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.
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?