Regarding 7 hints provided. Suppose you have a puzzle which contains 7 digits for hints. Assumming the provided digits are 1-7 placed around the grid and that they permit you to produce a unique solution for those digits (that is you can fill up all but 18 spaces). If you then fill in those remaining spaces with 9 8s and 9 9s, then, however you arranged them, the opposite arrangement is valid.

Essentially those two remaining hints would be variables that you could then substitute either symbol for yielding 2 potential solutions making it an invalid sudoku puzzle.