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Topic: Relatively Prime (Read 553 times) |
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ThudnBlunder
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Relatively Prime
« on: Jan 14th, 2009, 7:06am » |
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From a row of k  12 consecutive integers, players X and Y take turns erasing an integer of their choice, X choosing first, until there are two left, n and m. X wins if n and m are relatively prime, and B otherwise. Would you choose to play first or second if a) k is odd? b) k is even?
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Eigenray
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Re: Relatively Prime
« Reply #1 on: Jan 14th, 2009, 10:01am » |
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If k is odd, force adjacency. If k is even, force divisibility by 2 or 3.
The latter doesn't work for k < 12 though, and indeed for k=10, [1,10] is a win for Y while [4,13] is a win for X. For k=8 it also depends on the interval.
Show that X can always win for k=2, 4, and 6.
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| « Last Edit: Jan 14th, 2009, 10:01am by Eigenray » |
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