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From: geert@sparc.aie.nl (Geert-Jan van Opdorp)
Subject: Re: Chess - exhaustive searching
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In-Reply-To: karl@Xenon.Stanford.EDU's message of 11 Apr 95 08:23:22 GMT
Date: Tue, 11 Apr 1995 14:04:03 GMT


In article <karl.797588602@Xenon.Stanford.EDU> karl@Xenon.Stanford.EDU (Karl Brown) writes:
>
>   32
>   ___
>   \   (64 choose n)
>   /   
>   ___
>   n=2
>
>   This sums up all possible numbers of pieces and positions , assuming you can
>   have from 2 to 32 pieces, and all possible squares (64).
>   ...
>   In2:= Sum(64!/(x!*(64-x)!)), {x, 32}
>   ... which is ~ 10^19.

I think you ought to do Sum(64!/(64-x)!), {x, 32}, since different
distributions of the pieces over the same squares constitute
different positions. Again, of course, we are only talking of an
upeer bound, since pawns of same color *can* be exchanged.
Now we get ~ 5* 10^53 (!!).

>   ps: if the above is way off, please let me know.  :)
Before I calculated it I would never have guessed the
difference would be so huge. I wonder how much the
pawns bring it down again, I'll try to figure that out
now.

Geert-Jan
