1.2 Trillion Ways to Play the Same Sudoku

or, Group Theory on the Puzzle Page

Last week, I visited my dad, who still gets the newspaper.

(For my younger readers: that’s a stack of cheap paper printed with a detailed description of yesterday.)

Anyway, for an ungrateful millennial like me, a print newspaper means one thing: puzzles.

Like Sudoku.

You already know the rules: nine rows, nine columns, and nine medium squares, each containing the digits 1 through 9. You’re given some; you fill in the rest. It looks something like this (by which I mean, “here’s an example lifted from the Wikipedia page”):


Now, I’m not much of a Sudoku player. (Crossword guy, to be honest.) But glancing at the puzzle, my dad and I got to wondering: How do they generate these puzzles?

We weren’t sure.

So we found a more tractable question: What if you were a lazy Sudoku maker?


That is, suppose you managed to generate a single Sudoku puzzle. (Or steal it from the Wikipedia page.) And suppose you wanted to make a few bucks selling collections of puzzles in airport bookshops. But there’s a catch: You’re not sure how to make more.

How many “different” puzzles can you get from a single Sudoku?

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