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

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

Comments: ( Back to comment list | You must be logged in to post comments.)
Probablility | Comment 10 of 16 |
After looking at the URL Raveen submitted, it looks like the point is not to come up with a foolproof strategy, but to maximize the odds of winning. I am adjusting the problem accordingly.

TomM's answer seems to be the correct one.
  Posted by levik on 2002-12-11 07:25:19
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