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Topic: impossible variation single file hat execution (Read 1734 times) |
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dojo
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impossible variation single file hat execution
« on: Oct 22nd, 2004, 7:45pm » |
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10 prisoners are on death row. Tomorrow they will be arranged in single file, all facing one direction. The guy in the front of the line (he can't see anything in front of him) will be called the 1st guy, and the guy in the back of the line (he can see the heads of the other nine people) will be called the 10th guy.
An executioner will then put a hat on everyone's head; the hat will either be black or white, totally random. Prisoners cannot see the color of their own hat.
The executioner then goes to the 10th guy and asks him what color hat he is wearing; the prisoner can respond with either "black" or "white". If what he says matches the color of the hat he's wearing, he will live. Else, he dies. The executioner then proceeds to the 9th guy, and asks the same question, then asks the 8th guy ... this continues until all of the prisoners have been queried.
How do all the prisoner's live? And what was the color of the 10th guy's hat?
(There can be no communication between the prisoners, nor any voice inflection during the answer - or anything like that, and all prisoners have to respond).
my friend gave me this riddle.. and i find it quite impossible for an answer can any of you help me solve this riddle?
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Icarus
wu::riddles Moderator
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Re: impossible variation single file hat execution
« Reply #1 on: Oct 22nd, 2004, 8:03pm » |
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It sounds to me like your friend has the answer wrong. This is exactly the situation described in the Single File Hat Execution puzzle, and as has been discussed in the the threads for that puzzle, prisoners 1-9 can be saved, but prisoner 10 has only a 50-50 chance at surviving.
That the 10th prisoner cannot have a better than 50% chance is easy to see: he has no way of getting any information about his own hat before answering. The others can get information from the answers of their predecessors (with suitable planning and cooperation between the prisoners) and use that information to save their own lives. But he is first, and must trust to luck for his own survival.
And there is certainly no way of discerning from the information given what the 10 guy's hat was. Any scheme for figuring out that the hat was black, would also work for figuring out that the hat was white, if all of the hat colors on the prisoners were reversed. There is nothing in the information given that would make such a reversed solution invalid.
I suppose you could say that the answer to the first question is "The 10th guy got lucky, and the rest answered according to the scheme (explained in the other threads)". But even this cheat falls flat for the 2nd question. There is nothing in the puzzle or in the fact that all 10 lived which indicates what color the 10th guy's hat was.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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