Exactly. I would just feed this to a counting SAT, or constraint, solver. If I wrote the constraint solver, does that count as an acceptable answer? There ar

Exactly. I would just feed this to a counting SAT, or constraint, solver. If I wrote the constraint solver, does that count as an acceptable answer? There are some fancy ways of doing this, involving lots of bitshifting, which are quite fun. Edit: Remove mis-remembered bitshifting.