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Learn Sudoku

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How sudoku works

● Teal: reasoning● Blue: affected cells

Learn Sudoku

Read the rules and examples below, then try the interactive exercises above. Each lesson introduces a technique and lets you practise it.

How sudoku works

Each row, column and 3 × 3 box must contain the digits 1–9 exactly once. Start by finding the missing digit in the almost-complete row.

Worked example

A row contains 1, 2, 3, 4, 5, 6, 7 and 8. The missing digit is 9. Also check that the placement fits its column and box.

Naked single

Look at an empty cell's row, column and box. Digits already present are ruled out. If only one digit remains, you can place it with certainty.

Worked example

After excluding the digits in its row, column and box, an empty cell has only candidate 4. The cell must contain 4.

Hidden single

Choose a digit and examine a row, column or box. Even when cells have multiple candidates, that digit may have just one possible position.

Worked example

Three empty cells in a row have candidates {2, 7}, {2, 5} and {5, 9}. Digit 7 can only go in the first cell, even though that cell also has candidate 2.

Noting candidates

A candidate is a possible digit, not a final answer. Note all digits allowed by the row, column and box. Update your notes as you learn more.

Worked example

If a cell’s row, column and box rule out 1, 2, 3, 5, 6, 7 and 9, you can note 4 and 8. Notes show possibilities, not two final answers.

Locked candidates

If every possible position for a digit in a box lies in the same row, that digit must be in that row within the box. You can eliminate it from the rest of the row outside the box. The same reasoning works for columns and in reverse.

Worked example

In a box, 6 can only go in two cells on the same row. One of those cells must contain 6. You can therefore remove 6 from other cells in that row outside the box.

Naked pairs

If two cells in the same row, column or box have exactly the same two candidates, they must share those digits. Eliminate both candidates from other cells in that unit.

Worked example

Two cells in the same row have exactly candidates {2, 8}. Together they must use 2 and 8. Those digits can therefore be removed from the row’s other empty cells.

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