Article View: gnu.chess
Article #4618Re: chess positions --correction
From: Frits van Leeuwen
Date: Tue, 28 Feb 1995 18:16
Date: Tue, 28 Feb 1995 18:16
36 lines
2067 bytes
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.
Technical Details
Message-ID:
<1995Feb28.121659.20036@frontier.tno.nl>Path:
arc1-ca.pugleaf.net!nntp.gmd.de!news.rwth-aachen.de!news.rhrz.uni-bonn.de!RRZ.Uni-Koeln.DE!uni-duisburg.de!zib-berlin.de!Germany.EU.net!EU.net!sun4nl!news.nic.surfnet.nl!frontier.tno.nl!usenetReferences:
<60.1661.4070.0N1D0C54@canrem.com>Show Full Headers
Complete Article Headers
X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 10d71d,3641c9ec709ad63b X-Google-Attributes: gid10d71d,public X-Google-ArrivalTime: 1995-02-28 23:06:07 PST Newsgroups: gnu.chess Path: arc1-ca.pugleaf.net!nntp.gmd.de!news.rwth-aachen.de!news.rhrz.uni-bonn.de!RRZ.Uni-Koeln.DE!uni-duisburg.de!zib-berlin.de!Germany.EU.net!EU.net!sun4nl!news.nic.surfnet.nl!frontier.tno.nl!usenet From: F.vanLeeuwen@wt.tno.nl (Frits van Leeuwen) Subject: Re: chess positions --correction Message-ID: <1995Feb28.121659.20036@frontier.tno.nl> Sender: usenet@frontier.tno.nl (Usenet Postmaster id) Nntp-Posting-Host: wt7004.iw.tno.nl Organization: TNO WT X-Newsreader: WinVN 0.93.9 References: <60.1661.4070.0N1D0C54@canrem.com> Date: Tue, 28 Feb 1995 18:16:52 GMT Lines: 37