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===Eight queens===
[[File:Skak 8dronning.png|thumb|A solution of the eight queens problem]]
In the [[eight queens puzzle]], if the queens are considered to be distinct (e.g. if they are colored with eight different colors), then there are 3709440 distinct solutions. Normally, however, the queens are considered to be interchangeable, and one usually says "there are {{math|1=3,709,440 / 8! = 92}} unique solutions up to [[permutation]] of the queens", or that "there are 92 solutions modulo the names of the queens", signifying that two different arrangements of the queens are considered equivalent if the queens have been permuted, as long as the set of occupied squares remains the same.

If, in addition to treating the queens as identical, [[rotation]]s and [[Reflection (mathematics)|reflection]]s of the board were allowed, we would have only 12 distinct solutions "up to [[symmetry]] and the naming of the queens". For more, see {{format link|Eight queens puzzle#Solutions}}.