🚀 go-pugleaf

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.

Pascal.Jasmin@canrem.com