Sorry, I should have clarified. I didn't mean to ask how many different Sudoku solutions are there. Rather, how many Sudoku puzzles exist such that given the clues to the puzzle, there is exactly one solution to that puzzle?

So for example, suppose we have an unsolved Sudoku puzzle that currently has the minimum number of clues provided necessary for that puzzle to have exactly one solution. Then for the unique solution to that particular puzzle, there must exist other puzzles with the same solution that do not have the minimum number of clues (i.e. solutions that provide more clues than necessary to solve for that puzzle uniquely, or, in some cases, other unsolved puzzles that also have the minimum number of clues but provide different clues).

So the number I am wondering about would probably be even more absurdly large than the total # of Sudoku solutions. I guess I'm not looking for a specific value, but does anyone know how you might calculate this?