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:
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 albert will know his own hat color is if both hats in front of him are white, his is black because they are not all white. so after he says no, bill and carl know that both their hats are not white. the only way for bill to know his hat color, now, is if carl's hat is white, his hat must be black since from albert's statement both are not white. bill didn't know, so carl's hat much be black.