There are N = 6670903752021072936960 6.671×1021 valid Sudoku grids. Taking out the factors of 9! and 722 coming from relabelling and the lexicographical reduction of the top row of blocks B2 and B3, and of the left column of blocks B4 and B7, this leaves 3546146300288 = 27×27704267971 arrangements, the last factor being prime.

9^9 x 8^9 x 7^9 x 6^9 x 5^9 x 4^9 x 3^9 x 2^9 x 1^9 = 362880^9

Any given Sudoku puzzle has just one solution. This is so long as the puzzle already comes with at least 17 digits already placed on the grid. If there are any less than 17 digits, then the puzzle has more than one possible solution, and therefore cannot be solved properly. The total number of possible combinations of digits on a standard sudoku grid is 6,670,903,752,021,072,936,960. However it can be argued that many of these combinations could be the same as another, only backwards or rotated. Factoring out all logical duplicates, the number of possible combinations drops to 3,359,232. This is essentially the total number of possible sudoku puzzles. * My Friend Dev Oneal has completed an 'Impossible Level' Sudoku puzzle, as I checked the answer given by the "Auto-Solve" feature and compare with his solution and have found both was correct but with different pattern. Hence, it could have more than 1 correct answer.