29 lines
1.8 KiB
Text
29 lines
1.8 KiB
Text
;The Problem:
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* 100 prisoners are individually numbered 1 to 100
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* A room having a cupboard of 100 opaque drawers numbered 1 to 100, that cannot be seen from outside.
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* Cards numbered 1 to 100 are placed randomly, one to a drawer, and the drawers all closed; at the start.
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* Prisoners start outside the room
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:* They can decide some strategy before any enter the room.
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:* Prisoners enter the room one by one, can open a drawer, inspect the card number in the drawer, then close the drawer.
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:* A prisoner can open no more than 50 drawers.
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:* A prisoner tries to find his own number.
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:* A prisoner finding his own number is then held apart from the others.
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* If '''all''' 100 prisoners find their own numbers then they will all be pardoned. If ''any'' don't then ''all'' sentences stand.
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;The task:
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# Simulate several thousand instances of the game where the prisoners randomly open drawers
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# Simulate several thousand instances of the game where the prisoners use the optimal strategy mentioned in the Wikipedia article, of:
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:* First opening the drawer whose outside number is his prisoner number.
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:* If the card within has his number then he succeeds otherwise he opens the drawer with the same number as that of the revealed card. (until he opens his maximum).
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Show and compare the computed probabilities of success for the two strategies, here, on this page.<br>
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;References:
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# [https://www.youtube.com/watch?v=a1DUUnhk3uE The unbelievable solution to the 100 prisoner puzzle] standupmaths (Video).
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# [[wp:100 prisoners problem]]
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# [http://datagenetics.com/blog/december42014/index.html 100 Prisoners Escape Puzzle] DataGenetics.
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# [https://en.wikipedia.org/wiki/Random_permutation_statistics#One_hundred_prisoners Random permutation statistics#One hundred prisoners] on Wikipedia.
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<br><br>
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