10-11-08

I learned a new puzzle!

The Hat Game is played in teams of three. Each player in a team has a red or blue hat placed on his head, determined at random, and can see his teammates' hats but not his own. With no communication, each player must guess the color of his hat, writing down "red," "blue," or "I don't know." If all three players write down "I don't know," the team loses. If one or more players guess incorrectly, the team loses. If at least one player writes down a color and all of the colors are correct, the team wins.

Teams are given time beforehand to develop a strategy. The strategy can be anything, for example, "If Bob sees that Alice has a red hat, he should write blue," or whatever. What strategy should you use to maximize your odds of winning?