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?

It looks like if there were six people, and at least 1 of each color, there's only one way they all would have known.

Since they were all logicians, if any one of them would have looked around and seen only 2 different colored hats amongst the other 5, then they would have known immediately that his or her hat was the remaining color. However, this did not happen, and every one seen 2 hats with 2 colors, 2 hats with different colors, and 1 hat which had the color that was on his or her head. The act of each's hesitation prooved the hats were split equally among the 3 colors at 2 each.

 

Posted by Michael on 2004-11-27 05:50:14