Let's reformulate this in a mathsy way, because the underlying question is interesting. We'll start from gender binary, and let's see where we go from here. F

Let's reformulate this in a mathsy way, because the underlying question is interesting. We'll start from gender binary, and let's see where we go from here. First change: If you have n male/male couples, m female/female couples, and k male/female couples, how many seating orders can you produce. This both makes a more complex mathematical problem (possibly it's even more interesting, YMMV) and it puts a bit more light on the underlying assumption of "pair by preference". For this example, we've gone to "pair by sexual preference", but I think we can agree that for most parties, that isn't the primary factor in seating your guests. (I mean, maybe it is for some people, but my life isn't that exciting ;) So, this raises the question "if we don't pair by gender, what the heck do we pair by". Usually, if you throw a party with seating arrangements, you pair by "how well do these folks get along". So, reformulated, given a set of people and a set of "good" seating neighbor combinations between them, how many valid seating combinations exist? And from there, for bonus credit, let's realize that there is no binary in "good seating neighbor" either - so, for each pair of people, there exists instead a goodness-weight of their neighborhood. How do you compute the maximally good seating order? (God, now I have flashbacks to wedding seat charts ;) That sounds like a reasonably interesting problem, and I'd really like to hear if anybody tackled it.