Funny that you bring this up. These puzzles would not be considered distinct within group theory. A simple application of Burnside’s lemma would allow a person

Funny that you bring this up. These puzzles would not be considered distinct within group theory. A simple application of Burnside’s lemma would allow a person to recover the true number of distinct puzzles from this figure. A person playing the same puzzle every day that’s just been rotated or had the symbols permuted is going to quickly get bored. While the puzzle looks superficially different the graph structure and the logical steps in the solution will be identical. So doing this kind of combinatorial shenanigans is “cheating” and should be considered dubious, if not fraudulent, within the sudoku community.