Couples at a circular table

Reply #2

db101 — Wed, 22 Feb 2023 22:43:28 GMT

Nice solution, and thanks for the formal name. I looked it up in the OEIS and there a few different series with that name depending on whether you treat rotations and reflections as distinct or unnecessary repetition.

Reply #1

cottoneyedjoe — Sat, 18 Feb 2023 17:22:05 GMT

Let n be the number of couples and let A(n) be the number of distinct arrangements disregarding rotation. By hand it is possible to calculate A(n) for small values

n A(n)

1 0

2 0

3 2

4 12

5 312

For higher values, you can use the recursive formula

A(n) = n*(n-1)*A(n-1) + n*(n-1)*A(n-2) - 4*(n-1)*(n-3)! * (-1)^n

Now you can extend the table up to any n

n A(n)

6 9600

7 416880

8 23879520

9 1749363840

10 159591720960

Couples at a circular table

db101 — Fri, 17 Feb 2023 02:45:50 GMT

10 male-female couples are seated around a circular table. No male sits next to another male, no female sits next to another female, and nobody sits next to their partner. How many ways are there to seat the couples? Rotations of an arrangement are not counted as distinct, but reflections are.