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        riddles >> medium >> Relatively Prime
        
(Message started by: ThudanBlunder on Jan 14th, 2009, 7:06am)
Title: Relatively Prime
Post by ThudanBlunder on Jan 14th, 2009, 7:06am
From a row of k http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/geqslant.gif 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?


                                                                                                                                                                                                                     
Title: Re: Relatively Prime
Post by Eigenray on Jan 14th, 2009, 10:01am
If k is odd, force [hide]adjacency[/hide].  If k is even, force [hide]divisibility by 2 or 3[/hide].

The latter doesn't work for k < 12 though, and indeed for k=10, [1,10] is a win for [hide]Y[/hide] while [4,13] is a win for [hide]X[/hide].  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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