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Subject: Re: number of pawn positions in chess...

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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