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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 -

  Submitted by Raveen    
Rating: 3.6923 (13 votes)
Solution: (Hide)
TomM has submitted a solution here that would allow the players to win the prize three out of four times.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Proving best strategyGamer2008-07-12 16:57:03
solutionjim2003-10-29 18:14:24
Some ThoughtsNo SubjectCheradenine2002-12-18 23:07:37
re(2): ProbabilityTomM2002-12-15 18:50:39
re: ProbabilityJames2002-12-15 15:05:03
what i would doJames2002-12-15 14:55:52
Probablilitylevik2002-12-11 07:25:19
re: Best OddsJeremy2002-12-11 07:03:43
Best OddsChuck Bruce2002-12-11 04:46:00
Some ThoughtsHighest probabilityGeorgio2002-12-11 04:23:18
If movement is allowed....jagadish babu2002-12-10 23:27:52
Some ThoughtsProbabilityTomM2002-12-10 16:05:59
Coin toss / hats recievedabu2002-12-10 14:40:40
re: signalslevik2002-12-10 09:49:50
Some Thoughtsre: Cory'ssach2002-12-10 09:48:12
No SubjectCory Taylor2002-12-10 04:19:34
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