"Feed it to SAT solver" is a super useful technique every seasoned programmer should have in their toolbelt.
If you want to improve your programming skill, I suggest implementing your own version of these two interesting, satisfying algorithms:
- DPLL, the classic general-purpose SAT solving algorithm [3].
- Algorithm X (aka Dancing Links), Knuth's super elegant search algorithm for solving exact cover problems [4] [5].
You're not going to build something that beats CaDiCaL [6] in an afternoon, but writing your own implementation of these algorithms will teach you a lot, and a reasonable time investment will get you to a pretty satisfying endpoint of having a practical solver for your favorite application (Sudoku, polyomino packing, etc.)
[1] Reinventing wheels is not a bad way to spend your days at a retreat focusing on one's personal growth as a programmer. "I think I'll learn a lot and get some good practice at programming and algorithmic thinking" is an easy bar to meet.
In a professional context, telling your company or client they should commit scarce, expensive engineering resources (e.g. your time) to creating and maintaining their own wheel design requires justification [2].
[2] "Don't reinvent wheels" is good general advice for junior developers. Senior developers know that sometimes there are specific situations where this general advice doesn't apply. For example, if no existing wheels meet your application's requirements, or if you have ideas for proprietary features that give you a competitive advantage. Even in a professional setting, reinventing the wheel isn't always a bad idea; you just need to meet a much higher bar to justify the commitment of resources.
[3] https://en.wikipedia.org/wiki/DPLL_algorithm
[4] https://arxiv.org/abs/cs/0011047