41 of Ferguson hold For the second pile of 26 chips the rules of Exercise I42

41 of ferguson hold for the second pile of 26 chips

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For the first pile of 15 chips, the rules of Exercise I.4.1 of Ferguson hold.For thesecond pile of 26 chips, the rules of Exercise I.4.2 hold. For the third pile of 10 chips, therules of Nim hold.What is the Sprague-Grundy value of this position?Find an optimalmove.You may use the following facts without proof:the Sprague-Grundy function for Exercise I.4.1 is given byg(x) =bx/2c, except thatg(1) = 1, g(3) = 0.the Sprague-Grundy function for Exercise I.4.2 is given byg(3k) =k-1, g(3k+ 1) =k, g(3k+ 2) =k+ 1 for all integersk, except thatg(0) = 0.6. Grundy’s game(a) In Grundy’s Game, the only legal move is to split a single pileinto two nonempty piles of different sizes. Thus the only terminal positions are piles of sizeone or two. Compute the Sprague-Grundy function for a pile ofnchips, forn= 1,2, . . . ,13.(b) There are four winning moves from the position (6,9,13). What are they? 2

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