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?

I'm going to post a solution without reading those previously posted because (as I remember) it really pisses SilverKnight off.

Since all of the guests knew that there was at least one of every color of hat, if they did not see any one color they owould know that they were wearing that color.  None of them immediatly knoew the color of their hat so they must all have seen at least one of every color.

This means that there must have been at least two hats of each color (each guest would be able to see a hat on someone else that was the same color as the one the that first guest was wearing (the fact that the guest did not know at that point what color he was wearing is irrelevant))

Since there were at least two of each color and there were only six then there must have been EXACTLY two of each color. (this is obvious but then again I'm an obvious type)

The logicians are all cleverer than I so they would have already deduced all that I have deduced.  THerefore when they see only one hat of a specific color they now that they must be wearing that color as well.

I'm sure that penny will have come to the same conclusions in a much more elegant manner

Posted by FatBoy on 2004-11-17 09:46:14