If anyone wants an extra challenge: think, how would you write a solver for this?

(If I'm trying not to spoil anything, do I even post? Maybe I can encourage someone else to have fun giving it more thought.) At least one elegant and efficient answer is within reach for many. The person who first pointed it out to me didn't need to know the relevant branch of mathematics to do so; he intuited the shape of it without the formal terminology.

I'll be particularly curious to hear the pattern(s) in how many solutions there are, and/or the probability of a random board being solvable.

The haptic feedback on mobile is really on point in this implementation.

Tangentially related, have you heard of Bombe? It's a hexagonal minesweeper where you write rules to solve every possible scenario. It even checks your rules' satisfiability via SMT.