Is there a mathematical way to check if a KenKen (Mathdoku / Calcdoku) puzzle has at most one solution without trying every permutation and then checking if two different permutations both solve the puzzle?
If not, is there a way to generate such a puzzle so that it can only have one solution?
An obvious way to check if there is only one solution would be to solve it and check if there are at least two solutions (e.g. with backtracking algorithms), but with large grids this becomes unfeasible.
From what I've noticed it seems that from one solution you can create another one by swapping columns and/or rows (column and row constraints won't be broken) and hope that the cage constraint isn't broken. This would take n!^4 operations, with n being the size of the grid (column/row length).
Also checking for symmetry in cage disposition could be a possible approach, even though, from various attempts I made, it seems inconclusive.