I was recently watching a Sudoku Youtube channel which shows a large number of variants on the traditional Sudoku puzzle, some of them non-trivial to solve. I think there was some mention of a Sudoku puzzle which uses Euler's identity, although can't remember the details. Some of them use prime numbers or certain sequences like the Fibonacci sequence, and so on.
I was wondering if there could be anything more mathematically profound or useful in variants of these puzzles apart from the combinatorial search for a solution.
Something like this seems to be a recent paper of Greenfeld and Tao on undecidability of translational monotilings which uses Sudoku puzzles extensively (or at least, a so-called "Sudoku puzzle construction"). A variant of a Sudoku problem was used to encode a domino problem which can be viewed as a generalisation of the "Wang tiling problem". The Sudoku puzzle construction was also used in a related paper to produce an aperiodic translational monotiling.
