5" cell. We immediately know that it's impossible to give it a complete set of blue hexes without marking at least one hex in this column; the column restrictions tell us that only one will be marked. So every remaining hex in this column not connected to the "5" can now be erased; additionally, we can mark the hexes around the "5" not positioned in this column:

We've completed a large chunk of the puzzle but still have quite a bit to do:



The cells we just marked let us complete a diagonal. At the top of Bubble B-1 is a diagonal headed by a "6", which already contains six blue hexes. Let's erase the rest of that line. That immediately lets us complete Bubble C-3; by erasing a hex from the "4" at the bottom-right, we leave only one final hex it can claim for its fourth blue. Mark it to complete that bubble.

Let's shift now to Bubble A-2. When we erased the hexes from the line headed by a "4" a few moments ago, we uncovered a "2" up here; it has only two active hexes to claim, and they'll be shared with the empty "1" cells above and below it, as well as the "4" in the center of the bubble. We can use these relationships to solve this bubble, too:


Staying in Bubble A-2 for a bit, we've solved a lot of cells in its second column, which is headed by an "8". The line now contains only nine total active hexes; we've already established that only one of the column's two cells at the bottom, within Bubble C-2, can be marked. So now, the three in the middle, within Bubble B-2, are guaranteed blue hexes.

When we mark these hexes, we give the "2" at the bottom-right of Bubble B-2 a second blue hex, erasing two more. Follow the relationships to complete the bubble:






So over in Bubble A-3, we have another Blue 12 hub right in the center. The overlay covers that entire bubble, and nothing else. We already have five blue hexes; we need seven more. As before, though, we have to focus on the columns in which the remaining orange hexes fall.

The orange hexes to the left of the hub are in a column headed by a "6". The column contains four blue hexes, but its only remaining orange hexes fall within this overlay; as such, only two of these can be marked. Now, the hub itself falls into a column headed by a "5", which contains four blue hexes already (including the hub, of course); again, the column's only remaining orange hexes fall within this overlay. So only one of these can be marked.

Now, the next column over is headed by a "2", and it contains one blue hex. Unlike the other columns, however, there are additional hexes farther down, inside of Bubble B-4. At most, one hex here can be marked. The final column within this overlay has no restrictions.

The trick here is in determining whether or not we are required to mark hexes within the last two columns of this overlay, given that there are orange hexes farther down these columns. If we take the five blue hexes we already have and add together the maximum number of blue hexes we can mark in the bubble's second and third columns, we come up with eight. So in actuality, there is no choice; in fact, even if we mark all three hexes in the bubble's final column, we can only get 11 blue hexes.

That does two things. First, within our column headed by the "2" here, all three hexes farther down, within Bubble B-4, can be erased; we have no choice but to mark one of the hexes at the top in order to give the hub 12 blue hexes, and this column can only contain one more blue. Secondly, it establishes that all three hexes in the bubble's final column are guaranteed to be marked:


So now, we want to clean up Bubble B-4. Start by clearing that "0" we just revealed. This leaves the empty "1" cells above and below it with only one obvious hex apiece to claim. Marking them also gives shared blue hexes to the empty "2" cells we just revealed. The Blue 6 hub in the center of the bubble makes their second blue hex. Erase their remaining orange hexes; this uncovers a pair of empty "3" cells that we cannot immediately solve.

Return now to Bubble A-3, and expand the Blue 6 overlay in its upper-left corner. It already owns three blue hexes; it also covers the three remaining orange hexes in our column governed by a "6" and two of the orange hexes in the next column, which is headed by a "5". This gives us an important erasure. We've already established that we need to mark two, and only two, hexes in the column headed by the "6". So the hub's final blue hex will come from one of those two hexes in the next column over, and it will also complete the column's blue hex requirements. This means that the orange hex directly below the Blue 12 hub can be erased:

The {4} we just revealed is extremely important. It already has three blue hexes around it; we now just need to mark the last hex that links them all together, then erase the two on its right edge. If we then use the relationships, in conjunction with the column headers, we can solve all but two hexes within this bubble:



We want to look now to the column headed by a -4- on the right side of Bubble A-1. This line contains three blue hexes already; notice how only one orange hex separates the blue one in Bubble B-2 from the two blue ones in Bubble C-1. Since the four blue hexes cannot all be consecutive, we need to erase this orange one. That gives us a "2" which already owns two blue hexes. If we erase the two orange ones around it, we actually open up a chain to solve this entire bubble:

Go ahead now and expand the Blue 3 overlay that we just uncovered at the top-left of Bubble C-1. The overlay already covers three blue hexes, so just erase the orange hexes it covers within Bubble B-1.

The two hexes we just erased open up the solution to Bubble A-3. Notice that at the upper-right edge of that bubble, we have a diagonal headed by a "7". We have just reduced it to seven active hexes; by marking the two which remain unsolved, we also mark the 12th blue hex that our Blue 12 hub in Bubble A-3 needs. Now, erase that bubble's final hex:


We can also complete another column from this. The second column of Bubble A-1 is headed by a "3"; that last sequence gave it a third blue hex. Erase the rest of the column. Inside of Bubble B-1, we uncover a "1" along its right edge; can you get to this point by following the relationships that this establishes?



To complete Bubble B-1, then, we need to use two of its associated diagonals. First, the line headed by a "4" already contains four blue hexes; erase those which remain. Now, the line headed by a "5" two lines up has been reduced to five active hexes. Mark the last one. Guess what? We can finally solve Bubble C-2 from this, too!



This leaves five bubbles left unsolved. Let's see what we can do with Bubble A-1 now. We get one big clue by the positioning of the "2" at the top of its second column, and the "1" directly below it. We can tell two things from this. First: Since it's impossible to give the "2" a pair of blue hexes without sharing one with the "1", the "1" is not going to claim the hex on its bottom-left edge. Secondly: The hex on the upper-right edge of the "2" is now guaranteed to be marked:

That's about all we can do up here right now; anything we mark or erase would be guesswork. We still have two diagonals extending from this bubble; maybe we can solve it once we complete more hexes along those lines.

We're almost 3/4 of the way finished now:



We'll return to Bubble A-3 and the Blue 6 hub we abandoned earlier. Expanding this overlay shows that it covers four blue hexes. The only three orange hexes it covers fall into Bubble A-4, in a column headed by a "5". So far, this column has no blue hexes.

Follow this column into Bubble B-4; the four orange hexes here border two empty "3" cells that we abandoned a long time ago. They each have two blue hexes already. The trick is whether or not they each will claim their third from this column. If so, it would mean that at the bottom, in Bubble C-4, only one hex would be marked for this column. There are actually a few different scenarios that could play out here.

Further complicating matters is the Blue 6 hub in the center of Bubble B-4. The overlay already covers two blue hexes; we know that the third and fourth will come from the empty "3" cells in question. And since they do not share any orange hexes between them, we know to mark one hex per "3". That takes care of four blue hexes for the hub; regardless of how we ultimately allocate these two blue hexes, the last two have to come from the final column of the bubble.

That particular column is headed by a "2"; so now, we've determined that none of its hexes in Bubbles A-4 and C-4 can be marked. Let's erase these hexes next:






We'll need to skip around for a bit here. Move now to Bubble C-4. At the bottom, we have a pairing of a "3" and a "1", which we just uncovered. There is no way to give three blue hexes to the "3" without giving a shared blue hex to the "1". So the hex on the upper-left edge of the "3" is a guaranteed blue, and the one on the bottom-right edge of the "1" now has to be erased.

That establishes two very important relationships. The "2" located above the "3" now has two blue hexes; the "2" we just revealed on the bottom-right edge of the "1" has only two active hexes to work with, so they need to be marked. This lets us solve the entire bubble:




The last sequence gives us critical information for solving Bubble A-1. The diagonal headed by an "8" from this bubble has now been given the eight blue hexes it needs. Let's go ahead and erase the two at the start of the line, at the bottom-right of the bubble. We uncover another pairing of a "1" and a "2", and like before, we can't give the "2" a pair of blue hexes without sharing one with the "1". This guarantees that the hex on the upper-right edge of the "2" is marked.

That hex gives its associated column, which is headed by a "3", a third blue hex. We can now erase the top two hexes of the column. We're also left with only three orange hexes at the top of the column headed by the -4-; only one of these can be marked. So as we have seen in this type of setup, the correct solution will be to share a blue hex between the "2" and the "1" we just revealed. And from this, we can complete the bubble:

Three bubbles remain. With Bubble C-4 solved, we've also answered the question we had for Bubble B-4. Recall that each empty "3" cell here still has three orange hexes from which it can claim a third blue hex. So do their respective hexes within the same column work? (That is, for the top "3", can we mark the one above it, or, for the bottom "3", can we mark the one below it?)

With the bottom of the column headed by the "5" solved, this assertion now falls apart. The Blue 6 overlay in Bubble A-3 has already dictated that only two hexes at the top of the column can be marked; we are now forced to mark two hexes in the middle section, within Bubble B-4. If we mark either hex within the column containing the empty "3" cells, it becomes impossible to mark two hexes in the next column without giving a fourth blue to one of them. So in actuality, we have to erase the hexes within their respective column.

When we do this, we uncover a pair of empty "2" cells with only two active hexes apiece. Marking their second blue hexes completes each "3", as well, and we can erase the final two hexes bordering them. To solve the last column of the bubble, remember that it is headed by a "2". Each "3" in the preceding column needs one blue hex; in this case, we erase the shared orange hex and mark the other two:

This opens up a path to work on Bubble A-4. The diagonal headed by a "5" at the bottom-right corner of the bubble now contains five blue hexes; erase the remaining three within this bubble. That leaves only two obvious blue hexes for that -2- we opened a long time ago to claim. And when we mark them, we give the "3" above it a complete set of blue hexes; work carefully, and we can now solve this entire bubble, too:

Only Bubble B-5 remains, and even after everything we've done, we still have nothing but that empty "1" cell in the center. We have several diagonals yet to be completed; all of the columns are now solved. And there is nothng else feeding into this bubble to give us any more information.

When I first worked this puzzle, it took me forever to even find a way to get this bubble started. Remember how I said that the "REMAINING" counter is a resource? This is how we have to solve the puzzle.

Of the remaining cells, we need only six to be marked blue. Let's take the diagonals into consideration. From top to bottom, we need one blue hex in the upper line headed by a "5"; two in the line headed by an "8"; one in the line headed by a "2"; and two in the lower line headed by a "5". Doesn't that make six blue hexes??

We've just established that no blue hexes will be marked within the bubble's bottom-right edge; our next step is to erase these three:







We've uncovered a trio of empty "1" cells; the line above them has to get two blue hexes, and we also have to be mindful of that "1" in the center. Notice how the only orange hexes bordering the "1" in the middle of our trio are shared with the central "1"; in other words, we can't give a blue hex to the "1" in the middle of the trio without sharing it with the central "1". This means that the other four hexes surrounding the central "1" can be erased:

The diagonal headed by the "8" now contains only eight active hexes; complete it by marking the last two. Now, since the upper line headed by a "5" can only have one more blue hex, solve it by sharing a blue hex between the empty "2" cells in the line below:




To complete the line headed by a "2", we can see that the empty "3" cell will share one blue hex with a "1" along the bottom; since they share two orange hexes, only one of them can be marked. So mark the hex on the bottom-left edge of the "3", then erase the hex at the beginning of the line.

The "2" that we just uncovered has only one obvious second blue hex to claim; marking it gives a shared blue hex to the first "1" of our trio. So erase the next hex down the line; the "2" that we uncover tells us how to complete the puzzle:



Hexes Earned for Completing This Puzzle: 20

A flower with disconnected petals, maybe?




The disjointed nature of this puzzle is reminiscent of Puzzle 6-2 of Hexcells Plus. We're allocated a total of 28 blue hexes. Notice that in each of the outer clusters, there is one orange hex not connected to an empty hex. So we actually get to start this puzzle in the same manner as its predecessor.

If we add up the total number of blue hexes which will be connected to an empty hex, we get 22: 4 + 4 + 3 + 2 + 3 + 2 + 4. We have six outer clusters, which means six additional hexes not attached to an empty hex. This means they're all guaranteed to be marked:



Helpfully, one of the columns towards the left is headed by a "1", and it just received its blue hex. Erase the rest of that column.

We now have to deal with some dueling restrictions. If we expand the Blue 3 overlay in the bottom-left cluster, it covers two hexes of a column headed by a -2-, as well as two of the hexes surrounding the "4" in the center. The -2- column has only four active hexes in total; the way they are scattered tells us that one has to be marked at the top, and one at the bottom. From this, then, we can at least tell that the two hexes that the overlay covers in the middle cluster have to be marked:

There's one other determination that we can make from that -2- line, and it concerns the empty "2" cells beside of which the line's hexes reside. Since we can only mark one hex per pair of orange hexes in this column, each "2" can only claim one blue hex from this column. Which means their second will come from their left. These hexes fall into a column headed by a "3". By default, then, the column headed by the "3" will get one hex from the top cluster; one from the middle cluster; and one from the bottom cluster.

