Three logicians, Albert, Bill and Carl, are wearing hats, which they know are either black or white but not all white. Albert and Bill can each see the other two logicians, but not Carl, who is facing away and cannot see them.

Each is asked in turn if they know the color of their own hat. The answers are:

Albert: "No."

Bill: "No."

Carl: "Yes."

What color is Carl's hat and how does he know?

(Taken from http://einstein.et.tudelft.nl/~arlet/puzzles/logic.html)

Albert must have seen either 2 black hats or 1 white and 1 black.

Assuming that Carl was wearing a white, Bill would have known his was black since he knew Albert's answer.

So for both Albert and Bill not to know, Carl's must be Black

Posted by Henry on 2002-07-15 09:09:07