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345 logic/smullyan/black.hat.p




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This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

345 logic/smullyan/black.hat.p


Three logicians, A, B, and C, are wearing hats, which they know are either
black or white but not all white. A can see the hats of B and C; B can see
the hats of A and C; C is blind. Each is asked in turn if they know the color
of their own hat. The answers are:
A: "No."
B: "No."
C: "Yes."
What color is C's hat and how does she know?

logic/smullyan/black.hat.s

A must see at least one black hat, or she would know that her hat is black
since they are not all white. B also must see at least one black hat, and
further, that hat had to be on C, otherwise she would know that her
hat was black (since she knows A saw at least one black hat). So C knows
that her hat is black, without even seeing the others' hats.

 

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