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| Colorful hats (Posted on 2014-04-16) |
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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?
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Submitted by Math Man
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Rating: 2.5000 (2 votes)
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Solution:
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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.
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