The middle cluster here has a Blue 1 hub. If we expand it, it covers the whole cluster except for the two hexes farthest left. We've already determined that one of the blue hexes claimed by the column headed by the "3" will come from this cluster; the Blue 1 overlay covers those two possibilities. They also border an empty "3" cell. So whichever hex of this pair gets marked will go towards satisfying three separate sets of requirements at once. The Blue 1 hub dictates that the two hexes it does not cover within this cluster have to be marked; we can also eliminate the hexes above and below the empty "3" cell. The "2" that is uncovered above the "3" tells us how to solve the cluster:

From this cluster is a diagonal headed by a "2", which just received its second hex. We can now erase the two hexes at the end of the line from the bottom-right cluster. Now, the first column of this cluster is also headed by a -2-; we've just left it with three continuous active hexes. So like any -2- column or cell with this configuration, we can solve it by marking the endpoints and erasing the center hex:

At this point, we can solve the Blue 4 overlay in the bottom-right cluster. The overlay now covers only four active hexes, meaning we just have to mark the other two. This adds a second blue hex to the center column of the cluster, which is headed by a "3". In the top-right cluster, two of that line's hexes border the empty "4" cell at its center. We know now that only one of these can be marked, also guaranteeing that the two hexes to the right of the "4" have to be marked:

The two hexes we just marked fall into another column headed by a "3"; notice how this line passes through the only two remaining hexes in the bottom-right cluster. We have to mark one of them to give the "3" down there a third blue hex. This means we eliminate the two hexes from this line in the right-center cluster. The "4" here will then be left with only four active hexes, which will now be marked:

We can do several things now. FIrst, if we expand the Blue 4 hub in the right-center cluster, the overlay now covers only four active hexes. When we mark the fourth in the cluster above, we give that "4" a fourth blue hex and can erase the cluster's last remaining orange hex, also completing that column.

Next, we can solve the diagonal headed by a "3" extending from the right-center cluster. This line has been reduced to only three active hexes; when we mark the third, which lies in our remaining -2- column, we can immediately erase the hex above that one.




In the upper-right cluster, there are actually two diagonals headed by a "3". The lower one can be solved; it contains three blue hexes now. Erase the other two. This leaves the bottom-left cluster with only one final hex to mark, which will give the "2" in its center the second blue hex it needs.

Now, at the upper-left corner is a diagonal headed by a "4"; we've reduced it to four active hexes now. We just need to mark the other three. This completes the empty "2" cell in the top-left cluster, as well as the "4" in the middle cluster; erase the orange hexes still bordering them:




And just like that, we're done! To determine our final blue hex, use that remaining diagonal, headed by a "3", from the upper-left cluster. The line contains only three active hexes; mark the last one in the line, then erase the puzzle's final hex to complete this tricky stage.



This is a fairly short puzzle, but it's very difficult to get started. If you're familiar with Puzzle 6-2 from Hexcells Plus, this one incorporates the same type of logic. It's important to manage the line restrictions as you manage the overlays in order to eliminate those cells that are impossible to mark.

And with the completion of Puzzle 6-3, we are just three puzzles away from the end of Hexcells Infinite, and the end of our journey through Hexcells as a whole. But you know what that also means: Just one puzzle stands between us and the absolute hardest Hexcells puzzle we have ever faced. Until next time...

Hexes Earned for Completing This Puzzle: 22

We are down to the final three! If you're joining me for our third time around in concluding the Hexcells trilogy, thank you!! We've got just one more puzzle before we face the most epic challenge the series has to offer.


I'm thinking a flying carpet surrounded by wedges of cheese:



Or is it a wedge of cheese surrounded by four flying carpets and two smaller wedges of cheese? I'm not sure.

The simplistic look of this puzzle belies its overall difficulty. It's grueling. It requires thinking about lines and overlays in a different manner than we're used to in order to progress. In a practice run, it still took me a long time to complete it without making a mistake. It's going to be good practice for the next puzzle...

Puzzle 6-4 is relatively small, but it contains a fairly large number of line headers. Many of these lines are sub-divided, with Secondary and even Tertiary Line Headers making a return here. As such, revisiting the lines is critical. To start off, we want to examine the lines and see if we can solve any of them outright.

We have a couple of diagonals where the Secondary Line Header is the same number as the Primary Line Header. Remember that in this situation, everything between those line headers is automatically erased. We have a couple more where the number of hexes within the embedded line is equal to its respective line header; in this case, all of the included hexes have to be marked.

The first two lines we'll tackle begin in the upper-left grid. The first one is headed by a "4"; its Primary and Secondary Line Headers are both "4", so all hexes at this end of the line are automatically erased, since all four blue hexes have to come from below the Secondary Line Header. The second diagonal we want to work from this grid is the one headed by the "10"; its Secondary Line Header is a "4", and that segment contains exactly four hexes. So we want to mark all of these.

The next two lines we want to tackle extend from the upper-right grid. The first is the one headed by a "5"; like the previous diagonal, its Secondary Line Header is a "4", and that segment contains exactly four hexes. So again, we want to mark all of them. Finally, we want to tackle the line headed by a "4" one line up from the grid's final diagonal. This particular one has a Secondary Line Header of "4". As before, we want to erase all hexes above the Secondary Line Header.

And finally, the central column of the puzzle is also sub-divided. Both the Primary and Secondary Line Headers are "5", so we want to erase the top segment of this column, as well. Our opening, then, looks like this:



This leaves us with two lines of empty hexes to work with, in the top-left and top-right grids. We'll start with those in the top-right. The pairing of a "2" and a "1" in the top-right corner gives us a hint; since it's impossible to give the "2" a pair of blue hexes without giving one to the "1", the "1" will not be able to claim the hexes on its bottom-center and top-left edges. We can erase them immediately, and also mark the hex on the bottom-right edge of the "2".

The cells we just erased leave the "2" positioned on the upper-right edge of the -2- with only two possible hexes to claim. Both of these will be shared with the -2-; one will also be shared with the "1" we just uncovered. That gives us enough information to fill out the bottom three lines of this grid:



To continue with this grid, we need to use the line headers of the next line up. The Primary Line Header is "8"; the Secondary Line Header is "7". So only one of the line's blue hexes can come from this grid; well, in the next line down, we have a "3" that still needs a blue hex, and it can only come from this line. So our next move is to erase the two hexes in this line not connected to the "3".

We uncover a "1" and a "3" that cannot be immediately solved. Move up to the next line, which is headed by a "5". Recall from earlier that we have already marked four blue hexes here; its Secondary Line Header was a "4". The "1" that we just uncovered can only get its blue hex from this diagonal. Since it will also complete the blue hex requirements for this diagonal, we can erase everything in this line not connected to the "1":

The "4" that we just uncovered has only four active hexes surrounding it; marking all of them helps us fill out all but the top line of this grid:







Here's our first real head-scratcher of the puzzle. We have a dueling pair of Blue 5 hubs governing the last line of this grid. If we expand the top one of the pair, it covers four blue hexes, as well as the first three orange hexes of the unsolved line; as such, only one of these hexes will be marked.

Retract this overlay, then expand the second. This one only covers three blue hexes but also covers all four hexes of the unsolved line segment. We've already established that only one of the line's first three hexes can be marked. Since this particular overlay still needs two blue hexes, and there are no other orange hexes to choose from, the fourth hex of the line segment is now a guaranteed blue hex. It will also become the second blue hex for the "2" on its bottom-right edge, allowing us to erase the cell on top of the "2". The "3" that this uncovers shows us how to complete this section:

One grid down, six to go! The Blue 5 hub we revealed a moment ago expands to cover five blue hexes, as well as two orange hexes in the top-center grid. These can now be erased. The "1" uncovered at the right edge of that grid only has one obvious hex to claim; marking it uncovers a Blue 1 hub.

This hub gives the "2" right below it its first blue hex; its second will also give the hub the lone blue hex it needs. As such, the lone orange hex within the Blue 1 overlay not connected to the "2" has to be erased. The "1" uncovered naturally claims the hub for its blue hex; when we erase the cell below it, the "2" gets the final hex in this cluster.

We've got a long way to go! Here's the last sequence we completed:



For right now, that's all we can do at the top; there's still no way to know which hex that the -2- will receive for its second blue one. We do, however, have another line of empty hexes in the top-left grid to work on.

One interesting thing to note is that so far, the puzzle is symmetrical, with the exception of the line we erased in the main grid. We again want to work generally from bottom to top here. The bottom line of this grid is headed by a "6"; the embedded line is headed by a -3-. Don't let the negative notation confuse you; we're still going to mark three total blue hexes between the Secondary Line Header and the end of the line. They simply won't all be connected.

This means that we still need three blue hexes in the first line segment, too. We want to focus on the -2- in the next line up here; since it borders two of the four orange hexes in question, it effectively dictates that the endpoints in this segment are guaranteed blue hexes; since the -2- cannot claim two consecutive blue hexes, only one of the middle hexes will be marked.

The Blue 2 hub that we opened up at the gap here is in an awkward position. The overlay doesn't cover any blue hexes yet, but it seems that any of the orange hexes it covers could be candidates. What we need to do, then, is examine the environment of each orange hex to see if we can eliminate anything.

Our first clue is that the overlay covers both orange hexes that we're already debating between, on the underside of the -2-. We know for a fact that one of these will be marked; that's the first blue hex for this overlay. For the second, notice that the normal "2" on the upper-right edge of the Blue 2 hub has only two remaining orange hexes from which to claim its second blue hex--and the overlay, naturally, covers them. One of these will become the second blue hex for the overlay, as well. This means that the orange cell positioned two spaces above the hub, as well as one covered by the overlay in the grid below, can now be eliminated:

The "1" that we just revealed doesn't seem useful until we understand that it eliminates a cell from the -2-, leaving only one active hex above it. This cell can now be marked; when we do so, it erases three more hexes. We now leave both the "2" on the upper-right edge of the hub, as well as the one right on top of it, with only obvious blue hexes to claim; we can finish just about half of this grid now:


The last sequence also solved the first line segment of the diagonal headed by the "7" up here. The next line up, which is headed by a "3" and also sub-divided, is actually pretty cute. We just eliminated three hexes from this line segment; since the Secondary Line Header is a "2", the final hex at this end is now guaranteed to be marked. Look at what this does to the -3- we uncovered a moment ago; it gives that hex a second consecutive blue hex. Since the -3- only has four consecutive active hexes around it to start with, we just need to erase the next hex in line and mark the second endpoint. Since this also gives a shared blue hex to the "1" on the upper-left edge of the -3-, erase the hex on top of the "1".

The "1" that we just uncovered at the start of the diagonal headed by the "10" already has its blue hex, so we want to erase the one on its upper-right edge. Helpfully, that reveals another "1" which shares the same blue hex and allows us to clear two more. We actually won't even need anything more than the relationships between the cells until we get to the very last hex of this grid:


Go ahead and expand the Blue 4 hub we just uncovered; it covers four blue hexes already, so we can erase the three orange hexes within its radius. This takes us back to the top-center grid; we even uncover another coupling of a "2" and a "1" in the same relative positions. As before, the "1" will have only one obvious blue hex to claim.

When we mark that hex, we again get a Blue 1 hub. And as on the right side of this grid, its sole blue hex will be used to complete the "2" underneath it, meaning the hex at the top of the column will be erased. But here's where we break the symmetry; this time, we get a "2" from this erasure, and it will claim the hex below it. The final hex of this grid is now erased:


This solves three grids! We'll make some additional progress in the center of the main grid by tackling that diagonal headed by a "9". This one is also sub-divided; the Secondary Line Header is a -2-. We've left the upper portion of the line with exactly seven active hexes, so now, we can mark the rest of that line segment.

Now, we've added a third blue hex to the criss-crossing diagonal headed by a "4" in the upper-right grid. This line is also sub-divided; the Secondary Line Header is a "1". Now that the upper line segment contains three blue hexes, we can erase everything else down to the Secondary Line Header:



Great. Now what? Here's where it gets tricky again. Just as we had two lines of empty hexes in the upper-left and upper-right grids, we have two lines of Blue Hubs in the bottom-left and bottom-right grids. You guessed it: We have to find a way to reconcile these next!

It doesn't particularly matter which set we tackle first. We took the right side when working the top; let's start with the left side this time. We have a Blue 9, two Blue 10 hubs, and a Blue 5 hub. The trick is in examining which overlay gives us the clue on how to proceed; we also need to take into consideration the line headers influencing any hexes within each overlay.

