BrainKing - Diskusjonsforum (Chess variants (10x8))

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Chess variants (10x8)

Sam has closed his piano and gone to bed ... now we can talk about the real stuff of life ... love, liberty and games such as
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6. november 2003, 04:35:40

Grim Reaper

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Emne: Re: Total Number of Gothic Chess Positions

More on the pawn count...

Originally I had the non-captured pawn permutaion count at 774,468,423,574,600,034,220 which, as Thad pointed out, seems a little high. When using the concept of the "rammed pawns" constrained to a rank, there are actually 30 different configurations possible per file.

You can have an unmoved pawn in the a-file on a2, and the black pawn can be one of 5 different squares in the same file, a7,a6,a5,a4 or a3. If the white pawn were on a3, then there are 4 squares for the black pawn, etc.

There are always 5-r permutations for the black pawn for each rank of displacement, r, the white pawn has moved.

So, there are 5+4+3+2+1 = 30 possible configurations per file. The total number of permutations is therefore 30^10, which is 590,490,000,000,000. This is only 590 trillion, a lot less than 774 quintillion!