Three logicians, A, B, and C, are wearing hats, which they know are either black or white but not all white.

logic/smullyan/black.hat

Problem

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?

Show solution

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.