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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?

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    It would be better if this question describes the "eight queens problem" in more detail, or at least contains a link to a description of the problem elsewhere. At least one reason for this is that readers of this question want to know what you're asking about.2015-06-20

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$(a,b)\to(9-b,9-a){}{}{}{}{}{}$

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    @Algific: for the diagonal "/" it is (a, b) -> (b, a).2011-09-11