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When I am to reflect a current chessboard around say the horizontal line Y=4, would that imply that I need to reflect the bottom part to the top part, and then the top part to the bottom part?

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What does this have to do with the eight queens problem? –  Gerry Myerson Sep 10 '11 at 12:27
    
There are 92 solutions, only 12 unique if you those that differ only in rotation or reflection. –  Algific Sep 10 '11 at 18:55
    
@Gerry: It looks like part of set of exercises involving counting the number of distinct solutions to the eight queens problem modulo one or more sets of symmetries. –  Brian M. Scott Sep 10 '11 at 19:33
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up vote 3 down vote accepted

It’s done all at once: each square is interchanged with its mirror image. Thus, you should interchange the top and bottom rows, the second and seventh rows, and so on. The square originally in the upper left-hand corner changes places with the one in the lower left-hand corner, the squares immediately to their right change places similarly, and so on.

Here’s a question to be sure that you’ve got it: After you’ve done the reflection, what’s happened to the colors of the squares, if anything?

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