Author: Dan Ellwein
Date: 05:29:55 01/13/00
Go up one level in this thread
On January 13, 2000 at 04:31:18, Jeremiah Penery wrote: >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. Jeremiah... looks like the "a" pawn could in theory end up on the e f and g files... but not the h... so good point there... also... seems like the black pawns can also provide occupation by capture of any of the white pieces.. not just the pawns... (or simply by being captured by one of the white pieces) >> >>[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. thanks for the input here... (for some reason the diagram didn't show up) Dan
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