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Colorful hats (Posted on 2014-04-16) Difficulty: 2 of 5
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 The orthodox way (spoiler) | Comment 3 of 6 |
From A's statement, B and C know that their hats are not both yellow and are not both red.  If they were, then A would know that his hat was not the same color as the two hats ahead of him.

Considering that, B's statement tells C that his hat is not yellow or red.  If it was, then B would would know that his hat is not  the same color as the one hat ahead of him.

Therefore, C knows that his hat is blue.

Edited on April 16, 2014, 11:00 am
  Posted by Steve Herman on 2014-04-16 10:59:37

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