Three players enter a room and a red or blue hat is placed on each person's head. The color of each hat is determined by a coin toss, with the outcome of one coin toss having no effect on the others. Each person can see the other players' hats but not his own.

No communication of any sort is allowed, except for an initial strategy session before the game begins. Once they have had a chance to look at the other hats, the players must simultaneously guess the color of their own hats or pass. The group shares a hypothetical $3 million prize if at least one player guesses correctly and no players guess incorrectly. What strategy should they use to maximize their chances of success?

(From - http://www.princeton.edu/~sjmiller/riddles/riddles.html)

(In reply to re: Probability by James)

You are correct up to a point. In a coin toss, each coin is an independent event, so even thogh the if you just examine one specific coin, the chances are 50/50 whatever the configuration of the other coins. This corresponds to the gamemaster choosing which hat each man will wear.

If each man had to make a guess, and if he won or lost because of it, it would equally apply to his chances of winning. But they men confer beforehand, each man can pass, and they win or lose as a group. Their answers are not independant of each other, nor of the gamemaster's choices: they are uniquely determined by the configuration of the hats.

Construct a truth table and see for yourself.

Posted by TomM on 2002-12-15 18:50:39