Every line of hexes covered by the overlays here is governed by some kind of line restriction. Unfortunately, that's a lot of hexes!!! While it may seem like starting with the Blue 10 hubs is the best idea, this introduces a problem; after all, the other three hubs contribute three blue hexes to each one, leaving only seven of the orange hexes encompassed to be marked. We can't effectively isolate enough of them to determine what to mark or eliminate. And if we use the Blue 5 overlay, we even overlap into the central grid a little bit; as it covers two of the other hubs itself, we certainly can't isolate just three blue hexes from all of the orange ones covered.

We actually want to use the Blue 9 here. Expand this one; yes, it covers a lot of orange hexes, but notice that the hexes at the upper and lower limits each fall into embedded lines headed only by a "1". Now, count the number of orange hexes which fall outside of these two lines. There are five; the overlay also covers two of the other hubs. That makes seven; guess where the other two blue hexes will come from?

What we find, then, is that it is not possible to give this hub nine blue hexes without marking one hex from each of the embedded lines headed by a "1". In the lower such line, only one orange hex is covered; we can now mark it and erase the rest of this line segment. Additionally, all other hexes within the overlay not included in these two lines are now guaranteed blue hexes:

We're about halfway through now and working on the line of overlay hubs in the bottom-left grid:



All of the hexes we just marked give us a huge amount of information for the other overlays, and that -2- we just uncovered adds another missing piece. Start now with the Blue 5 overlay; it now covers four blue hexes. It also covers the -2- and two of its four active hexes; as we saw with the one above, this -2- also has two active hexes above and two active hexes below it. So also as before, only one hex in each pair can be marked. As this pertains to the Blue 5 overlay, its fifth hex will come from the one we give to the -2- on its upper rim. So the orange hexes it covers that are not linked to the -2- can be erased.

Unfortunately, that only gives us two "?" cells. However, if we now expand the Blue 10 on the bottom-left edge of the Blue 5, it covers eight blue hexes, but it also covers the -2- and the two active hexes along its top rim. This hub's ninth blue will naturally come from that pair; the tenth will come from the only other hex it covers, which is in our upper embedded line headed by a "1". So now, we can mark that hex and erase the rest of that line segment:

This is where the second Blue 10 overlay comes in; expand it, and we'll see it now covers 10 blue hexes. We can erase one of the hexes from the -2- now, then mark the hex next to the one we clear.

The blue hex we just marked is shared by the "4" we just revealed; the -2-; and the "1" on the upper-right edge of the -2-. Erase the two orange hexes still bordering the "1". If we follow the "0" uncovered and use the relationships on the grid, we can complete it down to just two final hexes:




Go ahead now and expand the Blue 2 we just opened up, but to solve this grid, we actually want to refer to the diagonal headed by the -2-, which runs through this hub. The negative notation dictates that we erase the hex on the hub's bottom-left edge; the "3" uncovered then claims the grid's final hex. Since the overlay now contains two blue hexes, we can erase from the bottom-center grid the remaining two orange hexes it covers. Go ahead and clear away the "0", too:

In the bottom-center grid, we now have a pair of empty "1" cells adjacent to an embedded line headed by a "2". The line header is particularly helpful here, because the embedded line contains only three hexes to begin with. Knowing that we have to mark two of them tells us that the shared hex between the empty "1" cells has to be eliminated, and the two endpoints marked. Of course, we can't solve the "3" that comes up right away...

It's almost time to tackle that line of blue hubs in the bottom-right grid, but before we do so, notice that one of the embedded lines here is headed by a -3-, and that it contains only four hexes. This means we can mark its endpoints:





Let's see what we can come up with regarding those three blue hubs now. As we saw when working the hubs in the bottom-left grid, the line headers of the hexes covered by these overlays play a crucial role themselves. Also as before, it takes some experimentation to determine which overlay to start with.

In this case, we want to start with the Blue 6 sandwiched in between the other Blue 6 and the Blue 7. Why? This one covers exactly the hexes we need to determine our next step. It already covers four blue hexes, meaning we only have to isolate two more. And because it covers the only two remaining orange hexes within the embedded -3- line, we know that the fifth blue one will come from here. We even cover two hexes within the embedded line headed by the -2- at the upper edge of the grid.

The reason that the -2- line is important here is because it is not possible to give it two disjointed blue hexes without including one of the two hexes the overlay covers. Number the hexes in order from 1 through 4. The possible combinations for two disjointed blue hexes are: 1 and 3; 1 and 4; 2 and 4. That's it. You have to mark either the first or second hex, but not both.

The end result of this is that every orange hex within this overlay that is not included in one of these two embedded lines can now be erased:







We just erased seven hexes! This gives the second Blue 6 overlay a lot more information; retract the first one and expand this one now. It only covers three blue hexes, but while it covers several orange hexes, we get some new clues.

First, this overlay also covers the remaining two hexes within the embedded -3- line; one of these will become the fourth blue hex for the overlay. We also expand up into the central grid a little bit, covering two hexes of that diagonal headed by a -2- to which we gave a blue hex in the bottom-left grid earlier. The only other orange hex it covers is the first one in the embedded -2- diagonal. As a result, the overlay's fifth blue hex will come from the -2- line in the central grid, meaning we can now erase from it the orange hexes not included within the overlay. So the overlay will now obtain a blue hex from the first one in the embedded -2- line from this grid:

Now that we have a blue hex for the embedded -2- line at the edge of the grid, we can at least erase the next cell down from it. The "2" that this erasure reveals actually shows us how to solve this line. We uncover a "1" at the end of the line; it pops up next to the line's second blue hex, letting us erase the final hex of this section.

And this is where the Blue 7 overlay comes in; if we expand it, it now only covers seven total active hexes. When we mark the seventh, we give our embedded -3- line its third blue hex and can erase the last one:





Erasing the final hex from the embedded line headed by the -3- revealed a "2" that already owns two blue hexes. We can erase the two orange hexes still bordering it. The "4" that we uncover in doing so only has four total active hexes around it, so make sure to mark them all.

Marking the blue hexes for the "4" contributes two blue hexes to yet another embedded line that is headed by a -3-; we haven't done anything with this one for a long time! Since these blue hexes are connected, we need to erase the next cell up this line. When we do this, we leave the "3" we uncovered on the upper-left edge of the "4" with only an obvious third blue hex to claim. Marking it allows us to erase the final hex of this grid:

We are almost done with this puzzle, having now completed five of the seven grids:



Go ahead now and expand the Blue 5 overlay near the left edge of the grid we just finished. It covers five blue hexes, letting us erase two from the bottom-center grid. Of course, the "0" we reveal lets us erase another one.

So as we had on the left side, we again have an embedded line adjacent to the two empty "1" cells we just revealed. The difference, however, is that this particular line is headed by a "1". So this time, we want to mark the shared hex between them, and erase the two endpoints.

It would seem that we can't solve those final three cells yet, but the "2" at the bottom of the embedded line borders only two active hexes. When we mark the second one, we give a third blue hex to the "3" we uncovered earlier towards the left. When we erase the final orange hex from the "3", we leave the "2" on top with only one final hex to claim, as well:


And with that, the six outer grids are completely solved, leaving only the center grid to complete. The biggest complication is the Blue 5 in the center; it still covers so many orange hexes! Expanding the Blue 3 at the top of the grid at least gives us a clue. This overlay covers two blue and two orange hexes. However, the two orange hexes fall into an embedded line headed by an "8". This line contains four blue and five orange hexes. We know that only one of the orange hexes covered by the overlay can be marked, leaving three more which now have to be marked if we are to attain eight blues for the line:

The embedded line in this section which is headed by the "2" just obtained its second blue hex from that sequence. We can erase the last two hexes in this line. It doesn't do much, but it does whittle down the puzzle more.

Our next clue comes from the Blue 4 hub we revealed from the last few cells we marked. If we expand it, the overlay covers three blue hexes. It also covers the two orange hexes remaining in our embedded line headed by the "8", telling us that one of them will also complete the hub's blue hex requirements. We can now erase the two other orange hexes covered by the overlay:


And now, if we look around the remaining line headers, we get...nothing! That's it; that's all the help we get for now with respect to solving the Blue 5 in the center of the grid. How on Earth do we reconcile the remaining lines and their hexes?

We have to start working on the Blue 5 now; go ahead and expand it. We need to treat it similarly to the hubs we worked in the lower-left and lower-right grids, paying great attention to the line headers of the orange hexes it covers. We at least have one blue hex accounted for already. So let's examine the orange hexes it covers.

At the bottom, the overlay covers the only remaining orange hexes within the embedded lines headed by the "4" and "5". Each of these lines needs only one blue hex to complete their blue hex requirements. As such, each will also contribute one blue hex to the overlay; this accounts for its second and third.

At the top, the overlay covers three of the five remaining orange hexes in the diagonal headed by a "10", and two of the orange hexes in the embedded line headed by a "1". The line headed by the "10" is our biggest clue here. It already contains six blue hexes. Since it needs four more, we know that at least two of those included in the overlay have to be marked. And since we've already accounted for where three of the overlay's five blue hexes will come from, we can only mark two of them. We get two things from this: First, the two hexes within this diagonal that are not covered by the overlay are now guaranteed blue hexes; and secondly, the two hexes within the diagonal headed by a "1" that are covered by the overlay are guaranteed eliminations:



This sets us up to complete three of the remaining diagonals outright, as well as the Blue 4 hub. Extending from the upper-right edge of this grid, the diagonals headed by the -2- and the "4" now each contain the blue hexes they need; erase the hexes which remain within each. Now, the diagonal headed by the "8" at the upper-right of this grid has been reduced to exactly eight active hexes; mark the last one:

We'll end up solving several more lines now, almost completing the puzzle. Start with our three remaining columns in the center of the puzzle, then the diagonal headed by the "1" at the top-left corner of the grid; each of these lines now contains the same total number of active hexes as blue hexes they need, so mark the rest of them. Two more diagonals will be simultaneously solved in this process:

We only need to complete one more diagonal to finish off this puzzle. We still have an embedded line headed by a "7" along the upper-right edge of this grid. It has been reduced to seven active hexes. Marking its final blue hex also allocates the last one the puzzle requires; erase the final two cells to complete this relative behemoth of a puzzle!



Whew!!! This is a very long and intense puzzle! But the way it's laid out is very interesting, and the solution, while long and involved, is actually pretty neat once it's all lined out. The biggest challenge is in determining which overlay to try and solve at any given time, as well as taking into account the line restrictions for all of the hexes covered by a given overlay. It's impossible to avoid making mistakes without carefully considering both types of restrictions before trying to proceed.

And with the solution of Puzzle 6-4, we finally come to the penultimate puzzle of the Hexcells trilogy. We've almost reached the end, but before we conclude the series, we have the largest puzzle of them all to contend with. So until next time, take care, everyone...

Hexes Earned for Completing This Puzzle: 25

This is it. The next puzzle is the largest and most challenging that the entire Hexcells trilogy has for us. We're almost at the end, but for now, behold the epicness that is Puzzle 6-5!!!




If poor Daniel from Amnesia: The Dark Descent saw this puzzle in the dark, his sanity would drop to "..." in about 3 seconds. :-P

This puzzle takes up almost every conceivable inch of the puzzle board. In fact, it's so large that, like I did for Puzzle 6-5 in Hexcells Plus, I have to switch from using PNG image format to JPG for this solution. It also means I will have to break a convention I have used with almost every Hexcells puzzle to date--again, 6-5 in the previous game notwithstanding. As I did there, I have no choice but to cover up parts of the grid with annotations. However, as before, I will attempt to only overlap parts of the puzzle we are nowhere near to working, or those parts already solved completely and which we will not have to revisit. I will also attempt to shift the positioning so as to still show, as much as possible, how a particular sequence relates to the puzzle at large.

With that said, we are given one enormous grid with a hub in the very center, whose overlay covers that entire cluster. There's a fairly large number of line headers, but none of those lines are sub-divided. We're given three more hubs, at the top and near the left and right edges. And we have a single empty hex--a "5"--near the right edge.

For this solution, I'm not going to focus much on relationships between hexes that at this point should be fairly straightforward. If a particular series more or less just involves, for example, eliminating all orange hexes from a "1" sharing a blue hex with a "2", I'm going to assume you can do this with little more than a nudge towards that step. Though I will point out relationships that may be tricky to spot and at least get you started on a particular sequence, I want to focus primarily on the hardest logic this puzzle has to offer; if you've read through all three guides to this point, we have worked over 100 puzzles together. Hopefully, I've taught you something by now. ;-)

I ended up using another save slot to test out various approaches to one particular section. It turned out that I ended up guessing without fully realizing it on my initial playthrough. The solution presented here, however, is airtight.

