[catpolice]

A while back I wrote a solver that uses no backtracking, just constraint propagation, and it wasn't substantially more complex than this.

One of the key insights comes from noticing a feature of groups of numbers in cells. For example, suppose you notice two cells in a given row and they're the only cells in that row that the numbers 1 and 2 can be placed in - then one of them is going to have 1 and the other will have 2, and you don't know which but you can eliminate any other possibilities in those two cells. This generalizes to groups of any size in rows/columns/squares. I think that and maybe one other heuristic along with the basic rules about number placement is enough to solve everything.

[53x15]

This sounds like Crook's Algorithm (https://www.ams.org/notices/200904/tx090400460p.pdf), which is a perfectly reasonable thing to do, especially for pencil-and-paper puzzle solving since pigeonhole inferences are easy for people to spot. But this inference rule does not suffice on its own for many hard puzzles. Crook's algorithm still requires backtracking.