I've done the code that generates all the solutions. But know I am suppose to filter out any redundant solutions based on symmetry and rotations. I have code for vertical symmetry, horizontal symmetry, rotation $90$, $180$ and $270$. The bit that remains is removing symmetry about the the diagonals. / and \ of the board. I guess I can rotate it $90^\circ$ instead of making code for both diagonals. I want to implement the diagonal "\". I drew up some points.
From bottom part to the upper part.
$(1, 3)$-> (6, 8)
(2, 1) -> (8, 7)
From top part to bottom part.
(4, 6)->(3, 5)
(5, 6)->(3, 4)$
I'm not sure what formulas would do this for me. And what about chess pieces on the diagonal it self, they would just stay put I guess?