It's not a numeric puzzle; the numbers are just place markers. You could use letters (some do) or pictures of kittens, so long as the same one doesn't appear twice in a square, row or column.
Logic puzzles in general were my most recent obsession - I don't mind sudoku but prefer things like masyu, slitherlink, futoshiki and nurikabe. Sadly, these are hard to find and my main source has gone out of print. This is kind of a blessing as I've got more time to use my brain for more productive stuff. But I do miss my puzzles at times when I just need to relax my brain for a bit.