Comment by Liftyee
Neat idea, though I didn't fully understand the details since I'm not experienced in constraint solvers. Might have to look into it.
Games often lead to interesting computational problems. Another example - I was designing a solver for Flow [0] which made me think about graph problems and applications in e.g. circuit board wire routing. Intuitively it's easy, but translating that into logic is more challenging.
Back in uni, we had to design a MIP program to solve flow, it was a nice and fun problem.
Turns out you can save a lot of time and effort by just cutting infeasible solutions out one by one, and resuming the solver, as opposed to writing some tricky constraints.