Author: Dann Corbit
Date: 13:03:04 05/27/99
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On May 27, 1999 at 15:56:07, Dann Corbit wrote:
>On May 27, 1999 at 15:10:44, J. Wesley Cleveland wrote:
>[snip]
>>I did some calculations. You can use 12 bits to represent kings and castling,
>>one bit for side on move, one bit for e.p., (if there is an e.p., you get back
>>the four bits from the pawn representations), 15^8 for the pawns, and
>>46!/(32!*2^6) for the pieces (this is from the number of combinations of 14
>>peices in the 46 remaining squares divided by two for each of the pieces there
>>are two of). If I calculated correctly, this takes 114 bits. Many, if not most
>>of these positions are legal (the exceptions are kings in check, and pieces that
>>could not move to squares because the pawns have not moved and they are
>>blocked).
>Could you spell out your method formally and in detail?
>If it works, it proves that there are less than 2.1e34 possible chess positions.
>In fact, the exact number would be less than:
>20,769,187,434,139,310,514,121,985,316,880,384
>{around 20 decillion}
This is especially important, since 144,115,188,075,855,872 is the square root
of that number. There are indications that a search tree holding that many
entries would solve the game of chess. 1.5e17 may be something that is
eventually calculable.
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