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?

(In reply to re: Solution by jmnw)

jmnw wrote: "3 yellow 2 blue 1 red. A person with a blue hat on would see all colors represented and would have no way of knowing which color they 'duplicated' "

But the logician in the red hat would have claimed the prize immediately. He would have known his hat was red, since he would have seen only yellows and blues, and he knew all three colors were represented. Since the puzzle states that the party guests all looked around the room at each other but no one claimed the prize immediately, the hats could not have been 3 yellow, 2 blue and 1 red.    

Posted by Penny on 2004-11-19 13:23:54