Author: Dan Ellwein
Date: 08:03:59 01/13/00
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On January 13, 2000 at 10:25:52, Andreas Stabel wrote: >On January 12, 2000 at 18:34:49, Dan Ellwein wrote: > >>Hi >> >>Just wanted to bounce this off of the group and see if this is an accurate >>representation of how many (non redundant) pawn positions there are in chess... >> >> >>(0,8)(1,7)(2,6)(3,5)(4,4) 8P 48x47x46x45x44x43x42x41 x5 = _______ >>(0,7)(1,6)(2,5)(3,4) 7P 48X47X46X45X44X43X42 x4 = _______ >>(0,6)(1,5)(2,4)(3,3) 6p 48X47X46X45X44X43 x4 = _______ >>(0,5)(1,4)(2,3) 5P 48x47x46x45x44 x3 = _______ >>(0,4)(1,3)(2,2) 4P 48x47x46x45 x3 = _______ >>(0,3)(1,2) 3P 48x47x46 x2 = _______ >>(0,2)(1,1) 2P 48x47 x2 = _______ >>(0,1) 1P 48 x1 = _______ >> >> >>Number of non redundant pawn postions in chess -- TOTAL: _______ >> >>haven't done the math on it yet, but it looks like about 75 trillion... >> >>thanks... >> >>PilgrimDan > >I don't think it's that easy. My numbers for 8 white and 8 black pawns are: >White pawns : 48 BNM 8 = 377348994 >Black pawns : 40 BNM 8 = 76904685 >(BNM is the binominal coeffisient) >Multiplying these two numbers give 29019905518636890 29,019,905,518,636,890 quadrillion positions! -- sounds like an awful lot of positions for just the pawns... (but you may be right) > >This calculation has to be done for all possible combinations of white and >black pawns (8,7 - 7,8 - 8,6 - 7,7 - 6,8 ...) and then added to get the >total number. > >Regards >Andreas Stabel
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