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You know, I think I'm horribly, horribly mistaken... I'll need to think about this a bit more. I haven't accounted for the case where Mr. and Mrs. Smith aren't linearly next to each other, but at the ends of the ordering -- they'd be next to each other at the table, because it's round. Also, I'd thought about it that we're forming 10 couples, and that the two Smith-containing couples can't be right next to each other... but that's only a problem in half the cases, depending on which member of the couples sits where. This is a very subtle problem, hrm...

Combinatorics is hilarious -- just wanting to know how many of something brings up glorious images of being asked this sort of question, thinking about it for a while, and then handing over this gargantuan number with no explanation at the end -- and the idea of having a class taught by an Eastern-European fellow with appropriate semi-lilting accent (he's really good) is endlessly amusing... brings back memories of Sesame Street. "74,504,322 ways to arrange people around a table! Hah hah hah hah..."

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Alex R

May 2022

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