Berkeley CSUA MOTD:Entry 23120
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2025/05/24 [General] UID:1000 Activity:popular
5/24    

2001/11/27-28 [Computer/SW/Languages/C_Cplusplus] UID:23120 Activity:high
11/27   http://www.CSUA.Berkeley.EDU/~ilyas/problems/hat_problem
        How many times are they allowed to pass and guess? God ilyas, you
        really need to clarify your questions.
        \_ once -!ilyas
        \_ Once.  There is an article in the NY Times about this problem.
           It's a genuine one, but see if you can get the correct answer.
           Hint:  It's not the trivial solution. -!ilyas
        \_ Yet another stupid problem. Two of the people pass, the other
           one will guess. That gives them a 50% chance of winning the price
           [sic]
           \_ Try again grasshopper.
        \_ How about this.  It's unlikely that all the hats will be the same
           color.  So if a player sees two hats of the a color, he guesses the
           other color, otherwise he passes.  This increases the chance of
           winning to 6 in 8.  (RRR, BBB are losers, other 6 combos are not.)
           \_ Congratulations.
              \_  Yes! I am the smartest man alive!
        \_ let each person decide for the other person, and then move to the
           left side of the room for blue hat, right side for red. So person
           A B C ( a decides for b, b decides for c, c decides for a). If person
           A is on the right side, b will say he (b) has a red hat.. etc
2025/05/24 [General] UID:1000 Activity:popular
5/24    

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www.CSUA.Berkeley.EDU/~ilyas/problems/hat_problem
Three people engage in the following contest: They are brought into a room, and each one has a hat placed on their head. Each of the three people can see the color of the hats the other two wear, but not the color of their own hat. Once the three enter the room, they are not allowed to consult with each other. Each of the three people must either guess the color of his hat or pass. If the following condition holds, they share a $3 million price: At least one person guesses correctly, and no one guesses incorrectly. The three people are allowed to consult before entering the room, and agree on a strategy to follow, but are not allowed to communicate in any direct or indirect way once they are in the room, they must guess simultaneously (with some people possibly opting to pass) and that is it. Question: What strategy should the three follow to maximize their chances of winning the $3 million?