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Anonymous
If you are talking about transforming a pawn into another piece when it reaches the other end of the board, then the new piece is placed on the square where the pawn was last.
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Since this requires each rank and file to only contain one rook, the answer would be 8!, which is equal to 8*7*6*5*4*3*2*1, which is 40,320.
Hope this helps
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