Two physicists, A and B, and a logician 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 C know?
I could not figure this one out.
A is the first to answer. Since he said no, that means B and C don't both have white hats. This leaves 6 possible cases (in order ABC).
WWB
WBW
WBB
BWB
BBW
BBB
Now, WBW is easy to exclude. If B sees two whites, then he knows his must be black.
Also we can exclude BBW. For, if A didn't know, but B sees black and white, he knows that he must be black, (for then A would know, as he would see two whites).
The only possibility then is that C has a black hat!