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:: Couple Permutation Problem ::

If the girlfriends of three couples are seated in fixed positions around a table, the is only one possible way to seat their boyfriends so that men and women alternate and no boyfriend is next to his girlfriend. With four couples, there are two possible arrangements.

How many possible arrangements are there with five, six and ten couples?

Answer: 13, 80 and 439,792 respectively.

Lots of people wrote to ask us how we get to the answers, well, perhaps this might help: http://mathworld.wolfram.com/MarriedCouplesProblem.html

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