Sudoku

How to Play Sudoku

Sudoku has exactly one rule, and you can learn it in a minute. What changes between an easy puzzle and an expert one is not the rule — it is which kind of reasoning the grid forces you into. This page covers the rule and the vocabulary once, then splits into a separate guide for each of the four levels, so you can read only the one you are stuck on.

The board

A Sudoku grid is 9 squares wide and 9 squares tall, so 81 squares in total. It is divided three ways at once:

  • Nine rows, running left to right.
  • Nine columns, running top to bottom.
  • Nine boxes — the heavier 3×3 blocks marked by the thick lines.

Rows, columns and boxes are collectively called units. Every square belongs to exactly three units: one row, one column, and one box. The squares that share a unit with a given square are its peers, and every square has 20 of them. On this site the peers of whichever square you have selected are shaded, which saves a lot of squinting.

The one rule

Fill every empty square with a digit from 1 to 9 so that no digit repeats within any row, any column, or any 3×3 box.

That is the entire game. The digits already printed when the puzzle starts are called clues or givens, and they never change. A properly formed Sudoku — including every puzzle generated here — has exactly one arrangement that satisfies the rule, and that arrangement can always be found by deduction alone. You never need to guess, at any level.

A guide for each level

The four levels differ in how many clues you start with and, more importantly, in which technique the puzzle is built to demand. Pick one below — the guide changes with it, and the button at the end starts a puzzle at that level.

Learn the rule by using it. Nothing here needs pencil notes.

Easy Sudoku

Clues to start
about 42
Key technique
Cross-hatching
Speed bonus under
8 min

Easy puzzles are not a watered-down version of the game — they are the same game with enough clues left in that every step is findable by looking. There is always, at every point in an easy puzzle, at least one square you can fill in with certainty. Your only job is finding it.

Start with the nearly-full unit

Look for a row, column or box with eight of its nine squares already filled. Whatever digit is missing goes in the ninth square — nothing else can go there, and it can go nowhere else. Beginners skip this because it feels too easy to count as a move. It is a real move, and easy puzzles are stuffed with them.

Every digit you place removes a blank from three units at once, which often creates a new nearly-full unit somewhere else. This is why easy puzzles unravel in bursts: nothing, nothing, nothing, then six squares in a row.

Then cross-hatch, one digit at a time

When no unit is nearly full, switch to scanning. Pick a digit — say 5 — and a 3×3 box that has no 5 in it yet. Three rows pass through that box; if a 5 already sits in one of those rows, the box's 5 cannot be anywhere in that row. Do the same for the three columns.

Very often that leaves exactly one square standing, and it must be the 5. Work the digit all the way across the grid — all nine boxes — before moving to the 6. Sweeping for one digit is far quicker than staring at one box trying to place all nine.

A worked example

Say the top-left box already holds 1, 2, 3, 5, 6, 8 and 9. Two squares are empty, and the missing digits are 4 and 7. On its own, that tells you nothing about which is which.

Now look outward. One of those two empty squares sits in a row that already contains a 7 further to the right. That square cannot be the 7, so it must be the 4 — and therefore the other one is the 7. Two placements from one observation, and neither came from staring harder at the box.

You do not need notes yet

The pencil button exists, but on easy puzzles writing candidates everywhere costs more time than it saves. Try to finish easy grids without notes at all. It builds the scanning habit that carries every harder level, and it keeps you honest: if you cannot see the reason, you are not meant to place the digit yet.

One habit worth starting now — finish the sentence "7 goes here because…" before you commit. A wrong digit is flagged the moment you enter it and three of them end the game, so a move you cannot justify is a move worth leaving.

Play an easy puzzle

Two habits that prevent most mistakes

This board flags a wrong digit as soon as you enter it, and three mistakes end the game. That is a deliberate constraint: it rewards placing a digit only when you can say why it goes there, rather than because it looks about right.

  • Say the reason out loud (or in your head) before committing. "7 goes here because the other two squares in this box are in columns that already have a 7." If you cannot finish that sentence, do not place the digit.
  • Update your notes immediately after each placement. Stale candidate marks are the single biggest source of confident wrong answers.

Where to go next

Work up a level at a time: when a level stops feeling like a puzzle and starts feeling like typing, move on. If a level feels impossible rather than merely hard, that is almost always one missing technique rather than a lack of talent — the solving techniques guide covers each one in the order you actually need them, and the FAQ answers the rest.

If nine columns still feel like a lot to hold in your head, or you are teaching a child, start on a smaller grid: Sudoku for kids has 4×4 and 6×6 boards where the same scanning works but a puzzle takes a couple of minutes.

Two other things here are worth knowing about. The Sudoku solver will finish a grid you have copied in from somewhere else, and tell you whether it was well-formed to begin with — a puzzle with two answers is not your fault. And the printable Sudoku sheets produce fresh puzzles at any level, one to six per page, if you would rather work on paper than on a screen.