RIP NEAMC 2016 - DON'T GO TO IT UNLESS YOU ARE THE BEST AT MATHS IN THE WORLD.

Check out the first messed up question below.

A question for everyone to solve: In a team building game, Charlie, Martha and Jamie have to figure out a 3 digit number. They are told the first, second and third digit, respectively. They are not allowed to say the digit given to them. They need to select the correct number from the following 15 numbers:

154, 171, 188
223, 236, 268, 273
328, 336, 466, 376,
423, 451, 462, 482

Martha: I don’t know what the number is neither does Jamie
Jamie: Martha is right, I don’t know the number. I know that Charlie also does not know.
Charlie: I still don’t know the number, but I know that Martha still doesn’t know too.
Martha: Unfortunately, it is true
Jamie: What a bummer, I still don’t know the number.
Charlie: Well now I know the number!

What is the correct number?