[Math Lair] Eight Queens Puzzle

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A classic chess-related problem (although it doesn't require much if any knowledge of the rules of chess) is the eight Queens problem. The puzzle can be stated simply: Place 8 Queens on a chessboard such that no two are attacking each other. Since chess Queens move any number of spaces along any row, column, or diagonal, the puzzle could also be stated as: place eight Queens (or any other items) on an 8×8 board such that no two are in the same row, column or diagonal. [incorrect solution to eight Queens puzzle]

The diagram on the right shows an incorrect solution to the problem. Note that the two Queens circled in red are attacking each other, making the solution incorrect. Can you find a correct solution to the problem?

Here are some hints if you're stumped. The problem is in fact possible. There are 12 unique solutions. Including rotations and reflections, there are 92 solutions. It may help to attack the problem in an organized fashion. Here are some possible ideas:

One solution can be found on the answers page.

This puzzle is also known as the eight checkers puzzle, with the object being to place eight checkers on a checkerboard such that no two lie in the same row, column, or diagonal. The problem, and the solution, are the exact same.