Sudoku

What is Sudoku?

Sudoku is a pure logic puzzle played on a 9x9 grid split into nine 3x3 boxes. A handful of digits are given, and your job is to work out the rest by elimination. Despite the numbers, there is no arithmetic involved and no counting or adding of any kind.

How to play Sudoku

Setting up the board

A standard puzzle is a 9x9 grid of 81 cells, divided into nine 3x3 boxes, with some cells already filled in. Those starting digits are called givens or clues, and they never change. Every remaining cell must be filled with a digit from 1 to 9.

How it works

1. Fill every empty cell with a single digit from 1 to 9.
2. No digit may repeat within a row.
3. No digit may repeat within a column.
4. No digit may repeat within any 3x3 box.
5. The given clues are fixed and can never be altered or moved.
6. A proper puzzle has exactly one solution, reachable by logic alone.
7. The digits are only labels, so no addition or arithmetic is ever needed.

How to solve

The puzzle is solved when all 81 cells are filled and every row, every column and every 3x3 box contains each digit from 1 to 9 exactly once.

Solving tips

• Scanning and cross-hatching: pick one digit and sweep the grid box by box. Rows and columns that already contain that digit rule out whole lines inside neighbouring boxes, and often only one cell in a box survives. This alone solves most easy puzzles.
• Hidden singles: look at a row, column or box and ask which cells could hold a particular digit. If exactly one cell can take it, place it there, even if that cell still looks like it has several options.
• Naked singles: work the opposite way and examine a single cell. Cross off every digit already present in its row, column and box. If only one digit survives, it belongs there.
• Pencil marks: once obvious placements dry up, write the remaining candidates small in each empty cell. Keeping candidates accurate is what makes advanced techniques visible.
• Naked pairs: if two cells in the same row, column or box carry the identical two candidates, those two digits must occupy those two cells, so you can erase both from every other cell in that unit.
• Pointing pairs: if a digit's only candidate positions inside a box all sit in one row or column, that digit must land there, so you can eliminate it from the rest of that row or column outside the box.

About this puzzle

Sudoku descends from Latin squares, arrangements of symbols in which no symbol repeats in a row or column, studied by Leonhard Euler in the 18th century.

The modern puzzle appeared in 1979 in Dell's Pencil Puzzles and Word Games under the name Number Place, and is credited to Howard Garns, a retired American architect, who added the nine 3x3 boxes.

Japanese publisher Nikoli picked it up in 1984, where Maki Kaji named it after the phrase suuji wa dokushin ni kagiru, roughly the digits must occur only once, later shortened to sudoku.

Wayne Gould, who wrote software to generate puzzles, brought it to The Times of London in November 2004, and within months it had spread to newspapers worldwide.

Frequently asked questions

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