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In how many ways can we arrange n married couples around a circular table so that no person is next to her (his) spouse and no person sits next to a person of the same sex?

As i see the solution of the meange problem here, i found that they are not taking the table as circular. By circular i mean that, if one arrangement can be obtained from other by rotation then they are same.So, i feel that it's not exactly the menage problem.

Any help will be appreciated.

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Every solution to your problem gives $2n$ solutions to the menage problem. In your solution, everyone has a unique solution relative to Peter. In the menage problem, Peter has $2n$ possible seats.
So just divide the Menage solution by $2n$.

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