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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?

  Submitted by Math Man    
Rating: 2.0000 (1 votes)
Solution: (Hide)
Suppose C's hat was red. If B's hat was red, then A would know that his hat is not red. Since A did not know that, B's hat cannot be red. Therefore, if C's hat was red, then B would know that his hat is not red. Since B did not know that, C's hat cannot be red. A similar argument shows that C's hat cannot be yellow. Therefore, C's hat is blue.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Three logicians walk into a bar ...Steve Herman2014-04-26 11:26:15
SolutionSolutionhoodat2014-04-22 01:06:22
Solutionsymmetry- spoilerAdy TZIDON2014-04-16 12:29:15
SolutionThe orthodox way (spoiler)Steve Herman2014-04-16 10:59:37
Some Thoughtsmini-spoilerAdy TZIDON2014-04-16 10:29:05
obvious answer if possibleJer2014-04-16 10:26:41
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