Here we go.

There are actually a couple of places we can start; for this walkthrough, we're going to start on the left side. Go ahead and expand the Blue 2 hub. It falls into a line governed by a "7"; this line contains a total of nine active hexes. If we include the hub itself, five of the hexes are affected by this overlay. With only four active hexes falling outside of its radius, we learn three things. First: All four of these hexes have to be marked. Second: Two of the line's remaining hexes will become the two required by the hub. And third: All other hexes within the overlay that are not included within this line have to be erased. That gives us our opening move:

Under the hub, we revealed a "?"; we want to focus now on the "1" on its bottom-left edge. It is surrounded by four active hexes, two of which fall into both our diagonal and the overlay. We still need two hexes within each, but the "1" itself tells us that we can only mark a single hex in this cluster. The only way we don't mark one of the hexes within this line is if at the other end, the conditions tell us we mark the opposite two hexes.

It turns out that if we look above the hub, we have a "?" and a "1" in the identical situation. In fact, the empty hexes in the lines directly above and below are a mirror image of each other. What we find, then, is that for each pair of orange hexes remaining within this diagonal, we have to mark one hex within each. The empty "1" cells bordering these pairs will thus get their blue hexes from this line, as well. So we can erase the orange hexes connected to each of them that are not also embedded within our diagonal:

At the lower end of this cluster, we uncover a very helpful -2- with only three continuous active hexes around it. We'll go ahead and solve it in the usual manner. This gives us a few new relationships which let us solve the trio of empty "1" cells extending from the top-right edge of the -2- itself:




We can use the two Blue 4 hubs adjacent to the -2- to erase a few more cells. Let's start with the one on its bottom-left edge and expand it. The overlay covers both the "3" above the hub, and the "3" under the -2-; it also covers all of their surrounding hexes. It also covers two of the blue hexes it needs and some extra orange hexes. The upper "3" has two orange hexes from which to choose its third blue hex; the lower "3" has three to choose from.

The nice thing here is that neither "3" shares any orange hexes with the other one; this means we have to mark one blue hex per "3", also giving the hub the two final blue hexes it needs. As a result, we can erase any hex not connected to either "3".

Now, retract that overlay and expand the second Blue 4. The positioning is different, but we have the same basic scenario: Two blue hexes are included within its radius, as are two empty "3" cells, all of their surrounding hexes, and a few extra orange hexes. Again, neither "3" shares any orange hexes with the other. So as before, we can erase any hex not connected to either of them:


Out of all of that, there's actually one guaranteed hex we can mark, and several we can erase. Near the bottom of the second column, we uncovered a "3". It is surrounded by five active hexes, but two pairs of them are also shared with an adjacent "1". This positioning means that it is impossible to give the "3" its three blue hexes without also giving each "1" a blue hex. This means that the hex directly below the "3"--the only one not connected to anything else--is a guaranteed blue hex. Additionally, for the "1" two columns to the right of the "3", we can erase the three orange hexes not shared between them:

Now, directly below the Blue 4 on the bottom-right edge of the -2-, we revealed another "3"; however, this one only has three total active hexes to worry about. When we mark the other two it still needs, we're going to share them with some of the other nearby empty hexes, and that's going to open this section up somewhat. Start by erasing cells from the empty "1" cells which obtain their blue hexes from this:

We're getting there, but we've only scratched the surface of this gargantuan puzzle:



This has brought us back up to the diagonal headed by the "7". We just gave the "3" located on the upper-left edge of the -2- its third blue hex. When we erase its final orange hex, we leave the "1" on top of the -2- with just one to claim--also giving our diagonal its sixth blue hex. The "2" we just revealed by eliminating the previous hex obtains its second blue hex, as well; erase the cell on its upper-left edge.

This erasure gives us another "1" with a blue hex right below it, allowing us to erase the next hex up the first column. We uncover yet another "1"; the only active hex is above it, so this time, we want to mark the next hex up the column, also giving a shared blue hex to the "1" on the upper-right edge of this "1". Erase the hex above the second "1":



We can use the Blue 2 hub we just opened to complete the first column, which is headed by a "5". If we expand it, it covers no blue hexes and only four total active hexes--including all three that the adjacent "2" will choose its second blue hex from. As a result, the only other orange hex that it covers at the top of the column is a guaranteed blue hex. When we mark it, the column gains its final blue hex; erase the column's final two hexes.

We reveal another pair of empty "2" cells from these eliminations, both of which pop up with the two blue hexes they need. This lets us clear two more. This, in turn, leaves the "2" on the upper-right of our Blue 2 hub with only one obvious second blue hex to claim:




We'll try to progress to the right. In the fourth column near the top is a "1" on the bottom-right of the Blue 4 hub we revealed during the last sequence. We want to go ahead and erase the cell on top of the "1". This gives us a "2", but we can't solve it yet.

So let's expand the Blue 3 hub at the top of the first column; it covers two blue and three orange hexes. The "3" on the hub's bottom-right edge still needs a third blue hex, so we know that marking it will also give the overlay a third blue hex, as well. We can therefore erase the third orange hex that it covers.

The "2" that this reveals doesn't really help much, either. We are, however, getting close to the {2} we uncovered during the opening sequence. It has a blue hex already; only two of the three remaining orange hexes around the {2} can be connected to it. This at least tells us to erase the hex on top of the {2}:



So none of the empty hexes we revealed there help us very much in solving that top-left cluster. We still eliminated a few more hexes, though. For now, let's expand the Blue 4 embedded within the diagonal headed by a "4" farther down. This overlay covers three blue hexes already; it also covers only three orange hexes, each of which borders either a "3" or a "2". These orange hexes are the only ones from which the "3" and "2" can choose their final blue hex; since only one of them can be marked, we have to mark the one shared between them, then erase the other two.

At the top-right edge of the overlay, we uncovered another "2"; it pops up with the two blue hexes it needs, letting us clear two more. Erasing them leaves the "2" above the one we just revealed with only one choice to mark for its second blue, uncovering a Blue 3:




We can't go any further with the empty hexes on the grid, and we still don't have enough information to finish another line yet. Are we trapped? Maybe we need to take a closer look at the top section...

We ignored the Blue 4 at the top earlier; let's examine it in detail now. It expands to cover two blue and four orange hexes, including all hexes surrounding the "3" and "2" up here. Clearly, we have to mark two of these four hexes. That requirement eliminates one of them immediately. Think about it...

If you're still stumped, we have to erase the lone hex shared between the "2" and the "3". If we were to mark this cell, all three of the other orange hexes inside the overlay would have to be erased, and we would not be able to give it four blue hexes. When we erase this hex, we uncover another "3"--only this one is surrounded by only three total active hexes. Marking the other two it needs gives a shared hex to it, the original "3", the "2", as well as the "2" at the top of this cluster. We'll carry out a few more relationships from here. Don't worry about the -2- and {2}; you might already see that we can solve them. If you're confident and want to work ahead, go ahead and do so. Otherwise, we'll complete them in the next step.

Now to solve that -2- / {2} couplet. The last sequence left us with only a standard ring of three consecutive active hexes around the -2-. So when we solve it as usual, we give the {2} its second blue hex. When we finish out the sequence, we also finally complete the diagonal headed by the "7":



The Blue 5 hub we uncovered a moment ago will help us eliminate a few more hexes. Expanding it shows that the overlay covers four blue hexes already; the orange hexes include those surrounding the "3" above the hub. The "3" still needs one more blue hex, which will become the fifth one required by the hub. So erase the three orange hexes it covers which are not connected to the "3".

One of the hexes we erased gave us a -3-. It comes up already owning two consecutive blue hexes; at the very least, we can erase the next hex over within its ring, since we cannot have a third consecutive blue:





Now, we can use that Blue 3 hub a few spaces below. Expand this one; it covers only one blue hex, but it also covers a lot of orange hexes. The "2" directly below the hub, as well as the "3" two hexes above it, each need a single blue hex to complete their requirements; this overlay covers every possible orange hex they can choose from. As a result, we can erase the other orange hexes it covers, leaving only these four:

We have to mark two of the four remaining orange hexes inside the overlay. The "2" we revealed on the hub's top-right corner leaves us in a similar position to the one we faced at the top-left corner. Recall how there, we couldn't mark the shared hex between the "3" and "2" because it would have forced us to erase all of the remaining orange hexes inside the Blue 4 overlay we were dealing with.

Well, the "2" under the Blue 3 hub, and the one on its top-right edge, leave us in a very similar place. One of the four orange hexes is shared betwen them. As in the previous setup, if we mark this particular hex, we have to erase the remaining orange hexes from the overlay. So we want to erase this one next.

We uncover another "2", but this one has only two active hexes surrounding it. We can immediately mark the cell underneath it. In fact, this blue hex is shared with four surrounding empty "2" cells. Additionally, the "2" on the upper-right edge of the one we just revealed is left with only two active hexes on its right side, which we can now mark, and we have additional relationships to complete, as well:

We're gradually working closer to the center, but we're still only about 1/4 of the way through:



So at the very upper-right corner of the Blue 3 overlay itself, we uncovered a "3". It is ringed by four total active hexes, one of which is already blue. Two of them are shared with the -3- a couple of spaces above; we gave the -3- two blue hexes on top of it earlier. The two orange hexes it shares with this "3" are the only ones from which it can claim its third blue; as only one of these can be marked, the hex on the upper-right edge of the normal "3" is a guaranteed blue hex.

We can now expand the Blue 6 overlay that came up during the previous sequence. If we expand it, it covers three blue hexes already, but it also covers a slew of orange hexes. Note, however, the "2" on the hub's bottom-right edge; the hub itself contributes its first blue hex, and there are three remaining orange hexes from which it can claim its second. Only one of these can be marked; we can count them collectively as the fourth blue hex for the hub. This leaves only two more orange hexes inside the overlay to deal with; they are now guaranteed blue hexes, as well:

Those last blue hexes give the -2- within the Blue 6 overlay its second blue hex, allowing us to erase an orange hex from the regular "2" we need to solve. Interestingly, we get another -2- from this. As it shares a blue hex with the first -2-, we can at least erase the next hex over in its ring of four continuous active hexes.

Another -2-?? Well, it shares the same blue hex, so go ahead and erase the next hex in its ring, as well. Another -2-. Rinse, lather, repeat!

At least this time, we get a normal "2"; we can't solve it yet without more information, though.








This gets fun. Expand that Blue 4 overlay. It covers all of the empty hexes we just revealed, and all of their surrounding hexes. Naturally, several of those orange hexes are shared with two empty hexes apiece; we can only mark two more blue hexes within the overlay's radius.

The trick is to isolate groups of orange hexes from which we are guaranteed to derive one of the hub's remaining two blue hexes. The best way to do this is to find the empty hexes with the fewest total number of surrounding active hexes, and which share the fewest number with an adjacent empty hex. This probably sounds very confusing; let's detail it further.

Remember that with Hexcells, it's best to try and isolate the simplest possible move. Given that, it's logical to want to work with the empty hexes with the least surrounding number of active hexes to handle. Here, these will be the -2- on the upper-right edge of the Blue 4 hub; and the "2" on the bottom-left edge of the hub. They both are surrounded by only three total active hexes, one of which--the hub--is already blue.

Each of these has only two orange hexes to deal with; but what also makes these the ones to use is the fact that of their remaining orange hexes, they only share one with an adjacent empty hex. The other empty hexes share two orange hexes with another one. This introduces more uncertainty as to which cells will be marked or erased.

This leaves only four of the seven orange hexes covered by the overlay that we actually have to deal with. The other three can now be erased:







What we end up with, then, is a pair of -2- hexes which now have only two surrounding active hexes--including the hub--to deal with! We can now mark these obvious blue hexes and erase what's left from the overlay. We open up several more relationships from this, as well:




We can finally complete another line. We uncovered a {2} near the bottom, embedded within a diagonal headed by a "4". The line contains three blue hexes; the {2} is surrounded by only three continuous active hexes. We know that the center one has to be marked; doing so gives this diagonal its fourth blue hex. Now, we can erase the final hex from the line.

Let's now work with the Blue 3 hub we uncovered in the bottom-left section, directly below the line we just solved. This one is pretty straightforward. It expands to cover two blue hexes already; while it covers multiple orange hexes, two of them belong to the "2" on the hub's bottom-right edge. We can easily see that whichever one we mark there will give the hub its final blue hex. So now, erase everything within the overlay not connected to this "2". When we do so, we uncover a "3" with only three surrounding active hexes; marking the third gives the "2" its second blue hex, letting us erase the last hex from that cluster:

From here, the "3" that we just solved has a "2" on its upper-left edge, and a "1" on its bottom-left edge. The "2" has only two active hexes to worry about. Marking the second gives a shared blue hex to the "1", letting us erase the cell on its bottom-left edge. We uncover another "1" which shares the same blue hex; erase the one on its upper-left edge. The "2" uncovered tells us that the last hex in this cluster will be marked:

We've solved a mssive chunk of the left half now. We can go up about halfway now, to the Blue 5 hub we left earlier. We couldn't do much with it before, but if we expand it now, it covers four blue hexes. It also covers the "3" on the hub's upper-left edge and all of its surrounding hexes. The "3" still needs a single blue hex, and we can see that it will also become the hub's fifth blue. As such, we now erase the two hexes the overlay covers which are not linked to the "3".

