Actually, no. The number depends on the position at the table—rotations are distinct. For 3 couples: Mrs A must sit between Mr B and Mr C. Mr B can be on her

Actually, no. The number depends on the position at the table—rotations are distinct. For 3 couples: Mrs A must sit between Mr B and Mr C. Mr B can be on her left or her right, 2 possibilities. After those two seats are chosen, everyone else’s seat is determined. But there are 6 places Mrs A might sit. Hence, for 3 couples there are 12=2x6 possible seatings, including rotations. This [1] site addresses your intuition. The number of seatings up to rotations is the total number of seatings, divided by the number of seats (2x number of couples). [1] http://oeis.org/wiki/M%C3%A9nage_problem http://oeis.org/wiki/M%C3%A9nage_problem