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?