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 Colorful hats (Posted on 2014-04-16)
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?

 See The Solution Submitted by Math Man Rating: 2.0000 (1 votes)

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 Solution | Comment 5 of 6 |
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

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