What Is Sudoku? A Beginner's Guide to the Rules
Sudoku is a logic puzzle played on a 9x9 grid. Some cells start filled in. Your job is to fill the rest so that every row, every column, and every 3x3 box holds each digit from 1 to 9 exactly once.
That is the whole thing. One rule, applied to three kinds of group.
The grid
The board is 81 cells arranged as nine rows, nine columns, and nine 3x3 boxes marked by the heavier lines. Every cell belongs to exactly one row, one column and one box, so every cell sits inside three groups at once. Those three groups are the only thing that constrains it.
Solvers call any of those groups a unit, and two cells in the same unit see each other. Two cells that see each other cannot hold the same digit. Most of solving is working out which cells see which.
The rule
Stated three times, because it applies three times:
- Each row contains 1 to 9, no repeats.
- Each column contains 1 to 9, no repeats.
- Each 3x3 box contains 1 to 9, no repeats.
There is no fourth rule. The diagonals do not matter in standard Sudoku, and neither does any relationship between neighbouring digits. Extra rules like those do exist, but they belong to variants, which always announce themselves.
The starting clues
The digits printed at the start are givens. They never change and they are never wrong. If you find yourself wanting to erase one, the mistake is somewhere in what you added.
How many givens a puzzle starts with is a weak signal of difficulty. Seventeen is the proven minimum for a puzzle with a single solution, but a 25-clue puzzle can be much harder than a 22-clue one depending on where those clues sit.
One solution, and only one
A properly built puzzle can be finished exactly one way, and that is the thing that makes any of this work. It means every digit you place can be forced by what is already on the board, instead of merely allowed by it.
Grids that fail this do exist. I met a lot of them while building the generator behind Sudoku Fog — some with no solution at all, some with two — and a grid with two solutions is nastier than it sounds. You can make placements that are each perfectly correct, follow one branch of the fork, and stall. From the inside that feels identical to being stuck on a hard puzzle, and you have no way to tell which one you are in.
Ruling that out turns out to be most of the work in generating puzzles, and I wrote up what it takes separately, including the two that shipped broken before I had it right.
What this buys you as a solver is simple enough: you never need to guess. If you find yourself guessing, either the puzzle wants a technique you have not learned yet, or you put a wrong digit in a while back and the board has quietly stopped agreeing with itself. Check for the second before you go hunting for the first — it is much quicker to rule out.
The digits are only labels
Nothing in Sudoku is ever added, subtracted or compared for size. A 9 is worth no more than a 2, and a 3 sitting next to a 4 means nothing at all. Swap the digits for nine colours or nine animals and every puzzle ever printed still works exactly the same way — which is what children’s editions do. Digits are just the easiest thing to write small in a small square.
Worth saying out loud, because “number puzzle” puts off a lot of people who would be perfectly good at this.
You also do not have to hold much in your head. Everything the puzzle knows is printed in front of you, and the notation solvers use — small candidate digits pencilled into the empty cells — is there so that whatever you work out goes back onto the board instead of being carried around.
What makes one puzzle harder than another
Difficulty comes from the hardest step a puzzle forces you to take, not from the number of empty cells.
An easy puzzle can be finished by repeatedly finding a cell with only one possible digit. A harder one reaches a state where no such cell exists, and you have to reason about a whole unit instead — where can this digit go in this box? — or about how several cells constrain each other at once. Every extra technique a puzzle demands moves it up a tier.
That is also why difficulty labels vary between apps and newspapers. There is no standard scale; each publisher rates against its own solver, so one paper’s Hard is another’s Medium.
Speed does not come into it, incidentally. Timers and leaderboards were bolted on long after the puzzle itself, and a Sudoku is no easier for being solved slowly.
Where to go next
How to play Sudoku, step by step walks through the order to actually work in — which cell to look at first, and what to do when scanning stops producing answers.