| 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? |
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. |