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?

You answer this problem by seeing the reactions of all the other logicians first before you can do anything. If you notice that no logician stands up immediately then you know there cannot be 4 yellow 1 red and one blue (or any mixture) or 3 yellow 2 red and one blue (or any mixture). So you can deduce there are 2 yellow 2 red and 2 blue hats in the room at the same time. This allows you to just simply count all the other hats and name the color you only see one of. But if the simpler situation occurs where you see 4 of one color and 1 or another you can just stand and call out the one color you dont see. Also, if you see 3 of one color and 2 of another you can stand and call out the color you dont see. To solve any doubt if you see 2 yellow 2 red and 1 blue you have to call out you are wearing a blue hat because if you were wearing a red or yellow the person in blue would be able to call out with no doubt he was wearing the blue hat seeing the 3 yellow/red and the 2 red/yellow.

Posted by james on 2005-02-22 01:56:58