Author: Jeremiah Penery
Date: 01:31:18 01/13/00
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On January 13, 2000 at 02:54:31, Timothy J. Frohlick 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 > > >Dan, > >I don't think the "a" pawn is going to end up on the e,f,g,or h files and don't >forget that the black pawns prevent occupation except by capture of the white >pawns. You also have to account for en passant which usually occurs only once >per game at most. > >[D] 8/pppppppp/8/8/8/8/PPPPPPPP/8 Also, you must account for positions such as: [D]4k3/8/8/PPPPPPPP/ppp1pppp/8/8/4K3 (I think that's a reachable one...I tried to construct a game just now to make sure, but I couldn't figure it out exactly. I've done it before, but I'm not sure if this is the exact position.
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