How many possible Sudoku puzzles are there?

There are 6,670,903,752,021,072,936,960 valid completed 9x9 Sudoku grids when rotations, reflections, and renamed digits are counted separately. There are 5,472,730,538 essentially different completed grids after those standard equivalences are removed.

What the famous number counts

Bertram Felgenhauer and Frazer Jarvis calculated the total by reducing the enormous search into manageable equivalence classes and exhaustively counting the remaining cases. Their Sudoku grid enumeration gives the programs, data, and the resulting 6.67 sextillion figure.

That number counts filled solution grids. Swapping every 1 and 2, rotating a grid, or reflecting it produces another grid in the large total even though the underlying structure is equivalent.

Completed grids are not the same as published puzzles

A playable puzzle is a completed grid with most digits removed while still preserving exactly one solution. Each completed grid can support many different valid clue patterns, so counting every possible playable puzzle is a separate and more complicated problem.

In practical terms, the supply is effectively inexhaustible. The Sudoku generator can vary the solution grid, retained clues, difficulty, and page layout without needing a database of every possible puzzle.