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A131469
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Grundy numbers of one pile short global nim.
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1
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0, 1, 1, 2, 3, 3, 2, 4, 5, 5, 6, 7, 7, 6, 4, 8, 9, 9, 8, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 14, 18, 19, 16, 17, 18, 20, 10, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 24, 26, 27, 27, 28
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OFFSET
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0,4
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COMMENTS
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The game short global nim is identical to nim except that the last move cannot be repeated. (For example, if 2 stones were taken last turn, any number except 2 may be taken this turn.) The i-th term is the Grundy number of a pile of size i.
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REFERENCES
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R. K. Guy and R. J. Nowakowski, Unsolved Problems in Combinatorial Games, More Games of No Chance, MSRI Publications, Volume 42, 2002, pp. 457-473, problem 22.
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LINKS
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Urban Larsson, Simon Rubinstein-Salzedo, Aaron N. Siegel, Memgames, arXiv:1912.10517 [math.CO], 2019.
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MAPLE
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mex := proc (list) local testn; testn := 0; while evalb(`in`(testn, list)) do testn := testn+1 end do; testn end proc
nextmoves := proc (move) local i, j, k, l, list1, list2, list3, list4, list5, list6; i := move[1]; j := move[2]; k := move[3]; list1 := `minus`({seq([n, j, i-n], n = 0 .. i-1)}, {[i-k, j, k]}); list2 := `minus`({seq([i, n, j-n], n = 0 .. j-1)}, {[i, j-k, k]}); convert(`union`(list1, list2), list) end proc
sgnimgrundy := proc (move) local nmoves, i, j, k; option remember; nmoves := nextmoves(move); i := move[1]; j := move[2]; k := move[3]; if i = 0 and j = 0 then 0 elif i = 0 and j = 1 and k = 1 then 0 elif i = 1 and j = 0 and k = 1 then 0 elif i = 1 and j = 1 and k = 1 then 0 else mex({seq(apply(sgnimgrundy, nmoves[i]), i = 1 .. nops(nmoves))}) end if end proc
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Mark Schlatter (mschlat(AT)centenary.edu) and Jeffery James (jjames(AT)centenary.edu), Jul 26 2007
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STATUS
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approved
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