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Topic: Prisoner guessing game (harder version) (Read 2644 times) |
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wonderful
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Prisoner guessing game (harder version)
« on: May 3rd, 2008, 7:25pm » |
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Note in this version: there are three colors for hats; the prisoners are asked from the first to infinity; they couldn't hear other answers.
Infinite number of prisoners are placed in a line, facing forward so they can see everyone in front of them in line. The warden will place either a red, white, or green hat on each prisoner’s head, and then starting from the beginning of the line, he will ask each prisoner what the color of his own hat is (ie, he first asks the person who can see all other prisoners). Any prisoner who is correct may go free. No prisoner can hear everyone else’s guesses. If all the prisoners can agree on a strategy beforehand, what is the best strategy?
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| « Last Edit: May 6th, 2008, 1:51am by wonderful » |
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Hippo
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Re: Prisoner guessing game (harder version)
« Reply #1 on: May 4th, 2008, 3:23am » |
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Does the prisoners receive any information ... does they know at leat the answer was OK?
Otherwise the order of answers is irrelevant and you can solve easier riddle ... answering in the reverse order ... the one knowing nothing first. I don't thing for random sequence of hat colors a strategy can save more than 100/3 in average.
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wonderful
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Re: Prisoner guessing game (harder version)
« Reply #2 on: May 6th, 2008, 1:50am » |
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Thanks Hippo. I editted the question to make it solvable. You might consider "Axiom of choice".
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temporary
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Re: Prisoner guessing game (harder version)
« Reply #3 on: May 6th, 2008, 5:04pm » |
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Is their strategy to each individually want to go free or to maximize total freedom? If they wish to maximize freedom, they could just guess randomly and get infinite free prisoners.
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