We uncover both a -2- and a normal "2". The "2" already has two blue hexes, so we can immediately clear the cell above it. Doing so actually tells us how to solve the -2-. We leave it with just three active hexes, one above and two below. One of the hexes below it is already blue, meaning the other one in that pair now has to be cleared. We can then mark the lone active hex remaining on top of it. This also tells us how to solve the "3" on the upper-left edge of the hub, as well as the "2" on the bottom-left edge of the "3":

Now, on the upper-right edge of the -2- we just solved is a "1" that shares a blue hex with the -2-. We can clear the two orange hexes still along the top rim of the "1". The "0" lets us clear a couple more cells, leaving us with a trio of empty "1" cells.

The "1" at the left edge of the trio gains its blue hex from the "1" that started this chain, on the top-right edge of the -2-. We can go ahead and clear its two orange hexes. On its upper-left edge, we uncover a "3" with only three active hexes; mark the other two. Doing so gives a blue hex to the "1" we uncovered on the upper-right edge of the "3". Now, just finish off the last couple of relationships this sequence establishes:

You may already have seen that one of the columns here is headed by a "10"; we have now reduced it to 10 active hexes. Mark those which remain. This also gives a second blue hex to the {2} we uncovered at the bottom a long time ago. Erase its remaining orange hex next. We uncover a "2", leaving the "1" right above it with only one possible hex to claim; when we mark it, we'll get to erase a few more cells:

We're getting close to the halfway mark now!



We still have a medium-sized cluster at the top-left corner of the grid to solve, and quite a few overlays to contend with in doing so. Let's start with the Blue 12 right on top of the "4" we uncovered and solved two sequences back. If we expand it, it covers 13 total active hexes. That might seem like a dead end, but notice that two of the orange hexes are in a column headed by a "4". The column already has three blue hexes; this means only one of the top two hexes will be marked. As such, we can actually mark everything else inside this overlay, leaving only these two unsolved:

So we don't quite have enough information to complete the top two cells of that column yet. Maybe the other overlays will help us. First, though, the "3" located near the top of the column headed by a "6" has the three blue hexes it needs, letting us erase the two on its right. The two "?" cells that this reveals block further progress in this section for now, though.

Let's work now with the Blue 10 hub positioned right below the Blue 14 hub. This one covers exactly 10 active hexes, letting us mark the final two it still needs. You may want to retract that overlay at this point. We'll now solve that Blue 14 overlay; this one actually covers exactly 14 active hexes, letting us mark two more yet. And when we do this, we actually give our column headed by the "4" its fourth blue hex, allowing us to clear the top hex of the column:

Let's take the other Blue 10 hub in this section now. When expanded, this overlay covers 11 active hexes; eight are blue, three are orange. Notice that two of them, however, are beside a "3" that still needs only one blue hex. We can't complete the hub's blue hex requirements without marking one of those two. This tells us two things. First, that we can mark the one orange hex inside its radius that is not linked to the "3"; and secondly, that we can erase the hex on top of that "3", since the overlay effectively forbids that one from being marked:

Next, expand the Blue 12 on the upper-left edge of the Blue 10. This one covers 13 total active hexes, but again, it covers the two orange hexes linked to the same empty "3" cell. So here again, make sure every hex except for these is marked within this overlay.

We're not going to solve the "3" this time, either. So as a final step for this sequence, let's go ahead and deal with the Blue 9 hub several columns to the right. When expanded, the overlay covers its required nine blue hexes; erase the only orange hex within its borders:




We'll move back towards the center just for a moment. The Blue 7 on the upper-right edge of the Blue 9 we just completed expands to cover seven blue hexes. Erase the remaining two orange hexes within its radius, as well.

We're now going to focus on the Blue 11 at the top-left, and the Blue 12 on its bottom-left edge. The overlay for the Blue 11 covers 12 total active hexes; 10 of them are blue. So only one of the two orange hexes can be marked. Remember these two hexes, then retract the overlay.

Now, expand the Blue 12 overlay. This one expands to cover 11 blue and three orange hexes, including the two orange hexes covered by the Blue 11 overlay. We've just established that one of those two has to be marked to solve the Blue 11 overlay; well, we've now learned that it will give the Blue 12 its final blue hex, as well. As a result, we can erase the third orange hex that the Blue 12 overlay covers:

We're still moving from hub to hub here. Now, expand the Blue 13 sandwiched in between the Blue 12 hubs. This overlay covers 12 blue and 3 orange hexes. Once again, the overlay covers that pair of orange hexes at the top, from which we have already determined one blue hex will be marked. The one we mark will also give this overlay its final hex; erase that third orange hex beside the empty "3" cell. This leaves the "3" with only three active hexes; we can finally mark its third blue one:

And now, that Blue 8 overlay will let us complete the top-left section of the grid. It expands to cover exactly eight active hexes; when we mark the last two, we give one to that pair we've been fighting with for the last few sequences. We can now erase the final hex of this section:




Let's move back towards the bottom-center now, and expand that Blue 5 we left earlier. This overlay covers two blue and five orange hexes. The "2" on the hub's upper-right edge needs one blue hex from the three orange ones the overlay covers. Since only one of them can be marked, the two additional orange hexes within the overlay can be marked.

Marking these two hexes does a couple of things. First, it gives the empty "3" cell right below the Blue 5 hub its third blue hex. Secondly, it gives a third blue hex to its associated diagonal, which itself is governed by a "3". So we can now erase the final hex of this line, and the final orange hex bordering our "3":

We uncover a "3" on the bottom-right edge of the hub; it appears with three blue hexes already surrounding it. When we erase the one orange hex it borders, we leave the "2" we've been trying to solve with only one final obvious blue hex to claim:




We get two more eliminations now. We gave a second blue hex to the "2" at the bottom-center of the grid, and the "3" at the top-right corner of the Blue 5 overlay we just completed has the three blue hexes it needs. Erase the remaining orange hexes from each.

We can complete one more diagonal from this. From the left-center are two diagonals governed by a "5"; the lower of these now contains only five active hexes. Now, mark the final one at the end of the line:





In the center of the puzzle, we are now left with no information except for some column headers and a few hubs. We've reached a logical dead end here; we can't continue into the right half of the puzzle without additional information. So we'll need to see what we can work on that side, then work our way back towards the center.

To start the second half, we want to focus on the diagonal headed by the {2}, which contains a "5" just past the center. The "5" is surrounded by the maximum of six hexes; however, it's impossible to mark five around it without marking at least one within this diagonal. The requirement that the line's two blue hexes be consecutive, though, means that it's only possible to give the "5" one blue hex from this line.

We get two things from this. First, since we have to mark two consecutive blue hexes from the line, and they will stretch outwards from the "5", we can erase all hexes within the line falling outside of their maximum reach. Secondly, we can safely mark the four hexes surrounding the "5" which do not fall into this line:

We're a little over halfway done now. Stick with it!



We have to work with that Blue 4 hub in the final column now. Let's expand it. The hub itself falls into a column headed by a "9", which contains only 10 total active hexes. The hub itself gives the line one blue hex, so we need eight more. Of the orange hexes remaining in this line, six of them are not contained within the overlay. This means that at least two of the overlay's blue hexes must come from this line.

Now, the overlay covers one blue hex already; we've just determined that at least two of the others have to come from the final column. The big question is whether or not we'll mark either of the hexes within the diagonal headed by the {2} that it also covers. And actually, we cannot! Marking one would require us to mark both, if the line is to gain two consecutive blue hexes; those, in addition to the two we have to mark from the final column, would give the overlay five blue hexes. So our next step is to erase the two hexes from the diagonal within the overlay, and then mark the final two, thus solving this line:

We uncovered a "2" on the bottom-right edge of that "5"; it pops up with the two blue hexes it needs, allowing us to erase two more. This, in turn, leaves the "2" on the bottom-right edge of this one with only one obvious hex to mark for a second blue. That also gives the overlay two blue hexes; since the other two have to come from the final column, we can go ahead and erase the final orange hex it covers in the next-to-last column. From here, erase the two orange hexes from the "2" we just revealed at the bottom-left corner of the overlay; it has two blue hexes now:

Now that we have firmly established that only two of the final column's blue hexes will be included within the overlay, let's mark everything else in the column.

We can at least briefly turn to the -2- we uncovered a few moments ago. It has a blue hex, so we can erase the next hex up from the blue one. That gives us a "2" with two blue hexes, helpfully letting us clear three more. The "1" we uncover on the upper-left edge of that same "2" shares a blue hex with it, letting us eliminate three more yet. The "3" on the bottom-left edge of that "1" already has three blue hexes, so clear the one on its upper-left edge; and even after all of this, we can carry out additional relationships If we play it right, we'll loop back over to the final column and will be able to solve it entirely!

The sequence we just carried out is not completely finished yet. In the diagonal headed by a "9" from the upper-right edge of the grid is a pair of empty "1" cells, each of which has a blue hex already. We need to erase their surrounding orange hexes next.

On the lower-left edge of the second "1" in this line, we uncover a "3" that we can't immediately solve. However, if we expand the nearby Blue 3 hub, the overlay provides us with several cells to eliminate. The overlay covers two blue hexes already; the "3" needs only one final blue hex, which will also give the overlay the last one it needs. So erase all hexes within the overlay not connected to the empty "3" cell:

Two columns to the left of the Blue 3 hub, we have a chain consisting of a "?", a "2", and a "3". Both the "2" and the "3" have only obvious blue hexes to claim to fulfill their requirements. Marking all of them also takes us back to the overlay and allows us to complete both it and the empty "3" cell that led us to this point. As a final step here, refer to the "1" on the bottom-right edge of the "3" at the bottom of our chain from the start of this sequence. It shares a blue hex with the "3", so go ahead and eliminate the cell beneath it:

Of the two remaining overlays, the Blue 7 is the only one we can really do anything with right now. Expand this one; it covers five blue and three orange hexes. Helpfully, two of those orange hexes border a "2" which needs a second blue hex. They're also the only ones from which the "2" can claim it. So we can safely mark the third orange hex the overlay covers.

This interestingly gives us a Blue 5 hub. This one is actually in a pretty great position; if we expand it, it covers four blue hexes already. It also covers those same two orange hexes the "2" at the overlay's upper edge needs to choose its second blue one from; naturally, one of them will become the overlay's fifth blue hex. This now lets us erase eight more cells:


We've just established a number of new relationships to work through. At the left side of the overlay is a chain consisting of two empty "3" cells and a -2-. The -2- is a good reference point; since it has only a normal ring of three consecutive active hexes, we'll solve it as usual. The two empty "3" cells above it have only obvious blue hexes to claim; completing them will also let us complete the overlay and that empty "2" cell at the top-left corner of the overlay. There are a few other relationships we can carry out from this, too:

In between the -2- cells here, we uncovered a Blue 3. If we expand the overlay, it covers only one blue hex. It also covers the "3" on the hub's upper-left edge, the -2- on its bottom-right edge, and all of their surrounding hexes. Each of these empty hexes needs only one blue hex apiece, and those blue hexes will also complete the hub's requirements. Erase the hexes not connected to the "3" or the -2-.

The {2} that we uncover is in an interesting position. It has two active hexes below it, and only one above it. Obviously, the pair of two will be marked, which erases the one on top of it. That leaves the "3" with only one final hex to claim:





We're going to abandon the Blue 3 overlay for a bit and move to the Blue 4 hub a few columns to its right. If we expand this one, it covers three blue hexes; at the left edge, it covers a "1" and both of its surrounding active hexes, so naturally, the hub's fourth blue hex will come from here. We can clear the other two orange hexes it covers.

By themselves, the empty "1" cells that we just uncovered don't tell us very much. However, the "1" on the bottom-left edge of the "?" here shares two of its four orange hexes with the "1" on the upper-right edge of the -2- we have yet to solve. Since these are the only two hexes from which this "1" can claim its blue hex, we can erase the other two orange hexes bordering the "1" adjacent to the "?":

We're about 2/3 of the way through now, but we'll need to strain our brains to finish:



So in my initial playthrough, I struggled for what must have been a couple of hours total to solve the dueling Blue 3 and Blue 4 overlays here. With only three orange hexes left between them, I thought that there had to be some way of solving them right then and there, especially given that one of the hexes is shared between the overlays.

