2QUESTION 2 OF 3
Answer & explanation
The official answer, with Fermi’s reasoning step by step.
Answer & explanation
Official answer
255,168
games
How to estimate it
Fermi’s official “Napkin math”
Start with the board itself, nine empty squares. That is 9 factorial ways to fill them in order: 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, about 363,000. Games actually end early once someone lines up three in a row, so the real total lands a bit under that.
- Squares on the board
- 9
- Ways to fill them all in order
- 9!
- 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
- ≈ 363,000
Rounded assumptions may give a slightly different estimate. The official answer above is the game’s reference value.
Source calculation & reference
- Games won by the first player (X)
- 131,184
- Games won by the second player (O)
- 77,904
- Games that end in a draw
- 46,080
- Total distinct games
- 255,168
Reference cited by Fermi: Game researcher Jesper Juul's full game-tree enumeration of tic-tac-toe (The Ludologist)
How close was your guess?
Your comparison will appear here.
Compare by ratio: divide the larger number by the smaller one. The closer to 1×, the better.