How to play Sudoku
Sudoku is a number puzzle on a 9×9 grid divided into nine 3×3 boxes. Fill every empty square with a digit from 1 to 9 so that each row, each column and each box holds every digit exactly once. Some digits are given at the start, and you work out the rest by logic, with no arithmetic and no guessing.
The rules
- Every row holds the digits 1 to 9, once each.
- Every column holds the digits 1 to 9, once each.
- Every 3×3 box holds the digits 1 to 9, once each.
That is all. The digits are only symbols: nothing is added up, and a 9 is no harder to place than a 1. This is a finished grid:
A puzzle starts with some squares filled in. A well-made Sudoku has exactly one way to fill the rest.
Your first move: the only digit that fits
Pick an empty square and look along its row, down its column and around its box. Every digit you see there is ruled out for that square. If eight different digits are ruled out, the ninth goes in.
Here the row holds 1, 2 and 3, the column holds 4, 5 and 6, and the box holds 7 and 8. Only 9 is left for the centre square.
The move you will use most: the only place left
Now turn the question around. Pick a digit and a box, and ask where in that box the digit can still go. Every row and every column that already holds the digit rules out the squares it passes through.
The 5s in rows 1 and 2 and in columns 1 and 2 rule out every empty square of the top-left box except one. The 5 goes in the bottom-right square of the box, even though other digits could fit there too. This is called a hidden single. On easy puzzles you may need nothing else.
Pencil marks
When neither move finds anything, write small candidates in the empty squares: the digits that are not yet ruled out. Keep them up to date every time you place a digit. Pencil marks turn the harder techniques into pattern-spotting, and they are how you check your reasoning when you get stuck.
When you get stuck
Go back to the hidden single and check every digit in every box; it is the move that is easiest to miss. Then do the same for each row and each column. If the grid still will not move, the puzzle needs a technique such as a naked pair or pointing. Our Sudoku techniques guide shows each of them on a grid.
The same idea in other puzzles
The habit Sudoku teaches, asking "where can this go?" until one place is left, sits at the heart of many logic puzzles. In Light Up it is the first deduction: a courtyard with one square left holds its lantern there. If you would like to try that version of the idea, there is a new Light Up board every night, free in your browser.
Nightwatch is on Android. On iPhone, play tonight's board here.
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Questions
What are the rules of Sudoku?
Fill a 9×9 grid so that every row, every column and every 3×3 box holds the digits 1 to 9 exactly once. Some squares are filled in at the start, and you work out the rest by logic.
Do you need to be good at maths for Sudoku?
No. Sudoku uses digits as symbols, and nothing is added or multiplied. You could play it with nine letters or nine colours and the puzzle would be the same.
Where do you start a Sudoku?
Pick the digit you see most often among the givens and look for its hidden singles, box by box. Then look for squares where only one digit fits. Each digit you place opens new moves.
Can a Sudoku have two answers?
A badly made one can. A proper Sudoku has exactly one solution, which is what makes logic alone enough to finish it.
Is there a trick to solving Sudoku faster?
Scan by digit rather than by square: take one digit and sweep all nine boxes for its hidden singles, then move to the next digit. Speed comes from spotting forced squares quickly, never from guessing.