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Article #4618

Re: chess positions --correction

#4618
From: Frits van Leeuwen
Date: Tue, 28 Feb 1995 18:16
36 lines
2067 bytes
In article <60.1661.4070.0N1D0C54@canrem.com>, pascal.jasmin@canrem.com says...
>
>See previous message for details:
>
>; So finally,
>; 44:
>; 45: 64! / 32! *
>; 46: 32 * 31
>
>I think the above is correct, and covers only the minimum assignment of
>empty squares, and the 2 kings.
>
>Of the 30 remaining pieces, assigning them to slots (that will later be
>placed on the board in the sequence of the slots from, say, a1 to h8),
>we get 30! orderings, that adjusting for transpositions / (8! * 8! * 8).
> Since each of these slots can have either their computed value, or be
>empty, this entire expression is squared.  So:
>
>[30! / (8! * 8! * 8)]^2
>
>And simplifying the entire statement:
>
>64! * 30! / 8!^4 * 64
>
>= 63! * 30! / 8!^4
>
>= 1.98 x 10^101
>This excludes impossible positions from required pawn movement and
>capture and too many simultaneous checks.  Even if as much as 1/2 of
>these positions were illegal (probably less than 1/10 are), there would
>still be 1 x 10^101 possible positions.
>
I'm not soure but I think, "The way that you're thinking is an other way"
I take 2 kings and count the possible positions (3612 for only 2 kings)
Than I take an other piece and go on.
But when I tel my computer the rules of counting. It counts for many days.  
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From: F.vanLeeuwen@wt.tno.nl (Frits van Leeuwen)
Subject: Re: chess positions --correction
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Date: Tue, 28 Feb 1995 18:16:52 GMT
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