It wasn't until I worked through the puzzle again for this guide that I realized that I actually ended up guessing here; my guess was right, and I finished the puzzle without making a mistake. But now, we're going to solve it the right way.

It turns out that we actually have to abandon these two overlays for right now, and instead turn our attention to the line of three hubs in the same column as the {2} we worked a little while ago. We have a Blue 6 and a pair of Blue 7 hubs here. These are tricky to work, but once solved, we'll fill in another pretty good chunk of the grid.

The trick with these overlays lies in the orange hexes that they share between them. Start with the Blue 6; it covers five blue and five orange hexes, meaning only one of the orange hexes can be marked. Pay close attention to which orange hexes it covers.

Now, expand the Blue 7 in the middle of the trio; this one also covers five blue and five orange hexes. However, four of the orange hexes are shared between both of these overlays; one is not. From this, we know that whichever hex we mark in the cluster shared by both overlays will also be shared by both; it will also complete the blue hex requirements for the Blue 6. This means that for the Blue 7, we can safely mark the one orange hex it covers that is not shared; for the Blue 6, we need to eliminate the extra hex that is not shared by both overlays:

That "2" we just uncovered is extremely important. It pops up with two blue hexes to its right, giving us four more to eliminate. The "0" that is revealed here is actually not important. Instead, focus on the "3" opened up above the "2", and the "1" opened up below it. The "3" has only three active hexes surrounding it to worry about; the "1" pops up with the blue hex it needs. From here, just use the relationships established:

Our next focus will be the Blue 7 we uncovered at the bottom of that cluster. This one is in a particularly interesting position. Go ahead and expand it; it has only three blue hexes at this point.

Six orange hexes are also covered by the overlay, and this is where it gets tricky; it's also what I missed in my initial playthrough that caused me to guess at the solution to the Blue 3 and 4 overlays off to the right. We can easily see that this particular hub's fourth blue hex will come from the hex we mark to complete the "2" on its upper-left edge. That accounts for two of its orange hexes, leaving four to contend with.

Notice that two more of the orange hexes fall into the diagonal headed by a "4" from near the top-right corner. This line already contains three blue hexes. At most, we can only mark one more in this line; it's also impossible to complete the hub's blue hex requirements without marking one of the two hexes the overlay covers within this line. This now accounts for four of the six orange hexes, and five of the seven blue hexes the hub needs.

What this means is that we can mark the other two hexes the overlay covers. Additionally, we can erase everything within our diagonal that is not included within the overlay:






We don't need to use the overlay at this point. Near the end of our diagonal, we uncovered a -2- with two active hexes below it, and only one above it; one hex in the lower pair is already blue. So we can solve it by erasing the lower pair's second hex and marking the hex above it. The "3" which appears on the bottom-right edge of the -2- has only three active hexes to deal with, and when they are all marked, the -2- above it will gain its second blue hex. We can erase the orange hex on top of it.

This erasure reveals a normal "2" with two blue hexes on opposite corners. This clears two more. That's as far as we can go using the relationships between the cells, however.






We need to go back to using overlays to fill in more information. Start with the Blue 5 at the bottom-center of the grid. It now expands to cover five blue hexes; erase the only orange hex it covers. The "3" that pops up from this has only three active hexes surrounding it, so now, mark the last one.

Now, if we expand the Blue 6 overlay positioned two spaces above the Blue 5, it covers six blue hexes. We can erase the two orange hexes it covers next. The "1" uncovered in the central column has a blue hex below it; erase the cell above it to gain a toe-hold into the central cluster:




We're given another problem with the Blue 6 overlay on top of the -3-. It would seem that we should be able to solve it, but if we expand and analyze it, the positions of the orange hexes are just such that there is too much uncertainty; we'll have to find another way to reconcile them.

Let's try the Blue 7 two columns to the right of the -3-. The overlay covers five blue hexes already; the sixth will come from the one we mark to complete the -3-. Where does the seventh come from?

It turns out that the hub itself is positioned in a column headed by a "9"; the line contains 11 active hexes, five of which are covered by the overlay (including the hub itself). Even if it turned out all four hexes at the top of the column were marked blue, it would be impossible to complete the column's blue hex requirements without marking a cell covered by this overlay. As a result, it turns out that we will mark those four hexes at the top of the column. We can also now erase everything within the overlay not tied to either the -3- or this column:

Let's start with the "4" we uncovered on the bottom-right edge of the hub. It has only four active hexes to worry about, so just mark the last one. This not only gives the "3" to the left at the very bottom its third blue hex, it also gives our column its ninth blue hex. We can erase the remaining hexes from the column and from the "3". When we do this, we only have to solve the empty "4" cells in this section to also provide shared blue hexes to everything else:

To locate our next focal point, start at the bottom of the column headed by the "9" that we just completed. Find the "4" with a "2" under it at the bottom of the next column to the right. That "2" has only one obvious choice for a second blue hex; mark it to also give a second blue hex to the "2" right above the hex we just marked.

Clear the hexes to the right of this "2"; the "3" uncovered is only surrounded by three total active hexes, so mark them next.

The Blue 3 we just revealed lies at the end of a diagonal headed by a "3", which now contains two blue hexes. Several of the line's remaining hexes are adjacent to a "1" and a "2" in the line above. Since we can now mark only one hex here, and these cells have no other orange hexes from which to choose a blue hex, we need to mark the one hex shared between them. Now, erase the rest of the line:

The end is in sight! Just a few more hexes at the bottom, then we just need to finish the top and center clusters:



Go ahead and expand the Blue 3 overlay now; it covers two blue hexes, as well as the only two orange hexes the "3" on its upper-right edge can choose its third blue hex from. Go ahead and erase from the overlay the hex not tied to that "3".

Now, on the upper-right edge of that "3" is a "1"; we cannot give the "3" its third blue hex without sharing it with the "1". This means there is no way we can mark the cell on the bottom-right edge of the "1". Erase it next.

Ah!! A "0"!! Clear it! Doing so fills in most of the section. Near the bottom of the next-to-last column, the "4" already has four blue hexes, so go ahead and erase the last one under it.

The "3" on the upper-right edge of the Blue 3 now has only one obvious blue hex to claim, which will be shared with the "1", as well as the "2" that we uncovered earlier. When we erase the hex above the "2", we leave the -2- above with only one obvious blue hex to claim, and when we mark it, the final hex of the section can be erased. This finally completes those dueling Blue 3 and Blue 4 overlays up in the middle of the section!

We're approaching the end now. Only the top section and the central cluster remain. We uncovered a Blue 4 quite awhile ago in the first column past the gap; it's positioned above the zeroes in that column. We couldn't do anything with it earlier, but now that the column headed by the "9" is finished, it's much more useful.

The overlay now covers three blue hexes; the fourth will come from the hex we give to the "2" on the hub's bottom-left edge, so we can now erase everything it covers that is not connected to the "2".

We uncover dueling {3} and -3- cells from this, but we can solve them both outright. Both already have two consecutive blue hexes. For the {3}, we just need to mark the next one in sequence, since we have an endpoint; for the -3-, we want to skip the next one in sequence and mark the second endpoint:



How often do we uncover a -3- that already has its three blue hexes??? That's exactly what we get here, and that immediately gives us two more eliminations. Above that -3-, the "2" we reveal pops up with its two blue hexes, clearing two more yet. The same situation occurs for the "2" we reveal at the top of that column, so just clear its orange hex, as well.

The "1" we uncovered a moment ago, as well as the Blue 6 hub below, are in an interesting setup. Go ahead and expand the overlay. The only two hexes the "1" can claim its blue hex from are in a column headed by a "3", which already contains two blue hexes. Since we have to mark one of the hexes beside the "1", the third hex down cannot be marked; erase it. This reduces the overlay to exactly six active hexes. When we mark the other two, we give the "1" its blue hex, and the top hex of the column is erased:

We can go ahead and expand the Blue 3 overlay we just uncovered before marking the obvious blue hex that "2" will claim. After marking that cell, the overlay will have the three blue hexes it needs, letting us erase that final orange hex in the corner.

Now, in the column headed by the "9", we have two Blue 6 hubs; let's take the lower one. It covers six blue hexes already; when we erase the last one, we eliminate a hex from the "2" on the bottom-left edge of the Blue 4 hub. This leaves it with only one possible hex to claim for its second blue one; it will be shared with the "1" above. Now, we can fill out this section just using the relationships established:

Let's work now with the Blue 3 hub in the central column; it expands to cover three blue hexes now. Erase the three orange hexes it covers. The "1" we uncover at the top-right corner of the overlay pops up with a blue hex; erase the two orange hexes it still borders.

The "2" we just uncovered also pops up with its necessary blue hexes; erase the last one on its top-right edge. That opens up another "2", and the final hex in this section is the only one it can claim for its second blue. Mark it:





We're down to the final cluster. We don't even particularly need to expand the Blue 8 overlay, because the cluster itself is the exact size of its maximum reach. We'll get the first blue hex it needs from the "1" at the top of the section, as it has no other active hexes to deal with. So mark the top-center hex of the cluster. This gives us a Blue 6 to contend with. We have to use it and the remaining lines to work through this section.

Expand the Blue 6. It covers two blue hexes already. Because so many lines intersect with this cluster, the trick is in determining which lines give us the most information. From the top-right, a pair of lines headed by an "11" intersect most of the hexes within the Blue 6 overlay; from the top-left, lines headed by a "9" and a "12" intersect most of them.

It turns out that it's the latter pair of lines that gives us the most useful information. Each of them needs only one more blue hex to complete them. The only variable surrounding the diagonal headed by the "12" is whether or not the lone orange hex not covered by the overlay can be marked.

So let's test it. If we mark this hex, that erases three from the overlay, leaving two blue and four orange hexes. In theory, this should work; however, because we can only mark one of the two blue hexes within the diagonal headed by the "9", marking this particular hex fails, since there wouldn't be enough orange hexes left to give the hub the six that it needs. So we can now safely erase this hex. Additionally, we can go ahead and mark the two hexes within the overlay not included in these two lines:

This last sequence gave the column headed by the "6" running through the left side of the cluster its final blue hex; go ahead and clear the last two hexes within the column. It also gave the upper diagonal headed by an "11" from the upper-right of the grid its final blue hex; erase its last cell, too. Now, from the upper-left is a diagonal headed by a "10". We've now reduced it to 10 active hexes and can mark the final hex in the line. Marking it gives a final blue hex to one of the columns headed by a "4", allowing us to erase one more cell:

We have finally arrived at the end of the most challenging puzzle in all of Hexcells:



So we get yet another Blue 6 to deal with now. Let's retract the first one before expanding it. Now, this overlay covers four blue hexes already; the question is just where the other two will come from. Again, this involves determining just which intersecting lines to focus on.

In this case, the answer is with the diagonals headed by a "9" and "11" from the upper-right. The overlay covers the only remaining orange hexes within each line. They each need just one blue hex to complete them. So the hub will gain its final hexes from those we mark to complete each line. As such, the lone orange hex it covers that does not fall into these lines can be erased.

Erasing that hex reduces the diagonal headed by the "12" from the upper-left to exactly 12 active hexes. We can now mark the final one. This simultaneously gives the diagonal headed by the "11" its final blue hex, and we can now erase its final cell:



Let's return now to the original Blue 6 overlay at the top of this cluster; it now covers exactly six active hexes. Mark the last one, thereby also giving its respective column, which is headed by a "3", its third blue hex. Erase the final hex of the line.

This is the end. The column headed by the "4" has been reduced to only four active hexes. Mark the last two, then erase the puzzle's final hex to WIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!



That's it. The hardest puzzle in the entire series has now been conquered. We have only one left to conclude the trilogy. I strongly advise breaking this puzzle up into several play sessions. It is an extremely long marathon with some genuinely tricky segments. If you can make it through this puzzle without a walkthrough and without making a mistake, then you are a true master of Hexcells.

Join me in the game's final puzzle as we conclude the Hexcells trilogy!

Hexes Earned for Completing This Puzzle: 25

There's no question that Puzzle 6-5 is brutal in its intensity, as well as a marathon to solve. I had to work through it in two sessions before I could complete it during my initial playthrough. But with the ultimate puzzle in all of Hexcells behind us, we come to the final puzzle. Fittingly, for both the name of this title and the (almost) endless puzzles that its Random Puzzle Generator has in store, it's an infinity symbol.




As always with the final puzzle, we're given some clues as to how to progress. First, each column will contain an odd number of blue hexes; secondly, the clusters of hexes inside of each infinity loop will each contain exactly seven blue hexes.

