A, B, and C were in a line blindfolded. They each had a hat put on their heads. They knew that the hats were taken from a box of 2 red, 2 yellow, and 3 blue hats. When the blindfolds were taken off, A could see B's and C's hats, B could only see C's hat, and C could not see any hats. They made the following statements.
A:I cannot tell what color my hat is not.
B:I cannot tell what color my hat is not.
C:I can tell what color my hat is.
What color is C's hat and how does C know?
If A sees two red or two yellow hats, then he knows that he cannot have that color. So that combination is not possible. This leaves seven possibilities for B and C in order:
RY, RB, YR, YB, BR, BY, BB
If B sees a yellow hat on C, then he will know that he doesn't also have Yellow, because if he did, then A would have known. Likewise, if B sees a Red had on C, then he will know that he doesn't have a Red hat. But if B sees a blue hat on C, then B will not be able to tell what color his hat is.
Therefore, C wears Blue.
Posted by hoodat
on 2014-04-22 01:06:22