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 An answer of balance *Fixed without typo by Michael)

"Many people have said that there are 2 of each colour hat and indeed this is correct (at least I believe so), however there has not been a valid explanation as to why this must be."

I object! There are several valid explanations. The first 3 comments are excellent explanations as well as several others including my own that I posted that are within this comment list. I believe it to be correct that it isn't necessary to go through each possible scenario to proove or explain this soltuion. They all seem fairly straight forward to me.

Posted by Michael on 2004-11-30 01:30:00