---
title: "How many Sudoku puzzles are there? 6,670,903,752,021,072,936,9"
description: "6,670,903,752,021,072,936,960 completed grids How the figure is estimated, how confident it is, and what makes the scale graspable."
url: https://atoneplace.net/how-many/possible-sudoku-grids/
site: "At One Place"
---

# How many Sudoku puzzles are there?

**How many Sudoku puzzles are there?: 6,670,903,752,021,072,936,960 completed grids**

Five and a half billion essentially different grids is roughly one for every 1.5 people alive — so the world could in principle be issued a personal Sudoku grid each, with a billion spare.

There are exactly 6,670,903,752,021,072,936,960 valid completed 9×9 Sudoku grids, computed in 2005. Once you discard grids that are the same puzzle relabelled, rotated or reflected, the number of essentially different grids collapses to 5,472,730,538 — a factor of over a trillion. A separate question, settled in 2012 by exhaustive computer search, is the minimum number of clues a puzzle can have and still have one solution: 17. There is no 16-clue Sudoku.

## How the figure is arrived at

Symmetry reduction and then brute force. Fix the top-left 3×3 block in a canonical order, enumerate the possibilities for the rest of the top band, then count completions of each by computer, and multiply back by the symmetry factor. Doing it naively would require 10^21 checks; the symmetry argument reduces it to something a 2005 desktop could finish.

## Other numbers and possibilities counts

- [How many combinations does a Rubik's Cube have?](https://atoneplace.net/how-many/rubiks-cube-states/) — 43,252,003,274,489,856,000 — about 43 quintillion
- [How many ways can you shuffle a deck of cards?](https://atoneplace.net/how-many/possible-shuffles-of-a-deck/) — about 8 × 10^67
- [How many possible chess games are there?](https://atoneplace.net/how-many/possible-chess-games/) — about 10^120 games; about 4.8 × 10^44 legal positions
- [How many combinations are there in the lottery?](https://atoneplace.net/how-many/lottery-combinations/) — 292,201,338 for Powerball
- [How many digits of pi have been calculated?](https://atoneplace.net/how-many/digits-of-pi-computed/) — about 202 trillion
- [How many possible passwords are there?](https://atoneplace.net/how-many/possible-passwords/) — 6.6 quadrillion for eight characters — 540 sextillion for twelve
- [How many prime numbers are there under a million?](https://atoneplace.net/how-many/primes-under-a-million/) — exactly 78,498
- [How many possible positions are there in Go?](https://atoneplace.net/how-many/possible-go-positions/) — about 2.08 × 10^170

## Common questions

### How many Sudoku puzzles are there?

6,670,903,752,021,072,936,960 completed grids

### How is that estimated?

Symmetry reduction and then brute force. Fix the top-left 3×3 block in a canonical order, enumerate the possibilities for the rest of the top band, then count completions of each by computer, and multiply back by the symmetry factor. Doing it naively would require 10^21 checks; the symmetry argument reduces it to something a 2005 desktop could finish.

## Related pages

- [How many combinations does a Rubik's Cube have?](https://atoneplace.net/how-many/rubiks-cube-states/)
- [How many ways can you shuffle a deck of cards?](https://atoneplace.net/how-many/possible-shuffles-of-a-deck/)
- [How many possible chess games are there?](https://atoneplace.net/how-many/possible-chess-games/)
- [How many combinations are there in the lottery?](https://atoneplace.net/how-many/lottery-combinations/)
- [How many digits of pi have been calculated?](https://atoneplace.net/how-many/digits-of-pi-computed/)
- [How many possible passwords are there?](https://atoneplace.net/how-many/possible-passwords/)
- [How many prime numbers are there under a million?](https://atoneplace.net/how-many/primes-under-a-million/)
- [How many possible positions are there in Go?](https://atoneplace.net/how-many/possible-go-positions/)
- [How many people are there in the world?](https://atoneplace.net/how-many/people-alive-right-now/)
- [How many stars are there in the universe?](https://atoneplace.net/how-many/stars-in-the-universe/)
- [How many countries are there in the world?](https://atoneplace.net/how-many/countries/)
- [How many bones are in the human body?](https://atoneplace.net/how-many/bones-in-the-human-body/)
- [How many grains of sand are there on Earth?](https://atoneplace.net/how-many/grains-of-sand-on-earth/)
- [How many ants are there in the world?](https://atoneplace.net/how-many/ants-on-earth/)

## Sources

- Calculated on this page — At One Place (/about/)