Talk:100 prisoners: Difference between revisions
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→No card viewed en route to a find needs further checking
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:So the start drawer is drawer_number= prisoner_number<BR>[[User:Horst.h|Horst.h]] ([[User talk:Horst.h|talk]]) 13:19, 7 November 2019 (UTC)
::That’s right, and thats why every prisoner starts exactly one full cycle length away from their card. Prisoners don’t talk to each other, but when the simulator has checked one number in the cycle it has checked them all. [[User:Hout|Hout]] ([[User talk:Hout|talk]]) 14:45, 7 November 2019 (UTC)
::Each prisoner in a particular cycle group enters that cycle at a different absolute position, but at exactly the same relative position - immediately after their target card, which itself points at (contains the 1-based index of) their start position. Every prisoner in that group needs exactly the same number of steps - the full cycle - to complete the chain and reach their target. If the cycle length is 50 or less, all prisoners with numbers in that cycle reach their card. If the cycle length is 51 or more, none of them do. [[User:Hout|Hout]] ([[User talk:Hout|talk]]) 14:55, 7 November 2019 (UTC)
:: Finally, not only does a single find (a single cyclical pathway of length <= 50) tell us that every prisoner with a number on that path can reach their card, and needs no further checking - it also tells us that once the combined (summed) lengths of the viable paths we have seen exceeds 50, no more further checking of any kind at all is needed. Survival of all has been established - no room remains for any path that is long enough to fail. [[User:Hout|Hout]] ([[User talk:Hout|talk]]) 15:14, 7 November 2019 (UTC)
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