Fill every empty square with a digit from 1 to 9, so that each row, each column and each of the nine 3×3 boxes contains all nine digits exactly once. Some squares are already filled in when you start; those are fixed, and every other square is yours to work out.
That's the whole rule set. There is no second page of it, no scoring, and nothing that happens on a timer. If you've been avoiding Sudoku because it looked like it needed explaining, that was the explanation.
What the rule means when you're looking at a board
Written down, the rule sounds like a constraint on the finished grid. At the board it works as something much more useful: a list of numbers that are already banned from the square you're looking at.
Every empty square sits in three places at once — a row, a column, and one of the nine 3×3 boxes. Any digit already sitting in any of those three is out. Not unlikely. Out.
So the question to ask isn't "what goes here?", which is hard. It's "what can't go here?", which is just reading. Look along the row, down the column, around the box, and cross off what you find. Whatever's left is what's allowed.
Here's a real puzzle at its starting position.
Thirty numbers are given, fifty-one squares are empty. The heavier lines mark the nine boxes — they're the part beginners most often miss, because rows and columns are obvious and the boxes have to be noticed.
Every one of those thirty givens is doing work on the squares around it, in three directions at once.
There's no arithmetic in it
This is the single most common reason people decide Sudoku isn't for them, and it's simply a misunderstanding of what the digits are.
Nothing in Sudoku is added, subtracted, or totalled. The nine digits are just nine distinct symbols. They could be nine colours, nine letters or nine animals and the puzzle would work exactly the same way — the only property that matters is that each is different from the other eight. The numbers are there because everyone already knows what order they come in, which makes them easy to keep track of.
If someone told you that you needed to be good at maths for this, they were wrong, and it may have cost you a few years of a decent hobby.
You never have to guess
A properly made Sudoku has exactly one solution — that's part of what makes it a puzzle rather than a worksheet. And on the puzzles you'll meet while you're learning, reasoning is always enough to reach it. You won't need to pick one of two numbers and hope.
That matters more than it sounds, because guessing is how most beginners lose an hour. A guess that turns out wrong doesn't announce itself. It sits there looking reasonable while you build twenty more squares on top of it, and by the time two 7s turn up in the same row, you can't tell when it went wrong.
So the rule that saves the most time is: if you can't justify a number, don't write it in. Early on, a board with nothing justifiable on it almost always means there's something you haven't spotted rather than something you can't deduce — and the next section is where to start looking.
Your first move
Look at the square in the dead centre of the grid, and do exactly what this piece has been describing. Read its row: 4, 8, 3 and 1 are already there. Read its column: 7, 9, 6, 2, 1 and 8. Read its box: 6, 8, 2 and 3.
Between them, those three regions have used up eight of the nine digits. Only the 5 is left, so a 5 is what goes there — not probably, not unless something contradicts it later. There is nothing else it could legally be.
That's a real move, made with nothing but the rule at the top of this page. It also has a name, and it's the first thing worth learning properly: naked singles: the square that can only be one number covers how to find them on purpose rather than by luck, which is the difference between finishing a puzzle and staring at one.
After that, the path is short. Two techniques finish almost every Easy puzzle in our app, and five finish almost every Medium one — the whole ladder is laid out in order, with the counts, and it's shorter than the long guides make it look.
A few things nobody tells beginners
- Write your maybes down. If a square is down to a 2 or a 5, pencil both in a corner. Holding them in your head works for about six squares, and most of what feels like being stuck is re-deriving things you already worked out once.
- Start where the board is crowded. A square in a busy row, a busy column and a busy box has the fewest options left. Empty corners of the grid are the worst place to look.
- Being stuck is normal and usually cheap to fix. It's five different problems with five different fixes, and most of them take under a minute.
- Difficulty isn't about how many squares are blank. It's about which techniques the puzzle forces you to use. A grid with more givens can be much harder than one with fewer.
The rules took two sentences. Everything else in Sudoku — every technique with an odd name, every guide with eleven chapters — is a shortcut for finding the square where only one number fits.