We need to start with the Blue 8 hub we're given to us. The overlay covers nine active hexes; one is already blue, and the others are orange. So we have to mark seven more. Our biggest clue here is that both the hub and the blue hex we're given fall into the central column, which contains only four active hexes. Since the column has to contain an odd number of blue hexes, only one of the two remaining orange hexes can be marked. As a first step, then, we can mark all hexes inside the overlay which do not fall into this column:

One of the blue hexes we just marked falls into a diagonal governed by a -2-, so we can eliminate the hexes immediately adjacent to it within that line. Doing so eliminates a hex within the central column, leaving just one left to mark. This will also complete the blue hex requirements for the Blue 8 overlay.



We can now immediately complete the Blue 7 overlay we just uncovered at the bottom-center. When expanded, it covers only seven total active hexes; just mark the last two that it covers.

One other thing we want to do. Notice that the columns on either side of the middle contain only two total hexes; we've already marked one hex within each. Since all columns only get an odd number of blue hexes, we can erase the top cells from each of these. The "1" and "0" revealed are then easily solved:



Go ahead now and solve the "1" on the upper-right edge of the "0" if you didn't do so with the last step. Now, the column in which that "1" resides has been reduced to four active hexes, three of which are blue. We have to erase the final hex of the column, since marking it would give it an even number of blues. The "1" that this uncovers has a blue hex below it. Erase the two orange hexes on its right. The "2" that we'll uncover has only two active hexes to work with. Marking both also gives a second blue hex to our diagonal headed by a -2- from before, letting us erase the rest of that line:

Let's now erase the hexes from the "0" we uncovered at the top-right. Doing so gives us three more obvious blue hexes to mark. First, the two empty "1" cells uncovered have only one active hex apiece to deal with. Secondly, the "1" on the bottom-right edge of the "0" falls into another column containing only two cells; we now need to mark the bottom hex of the column.

Now, expand the Blue 5 overlay in the cluster we're trying to solve. It already covers four blue hexes; we can easily see that the fifth will come from whichever hex we mark to complete the empty "3" cell we uncovered during the last sequence. So erase the two hexes covered by the overlay that are not connected with the "3":



The -2- that we just revealed is easily solved due to the way its active hexes are distributed. Erase the one connected to the blue hex, then mark the lone hex on its bottom-right edge. This leaves the "3" with only one final hex to claim for its third blue one, and marking it gives the "2" we just uncovered on the upper-right edge of the -2- its second blue hex. We can now erase the orange hexes to the right of the "2":

We can solve two of the columns here now. Let's take the second and third columns within our cluster. Each now contains an odd number of blue hexes, with only one unsolved active hex at the bottom of each. We need to erase these hexes next. At the bottom, we will uncover another "1" with only one possible hex to claim, so mark it next.

Now, expand the Blue 4 overlay at the bottom-center of that cluster. It expands to cover four blue hexes; erase the two orange hexes inside its radius, then erase the hex above the "0" we uncover.

Remember our rule: We need seven blue hexes inside this cluster. We have six. Where will the seventh come from? Well, the hexes we just erased reduced their respective column to only one active hex. Since we still need a blue hex for that column, marking it will actually satisfy both requirements. So mark that hex, then erase the final two hexes from this cluster:


We still have the cluster inside the first infinity loop to complete. Helpfully, the final column in that section contains an even number of blue hexes and has only one remaining unsolved. So now, we want to mark this hex to give it an odd number.

We're left with a Blue 6 and a Blue 5 on top of each other, and reconciling them is the only way forward. First, we'll examine the Blue 5; expanded, the overlay covers four blue hexes already, but it also covers six orange hexes! Take note of the six it covers, then retract the overlay.

Now, expand the Blue 6 overlay. This one only covers four blue hexes. Like the Blue 5, it also covers a total of six orange hexes. However, five of those are shared between both overlays. The fact that the Blue 5 overlay only needs one more blue hex tells us that of the five shared between each, only one of these can be marked. So the sixth orange hex covered by the Blue 6 overlay is now a guaranteed blue hex; additionally, we can eliminate the one orange hex covered by the Blue 5 overlay that is not shared by both:

The cell that we just marked allows us to complete the diagonal headed by a "4" from the upper-left corner. Now that the line contains four blue hexes, we can erase the last two. Next, clear out the "0" that we just uncovered. This actually opens up a chain that takes us down the left side. The empty "1" cells at each end of this chain have only obvious blue hexes to claim. Mark both; then, because the second column now has only one active hex, mark its bottom hex. That gives a blue hex to the "1" at the bottom, and we can erase the hex from its bottom-right edge. Follow that "0" out, as well:

We're coming to the end of Puzzle 6-6 and of Hexcells Infinite! Here's where we left off:



We'll get one more elimination from the Blue 1 overlay we uncovered at the bottom-left. When we expand it, it covers one blue hex already; we can erase the lone orange hex in its radius.

Now, the inner cluster within the first infinity loop has four blue hexes, so we need three more for it. Ignoring all of the overlays for just a minute, we can take a more straightforward approach due to the layout.

The first column included within this cluster now contains only two active hexes; we have to mark one of them. This will become the cluster's fifth blue hex. Now, at the bottom-center of the cluster, we still have an empty "2" cell with no blue hexes. So the overall cluster's sixth and seventh blue hexes will come from the blue hexes we give to the "2". So wouldn't it make sense to be able to eliminate everything not connected to these entities?

The column in which our "2" is embedded has now been reduced to three total active hexes, two of which are already marked. We have no choice now but to mark its final hex. Doing this gives the "3" we just uncovered a third blue hex. Erasing the final hex directly below the "3" leaves the column with just two active hexes. Since one is already blue, we need to erase the other one.

Now, we can return to the overlays. The Blue 5 at the top-center of the cluster now covers just five active hexes. The one we mark to finish it will also give the first column of the cluster the sole blue hex it needs. When we erase the last orange hex from the column, we uncover a "2" with only two active hexes to work with. Marking its second lets us complete the cluster by erasing its final hex:


We're done now. The puzzle contains only four final orange hexes, and the "REMAINING" counter shows that we have exactly four blue hexes to mark. So mark the final four to complete the puzzle, Chapter 6, and Hexcells Infinite!!!!!!!!



So we end the game with an honest-to-goodness puzzle to solve! This one, despite its small size, is actually reasonably difficult to to work through, though certainly not of the difficulty of 6-5. When I first worked through it, I was convinced that it could not be solved logically; amazingly, perhaps even ironically, while I solved 6-5 the very first time without making a mistake, it took me a few tries for this one on my first playthrough. Even working through the solution a third time in writing this guide, I realized a few things that never occurred to me on the initial playthrough--in particular, erasing the hexes from the first cluster that were not connected to the empty "2" cell or the first line of the cluster towards the end.

So the campaign levels of Hexcells Infinite are finished. But we're not done yet! We still have one more achievement to unlock, and one more feature of the game to talk about: The Random Puzzle Generator! This also features the ability to load custom puzzles; we'll talk about that a little bit, as well. And at the end, I'll share my final thoughts on the game and the series, as well as a special treat that I think you guys will enjoy. :-)

Hexes Earned for Completing This Puzzle: 25

Hexcells Infinite gives us a new feature that ensures the experience doesn't necessarily end with completion of the campaign: The ability to generate random puzzles. By clicking on the Infinity Button at the bottom of the title screen, you'll load a special menu from which you can choose several different options:



The game's final achievement is, "60 down 999,999,940 to go." To unlock it, it is necessary to complete 60 random puzzles!!!

As you can see in the graphic, I'm at 57 as of this writing. I'm going to go through puzzles using the current date, a random seed, and a number of my choosing for this guide, and for my final three to unlock the achievement. However, I'm not going to do walkthroughs of them. I will illustrate how the first random puzzle evolves through screenshots and annotations and then just briefly touch on the other two I will use to unlock the achievement. The mechanics are exactly the same, and all of the puzzles I have encountered can be solved logically just like any other. What makes these puzzles different, however, is their construction; you can easily tell the difference between most of these puzzles and the hand-crafted ones we have worked up to this point.

That said, I'm going to launch a puzzle using today's date (19042015 as of this writing) and get started!



Here's the puzzle:



Notice that we are given a lot of blue hexes to start with; this is fairly typical of the random puzzles. Sometimes, we'll find empty hexes that have their necessary blue hexes from the outset. It's also common to find zeroes scattered around. In this particular puzzle, there is one on the left side about halfway down. We're also given line headers to work with. Another trait is that you will sometimes see patterns repeat themselves. For example, you might find a lot of empty "4" cells with exactly four active hexes around each one, stacked diagonally down the grid like a staircase.

I'm not going to write too much about these puzzles. I will add annotations to the screenshots to show how they evolve, but the main focus is on showing off the types of puzzles you will encounter.





Another trait of custom puzzles is that it's sometimes helpful, if not outright necessary, to skip around.




The puzzle is about 3/4 of the way solved; I'll need to focus on specific clusters to continue further:







I found a move I missed. :-)







And here's the screen you get when you complete a random puzzle:



And with that, there are only two more puzzles I need to unlock the achievement. The next one will use a random seed:



This one is very similar to some of the campaign puzzles. I won't walk through it; punch in the seed and give it a try! Start at the bottom-center and work upwards; be very careful with shared hexes as the vast majority of the puzzle logic depends on them. Here's how it evolves at the final step:



And for the final puzzle, we're going to use my birthday: 02191978 (I'm using traditional MMDDYYYY format here):



This one is in the vein of our first random puzzle; here's how it evolves at the final step:



And with that, the 60th random puzzle is finished; I messed up a bit here, but you can sort of see the "Achievement Unlocked" graphic at the bottom-right:



Here are a few more random seeds you may enjoy playing through:

13572468
11335577
24681012
00000000 (This is much more interesting than you might think!)


The final new feature of Hexcells Infinite is its ability to load custom levels. To find them, go to this page on Reddit:

http://www.reddit.com/r/hexcellslevels/

One word of note: Custom puzzles do not count towards the final achievement! Only those generated by the Random Puzzle Generator are counted.

Puzzles are distributed in a plain text format. When you find one, you highlight and copy the entire text of the level to the clipboard. Then, launch Hexcells Infinite, and on the title screen, the option "LOAD CUSTOM LEVEL" will become available as seen here:



Now, just click on this button to load the customized level:



That image comes from the following custom level:

https://www.reddit.com/r/hexcellslevels/comments/2zs8tw/levelwelcome_to_hexcells/

These new features ensure that Hexcells will live on far beyond the campaign levels. Happy puzzling!!!

Well, we have reached the end of our journey through the Hexcells universe. But before I wrap up the series with my own final thoughts, I have something special for you. About 3/4 of the way through creation of the Hexcells Plus and Infinite guides, I got the idea of asking creator Matthew Brown if he might be open to an E-mail interview, so that we might be able to get a glimpse into the the thought processes involved with making the games. Much to my surprise and delight, he agreed, and I have it available for all of you. I thought this would be a great way to conclude this series of strategy guides. I want to thank Matthew for taking the time out to do this, and I hope you all enjoy it. :-)

1. How did the idea for Hexcells come about?

After completing my first game, which had a long and messy development, I wanted to try a smaller and more focused project. I thought a logic puzzle game would be a good fit for this, and being a big fan of Picross I wanted to try something in that style. I tried to emulate some of the logic and thinking that goes into solving a Picross, but in a new format and style.

2. Approximately how long did it take you to complete each game?

Hexcells was roughly 5 months, Plus was around 3 and Infinite was about 7.

3. When you created the first game, did you always know that you wanted it to be a trilogy, or did that decision come about after watching the reception of the original?

No, it was only planned as a single game, but it had such a great reception that I immediately started work on a follow up - intended as an advanced set of levels for people who had played the first. After Hexcells Plus I moved on to working on a brand new game but again the reaction was so positive and people were keen for more, so I went back to make one final game in the series.

4. As I mentioned in my original E-mail to you, I first learned of Hexcells from Rock, Paper, Shotgun's initial coverage. As far as I've seen, there are still no other games journalism outlets covering the series. What is your reaction to this? Did you personally contact any other games journalism outlets to try and garner more coverage of the games?

With the first game I made a big effort and tried contacting a lot of different places, but RPS was one of only a handful of sites who were interested in the game. With the subsequent games I didn't really do any promotion because I figured if the sites weren't interested in the original game they probably wouldn't be interested in the sequels. I think it didn't get a lot of coverage because at first glance it looks a lot like Minesweeper and so didn't really stand out.

5. I have heard Hexcells likened to be a sort of spiritual successor to the old game Minesweeper. Do you feel that this is a fair comparison?

The 2 games do share the same basic mechanic and a similar look but I think the logical steps a player goes through when solving them are quite different. I've never really played much Minsweeper because of it's lack of logical solving, so it wasn't really an inspiration for the game.

