This sounds like Crook's Algorithm (https://www.ams.org/notices/200904/tx090400460p.pdf https://www.ams.org/notices/200904/tx090400460p.pdf), which is a perfect

This sounds like Crook's Algorithm (https://www.ams.org/notices/200904/tx090400460p.pdf 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.