Will Crichton

Combinatorics problem: you're arranging 10 people (A .. J) in a row. A and B must sit next to each other. How many arrangements? How could writing this problem as a program help scaffold the problem-solving process?

I would reframe it as arranging 9 units: (AB) and C .. J. The result is the number of permutations of 9 things × 2 — one set for AB and another for BA. I find a lot of tricky problems get simpler if you can find a non-obvious thing to treat as a first-class entity.

Agreed! That's the "additive" solution I mention (see down in the thread). My question: what is a general strategy to help people reach this solution from the problem statement?

I don't think there is one. The problem is that "insight" is fragile: if you instead asked "where A and B are NOT adjacent", I don't think you can use the same constructive solution. You could instead say it's 10! - (9!*2), but that's another leap of insight

And if we instead perturbed to "A and B have *exactly one* person between them", I don't see what the constructive solution would be at all