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What color hat am I wearing?
... random thoughts , logic , math
tue 2005-may-10 15:07:22 pdt
... permalink
The 2-player game
Two players sit facing each other, each with a red or blue hat placed
on her head; each can see the other's hat but not her own. Each
player must write down a guess, "red" or "blue", for her own hat
color, without knowing the other player's guess. The guesses are then
revealed and:
if at least one player is correct, both get a million dollars;
if both are wrong, they get nothing.
They can of course agree on their strategy ahead of time but cannot
communicate once the game begins. Obviously if they both just guess
randomly, they win with 3/4 probability. But can you come up with a
strategy that has a better chance of winning? Can you guarantee a
win?
Yes, you can guarantee a win.
Hint: Think about different ways of dividing up the four
possible hat configurations into two cases.
(the full solution with explanation)
Please do NOT post solutions in the comments below. Thanks.
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