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Return of the hats (Posted on 2002-12-10) Difficulty: 3 of 5
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 -

See The Solution Submitted by Raveen    
Rating: 3.6923 (13 votes)

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solution | Comment 15 of 16 |
The possible hat configurations areas follows (each occurs with equal probability 1/8)


In six of these 8 cases, 1 player will see two hats of color opposite to his. In these six cases, the other 2 players will see two different colored hats. If the players agree to the rule that they will pass if they see different hats, and guess the opposite color if they see the same color hats, then they will win in these 6 cases. In the other 2 cases they lose.

Overall, they win 6 out of 8 times with this strategy. (I offer no proof, just this example strategy - proof by jawboning?)
  Posted by jim on 2003-10-29 18:14:24
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