How many ways can 8 mutually non-attacking rooks be placed on the 9×9 chessboard (shown here) so that all 8 rooks are on squares of the same color?
(Two rooks are said to be attacking each other if they are placed in the same row or column of the board.)
[asy]unitsize(3mm);
defaultpen(white);
fill(scale(9)*unitsquare,black);
fill(shift(1,0)*unitsquare);
fill(shift(3,0)*unitsquare);
fill(shift(5,0)*unitsquare);
fill(shift(7,0)*unitsquare);fill(shift(0,1)*unitsquare);
fill(shift(2,1)*unitsquare);
fill(shift(4,1)*unitsquare);
fill(shift(6,1)*unitsquare);
fill(shift(8,1)*unitsquare);fill(shift(1,2)*unitsquare);
fill(shift(3,2)*unitsquare);
fill(shift(5,2)*unitsquare);
fill(shift(7,2)*unitsquare);fill(shift(0,3)*unitsquare);
fill(shift(2,3)*unitsquare);
fill(shift(4,3)*unitsquare);
fill(shift(6,3)*unitsquare);
fill(shift(8,3)*unitsquare);fill(shift(1,4)*unitsquare);
fill(shift(3,4)*unitsquare);
fill(shift(5,4)*unitsquare);
fill(shift(7,4)*unitsquare);fill(shift(0,5)*unitsquare);
fill(shift(2,5)*unitsquare);
fill(shift(4,5)*unitsquare);
fill(shift(6,5)*unitsquare);
fill(shift(8,5)*unitsquare);fill(shift(1,6)*unitsquare);
fill(shift(3,6)*unitsquare);
fill(shift(5,6)*unitsquare);
fill(shift(7,6)*unitsquare);fill(shift(0,7)*unitsquare);
fill(shift(2,7)*unitsquare);
fill(shift(4,7)*unitsquare);
fill(shift(6,7)*unitsquare);
fill(shift(8,7)*unitsquare);fill(shift(1,8)*unitsquare);
fill(shift(3,8)*unitsquare);
fill(shift(5,8)*unitsquare);
fill(shift(7,8)*unitsquare);draw(scale(9)*unitsquare,black);[/asy] combinatoricscombinatorics solvedChessboardgridsCanada