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)

The only way any of them could know their own hat color is if they were able to see that the other two were white.

Since neither Albert nor Bill knows his hat color, each must have been able to see at least one other black hat.  If Carl's hat were white, then at least one of the first two would have seen two white hats and known that his must be white.

Therefore, Carl knows he must have a black hat.

Posted by Kevin on 2006-04-13 19:28:03