Author: J. Wesley Cleveland
Date: 13:52:31 11/21/02
Go up one level in this thread
On November 20, 2002 at 11:24:39, Frank Sgarra wrote: > > >ops, i forgot to mention that all 5 pieces are white pawns ! Try this: Assuming that pawns are limited to the 2-7 ranks, the number of different positions are 48!/(43!*5!) or 1712304. So, if we can enumerate the positions, this will be the smallest integer. If the 5 pawns are on squares a,b,c,d,e where a<b<c<d<e, we can calculate the number by adding the number of permutations of 5 pawn positions which have the first pawn on a square < a, plus the number of permutations of 4 pawn positions which have the first pawn on a square > a and < b, plus the number of permutations of 3 pawn positions which have the first pawn on a square > b and < c, plus the number of permutations of 2 pawn positions which have the first pawn on a square > c and < d, plus e-d-1. The number of permutations for 2-5 pawns can be put into tables making the calculation 4 table lookups and a few adds.
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.