6. Hexcells is a very simple game to play, with a very simple, even minimalist, interface: Just the board, the two progress counters, and the music. Did you consider making the games more complicated? Was there a particular atmosphere you had in mind for players?

Minimalism was definitely a theme of the game. I tried wherever possible to cut additional rules, mechanics and UI stuff and only make things as complicated as they needed to be. I think a sign of a good puzzle game is when it is able to produce many interesting puzzles from few mechanics, and only introduces new rules when all possible combinations have been exhausted.

7. What do you want players to feel when they play Hexcells, especially for the first time?

I wanted it to be a relaxing experience. I think the process of solving a puzzle can be very satisfying and calming, so I tried to emphasize that in the music and visuals as well.

8. In terms of difficulty, I found Hexcells Plus to be, overall, the most difficult of the trilogy, mainly because the difficulty seems to spike much more quickly than in the original and even in Hexcells Infinite. Was this intentional? How did the overall difficulty curve come about for each game, and for the trilogy as a whole?

Yes, Hexcells Plus was a reaction to the most common complaint about the first game, that it was too short and too easy. I think with Infinite I realised I may have over-done it and tried to make the ramp up in difficulty less sudden.

The difficulty across the puzzles in each game is structured like a sawtooth wave that increases with each level set. So the last level of the previous set is harder than the first level of the next set. This gives a nice escalation but also gives the player a rest after a particularly hard puzzle, before building back up again.

9. One of my favorite puzzles from a design perspective is Puzzle 6-3 of the original. I really liked the idea of having large, concentric hexagons comprised of the individual smaller hexes. What are some of your favorite puzzles from both a design and a player's perspective?

I really enjoyed designing levels where I placed a restraint on myself, such as making a complex puzzle using only column numbers etc. My favourites of these are the smaller puzzles in Infinite like 6-3. They're very concentrated puzzles where every step is a mini-puzzle and every piece is there for a reason. They are quite fatiguing for the player so you have to space them apart, but I think they are the most fun to solve as well.

10. One of the more unusual aspects of Hexcells, compared to a lot of other puzzlers I've personally played, is that all of the puzzles truly can be solved using logic alone. Was it always a goal to ensure that players who took the time to learn the game could win without ever having to guess?

This always surprises me when people say this. I don't consider anything that requires guessing to really be a puzzle, and I don't play any games like that. So there was never any question, the game always had to be 100% logic driven.

11. How would you describe the overall response to the series by the gaming community?

It's been incredible! I've received a lot of emails from people who really loved the series and the games have a lot of really positive reviews on Steam.

12. As of this writing, the original Hexcells has almost 1,000 user reviews on Steam. How do you feel that the games' availability on the Steam platform has helped or hurt you in terms of exposure?

It's helped enormously. Before releasing on Steam the only way people had heard of the game was through RPS, but releasing on Steam exposed the games to a vast new audience. In the first few days on Steam the games sold more than they had in all the months I'd been selling them through my website.

13. Some of the puzzle solutions are incredibly involved and intricate. When you were designing some of those levels, was there ever a point where you got turned around in the design or even stumped yourself during playtesting?

Absolutely. Even coming back to play a puzzle a few hours after I'd finished designing it I was essentially playing the puzzle from scratch. I think there's just too much information to hold in your head at once, and even if you have a vague idea about how the puzzle is laid out, it misleads you more often than it helps . There were more than a few times in play testing where I was convinced there was a fault in the puzzle and I'd have to go back and change it only to discover I'd missed something.

Here's the conclusion of my E-mail interview with series creator Matthew Brown.

14. What are some common criticisms that you may have received about the Hexcells games?

I think the level generator in infinite is the main one. It is only able to produce puzzles of low to moderate complexity due to limitations in the AI solver I use to check that the generated puzzle is solvable. As most people complete the campaign first and then try the random levels, they are often a disappointment.

15. What are your favorite memories about designing the games?

I think the first time the prototype yielded a complex interesting puzzle was really exciting. I messed around with a few different prototypes (originally the pieces were all triangular!) but at that moment I knew I was onto something interesting. The RPS review of the first game was a big deal as well. I'd been reading the site for years so to see a review of something I'd made on there was really special.

16. One feature of Hexcells Infinite that I know is appreciated by players--and that I personally utilized in the course of writing the strategy guide--is the ability to save your progress. Do you think this is something you might ultimately adapt to the first two games?

I've thought about it, and it would be nice to have parity across all 3 games. It would require a bit of re-engineering in how the levels are stored in the older games and I would also need to swap over to the new save file format introduced in Infinite, without losing anyone's existing save data. If enough people were interested it's something I could do, but unfortunately it's not trivial.

17. Hexcells Infinite is the end of the trilogy, but the Random Puzzle Generator and ability to load custom levels ensures that the Hexcells experience can live on. Did you always have in mind to do something like that for Infinite, or is it something which came about later in the development process?

Yes, after Hexcells Plus it was clear that people's appetite for Hexcells puzzles was far greater than the rate I could produce them at, so I set about designing a new game with the puzzle generator being the focus from the start. Custom levels were not in the game's original release and were entirely the creation of 2 fans of the game on the Steam forums (BlaXpirit + sekti), I just added support for their levels at my end. If anyone has not tried any custom levels yet there are some great puzzles on the reddit ( http://www.reddit.com/r/hexcellslevels/ ).

18. Do you think you would ever do another entry for the Hexcells series down the road if the community encouraged it?

Probably not. I think I exhausted all the ideas for Hexcells puzzles that I have, and don't want to end up re-treading the same ground. Also adding more rules or mechanics to the game would get away from the idea of minimalism at the game's core. I'd rather take what worked from Hexcells and start fresh with a whole new puzzle game in the future.

19. I know that Hexcells isn't the only game/series you have worked on. Admittedly, I need to check out your other works, as well, LOL. What else can we expect from you in the future?

Outside of puzzle games I've also worked on 2 music based games. I have background in Music and am interested in how audio can synchronise with gameplay (there's even a little bit of that in Hexcells). I'm currently working on a music game called Sound Shift which is a sort of endless runner with obstacles created by the player's music. After that is complete I'd quite like to have a go at a new puzzle game.

20. When you aren't designing games yourself, what types of games do you like to play? What are some of your personal favorites?

I play all sorts of games, at the moment I'm hooked on Bloodborne. Some of my favourites include Super Metroid, Resident Evil 4, Portal, wip3out , Shadow of the Colossus, Rez and of course Picross!

21. And finally, is there a message that you would like to pass along to your fans and supporters?

I'd like to say a big thank you to everyone who supported the games, sent me kind messages and recommended the games to friends. Because the games didn't get much press coverage a lot of their success is due to word of mouth and user reviews etc, so I really appreciate it. :)

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

After I submitted the original interview, I sent him a follow-up question regarding the possibility of porting Hexcells to mobile devices, either as a straight-up conversion or perhaps as a compilation of some sort. Here's what Brown said:

"I briefly looked into doing mobile versions but could never solve the problem of how to fit them on the screen. If they were left the size they are now you would need to add in some sort of screen scrolling function, but I've always disliked scrolling in these kinds of games and think all the information needs to be visible at once. If you scale everything down too much you can no longer accurately tap on the correct hex. All the solutions I could come up with to these problems seemed in-elegant and added too much complexity, so in the end I decided not do a mobile release."

While I think it's a shame that we probably won't see Hexcells on portable devices, Brown's reasons make sense. It's easier to work a complex puzzle when you can pore over the entire board without having to scroll around. Still, I hope it someday becomes feasible as this type of game seems like a natural fit for such devices--but only if it can be done well.

I am greatly appreciative to Matthew Brown for taking time out to grant me this interview. It really meant a lot to me to let me include his thoughts in this final guide of the trilogy. It's a great send-off to the series.

And with that, we end our journey through Hexcells, but the Random Puzzle Generator and the ability to load custom puzzles within Infinite ensures that we can still get another taste of Hexcells whenever we want. If you would like to try your own hand at making custom levels, you can download the Sixcells level editor here:

https://github.com/BlaXpirit/sixcells#windows

I find it a travesty that almost no games journalism outlets have bothered to cover Hexcells. If I didn't happen upon Rock, Paper, Shotgun's review of the original, I might never have heard of it unless it came up in my Steam discovery queue. I don't understand how a game so masterfully crafted can be ignored by so much of the gaming press, but I guess that's the chance any game developer takes. I, for one, am glad to have this series. Sometimes, I want something I can just pick up and play, and something I can use my brain on instead of needing to smash four buttons at a time to pull off a complicated technique, or a game that only gives you mindless slaughter. Hexcells gives us that.

It's easy to see how much thought had to have gone into creating the levels. While I like the Random Puzzle Generator, it is true that a lot of the puzzles don't show the same attention to detail that Brown's hand-crafted levels demonstrate. Still, I am grateful to be able to punch in a random eight-digit number and generate a fresh puzzle whenever I want. And the campaign puzzles are difficult enough to warrant replaying.

It also heartens me that the gaming community overall has been so receptive. It seems that just about everyone who has played the games has enjoyed them, and I'm always glad to see a new game developer who has crafted something this good be able to succeed, in spite of the lack of attention given to it by the gaming press.

Naturally, the games have their frustrating moments, and it can be annoying to stare at a puzzle for half an hour without being able to make a move. But then, there's that "Ah-ha!" moment that triggers something you missed earlier. In the course of writing now three strategy guides, I continued finding simpler approaches to some of the puzzles that I never found in one or even two playthroughs. This is a great series of puzzle games, and gaming is better off for having them.

With that said, I want to thank everyone for reading through these guides and playing through the games with me. When I published the original Hexcells guide late last year, the comments I received were very positive, and seeing the overall response over the last six months has been a big encouragement to completing these entries. I apologize that it has taken me longer than I had hoped, but I hope you guys agree that the extra time was well spent in putting out a comprehensive series of guides. Your support of this project means the world to me. And for Matthew Brown himself to show his support by granting me an interview is, to me, something special. Thank you again for joining me on this trip through the Hexcells series. Take care, everyone. :-)

I intend to perform a second round of revisions to this guide; due to its length and complexity, I want to be doubly sure that there are no major flaws. As far as I can tell, anything truly major has been fixed. The next round of revisions will focus more on grammar, formatting, spelling, and the screenshots. I believe all of the screenshots are fine, but I may make tweaks to some of them. If anyone finds anything truly glaring that needs to be fixed right away, please let me know. Otherwise, expect the new revisions to be complete within the next few weeks.

For right now, I'm going to focus on completing the Hexcells Plus guide within the next couple of weeks. Only Puzzle 6-5 remains to actually be written out. My plan is to begin revisions on the earlier sections so that by the time 6-5 is complete, there will be very little left to revise, leading to a quality release.

Once all three guides are up, I'll go back through the original Hexcells guide and clean up any minor problems it may have, as well.

Happy reading!!


Sunday, April 26th, 2015: Version 1.0 published (original release)

Saturday, May 9th, 2015: Version 1.0A released (adds links to the previous two guides now that Hexcells Plus is complete)

Saturday, July 18th, 2015: Version 1.5 revisions completed:

Screenshot edits/redos in the following puzzles:

• Chapter 1: Puzzle 1-6
  
• Chapter 2: Puzzles 2-2, 2-3, and 2-6
  
• Chapter 3: Puzzles 3-1, 3-2, and 3-4
  
• Chapter 4: Puzzles 4-1, 4-2, 4-4, and 4-5
  
• Chapter 5: Puzzles 5-1, 5-2, 5-4, and 5-6
  
• Chapter 6: Puzzles 6-3 through 6-5

Most screenshot revisions only required reworking of annotations, such as clarification or fixing typos. A few required that additional highlights be added.

None of the puzzle solutions required any major overhauling. While virtually all pages required some degree of editing for clarity or the occaional typo I missed before, the vast majority of the guide is the same as before.

Monday, December 28th, 2015: Version 2.0 revisions completed:

I've changed the image coding throughout the guide to help speed up page loading times, consistent with the previous two entries. However, because of the sheer number of images, the Steam renderer may very well continue to lock up, even with the reduced bandwidth being consumed. If this happens, please view the guide in an external browser; you should notice that it loads considerably faster. I apologize as there is essentially nothing I can do about this. I'm hoping that Steam will make this feature more robust so that it will be able to more easily support strategy guides of this size.

I've also made very minor edits in a few places; these were so minor that I didn't even bother keeping much track of them. I also added highlights to a couple of screenshots and reuploaded; again, these were not significant alterations.

These are intended to be the final revisions to the guide unless something major is uncovered in the future. Please leave a comment if you find anything that I have missed to this point, and I will look at it ASAP. In particular, let me know if there are any issues with image corruption or anything just not loading properly so I can reopen a support ticket with Steam.