This question was posed to me by my mother-in-law, and I am stumped. There are 12 people sitting in a circle. They must rearrange themselves so that no one is sitting next to any one they were sitting next to to begin with. How many different ways could they have rearranged themselves?
I was thinking some kind of inclusion-exclusion could be applied, but it gets rather complicated rather quickly. It seems similar to this question, but the setup is slightly different.
Edit: I should be clear that here I don't count rotations of the same arrangements to be different arrangements.
