Every Sudoku strategy generalises to its variants, because they all deductively eliminate penciled-in possibilities.

Perhaps if we express the puzzle in terms of boolean logic it can be solved more easily using some existing mathematical technique like linear programming.

Or this could just be another way of expressing the same thing, and the constraints fundamentally aren't easy to solve.

Nevermind, people already do this. Pretty cool.

My intuition is that whatever linear programming algorithm you use has to be faster than any other backtracking search with whatever advanced strategies, since Sudoku can be perfectly represented in this way without information loss.

According to a friendly LLM, the regular search is probably faster since it can use a heuristic to guess squares with the fewest options (which was what I was already doing).

It would be really nice to be able to express all constraints mathematically, so I'll at least try and see if it can solve the hard puzzle that my semi-naive solver took too long to solve.

This is fun. It's like chess programming except I'm actually able to understand it.