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Colored Hat Puzzle
Jan. 9th, 2013 10:00 amFrom my friend Dorian:
Ten prisoners are told that, in a few minutes, they will be arranged in a circle, and a hat will be placed on each of their heads. There are ten possible hat colors: white, black, red, orange, yellow, green, blue, purple, brown and pink. The hat arrangement might be any mix of these, and no hat color is guaranteed to be represented at all. (So while there might be one of each color, there might also be 7 pink, 2 black and a green. Or 10 purples. Or 5 yellows and 5 whites. Etc. ) Each prisoner will see the hats of everyone else, but not his own hat.
Once in the circle, the prisoners will not be allowed to communicate with one another in any way, and after exactly one minute, they will all have to shout out a hat color *at the same time.* If a prisoner says the color of his own hat, he goes free. Otherwise, he's put to the sword.
The riddle is: find a strategy they can work out ahead of time, that guarantees at least one prisoner survives.
(The answer, just to let you know, is an actual math-y one, and not a figure-out-how-to-bend-the-rules solution.)
No spoilers in comments, please! If you think you know the answer, or want a hint (several levels available), please message me.
Ten prisoners are told that, in a few minutes, they will be arranged in a circle, and a hat will be placed on each of their heads. There are ten possible hat colors: white, black, red, orange, yellow, green, blue, purple, brown and pink. The hat arrangement might be any mix of these, and no hat color is guaranteed to be represented at all. (So while there might be one of each color, there might also be 7 pink, 2 black and a green. Or 10 purples. Or 5 yellows and 5 whites. Etc. ) Each prisoner will see the hats of everyone else, but not his own hat.
Once in the circle, the prisoners will not be allowed to communicate with one another in any way, and after exactly one minute, they will all have to shout out a hat color *at the same time.* If a prisoner says the color of his own hat, he goes free. Otherwise, he's put to the sword.
The riddle is: find a strategy they can work out ahead of time, that guarantees at least one prisoner survives.
(The answer, just to let you know, is an actual math-y one, and not a figure-out-how-to-bend-the-rules solution.)
No spoilers in comments, please! If you think you know the answer, or want a hint (several levels available), please message me.