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A handbook for solving Sudoku

Every digit has a reason.

Sudoku needs no guessing. This handbook teaches you to reason your way to every cell: from moves you can see at a glance to the multi-link chains of hard puzzles.

Start with the rulesBrowse 21 techniques
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Pick a box and a digit. Look at digit 4 in box 4. The box has no 4 yet and 6 empty cells. Every 4 already on the board is shaded green.

Three levels of reasoning

Techniques are ordered by how many steps of reasoning you need before you can write a digit: one step means fill it now, two steps means eliminate first and then fill, N steps means follow a chain of consequences.

  1. See it, fill it

    1-step reasoning

    At this level every conclusion takes a single observation: you look at the digits already placed and see that a cell can take only one digit, or that a digit has only one place left. No notes, no assumptions.

    Understood 0/4

  2. Eliminate first, then fill

    2-step reasoning

    When no cell can be filled directly, you need an intermediate step: prove that a digit cannot be in certain cells. Step one is finding a locked structure — a digit trapped in the intersection of a box and a line, or a group of digits that takes over a group of cells. Step two is using that elimination to open up a new placement.

    Understood 0/6

  3. Chains of deductions

    N-step reasoning

    Hard puzzles need longer arguments: "if cell A is x then cell B cannot be y, so cell C must be y, so…". The techniques at this level are such chains packaged into recognisable patterns: fish (X-Wing, Swordfish), wings (XY-Wing, W-Wing), chains and colouring, plus tricks based on the uniqueness of the solution.

    Understood 0/11

How to read the boards

Cells are named by row and column: r3c5 is the cell in row 3, column 5. Row numbers are on the left of the board, column numbers along the top. Boxes are numbered 1–9 in reading order, starting top left.

Every example is a real board taken from the middle of a puzzle's solution. Click through the steps to watch the argument form, and turn on “Show candidates” to see every possibility of every cell.

Watch a puzzle solved from start to finish

65 steps from the puzzle to the solution, using 9 different techniques. Each step names the technique and the reason, so you can see how techniques work together in a real game.

Open the walkthrough
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