A logician invites 6 of his logician friends to help him celebrate his birthday. Each of the 6 guests is wearing a hat which is either red, yellow, or blue, and the logician host informs them all that there is at least 1 of each color. After they eat the cake, the host stands up and exclaims there is a special party prize for the first person who can deduce what color hat is on their head. The party guests all looked around the room at each other but no one claimed the prize immediately. Suddenly all 6 guests stood up and correctly identify what color hat was on their head.

What were the colors of their hats and how did they know?

There are two hats of each color. If there were only one hat of any given color, then the person wearing that hat would know immediately from the fact that no-one else was wearing one. THEREFORE, there must be two hats of each color, and all the logicians have to do is notice which color hat they can only see one of, and they must be wearing the other of that color.

Either that, or they all suddenly realised that they could see their own reflections in a glass table. ;-)

Posted by Jenny Turner on 2004-11-17 07:10:13