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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:::: The '''first''' point is that the rules of the optimal strategy define '''any''' successful path from starting box to found card as a cycle. (If this is not immediately clear, consider taking '''one more''' move '''after''' we find our card. Where are we now ? Back at the start - by definition - our card contains the index of the box which the optimal strategy instructs us to start with).
:::: The '''second''' point is that when we have run the test for '''one''' prisoner, and reached their card in 50 moves or less, we have collected a full cycle of this kind, from starting box to found card, (and any next move would lead us to the start again), so now we now know the whole route/path/cycle not only for our first prisoner, but for '''every prisoner''' whose number we met on that journey from first box to found card. We now know that all of those prisoners (because
::::The '''third''' point is that after any successful test for a single prisoner we need to do two things: 1. Only consider prisoners whose numbers have never yet turned up on any path seen so far. 2. Exit the test for that shuffle immediately, with an '''all survive''' result, if the total count of prisoner numbers seen so far, on all successful tests, already reaches 50.
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