Sudoku Rules and Solving Tips

Sudoku is a logic puzzle played on a 9×9 grid divided into nine 3×3 boxes. The goal is to fill every empty cell with a digit from 1 to 9.

9️⃣ Play it now: open Sudoku with Easy, Medium and Hard puzzles.

The rules

• Each row must contain the digits 1 to 9 once each.
• Each column must contain the digits 1 to 9 once each.
• Each 3×3 box must contain the digits 1 to 9 once each.
• Some cells are filled in at the start (the clues). A good puzzle has exactly one solution, and you never need to guess.

Beginner techniques

1. Scanning

Pick a digit, say 5. Look at where the 5s already are. Each 5 rules out its whole row, column and box. Often a box has only one cell left where a 5 can go.

2. Single candidates

For an empty cell, list the digits that are not already in its row, column or box. If only one digit is left, that is the answer. Notes make this easy.

3. Hidden singles

Sometimes a digit can go in only one cell of a row, column or box, even though that cell has several candidates. Place it.

Intermediate techniques

• Naked pairs: if two cells in a unit both have only the candidates 3 and 7, then 3 and 7 must go in those two cells. Remove 3 and 7 from every other cell in that unit.
• Pointing pairs: if within a box a digit can only go in two cells of the same row, that digit cannot appear elsewhere in that row, outside the box.
• Box/line reduction: the reverse of pointing pairs; if a digit in a row only fits inside one box, remove it from the rest of the box.

Example: In a row you have 1, 2, 3, 4, 6, 7, 8 and 9 filled. The only missing digit is 5, so the empty cell is 5. In a box where only one cell is empty, the answer is the one digit that box lacks.

Difficulty levels

• Easy: about 40 clues; singles are enough.
• Medium: about 32 clues; you will want notes and hidden singles.
• Hard: about 26 clues; expect naked pairs and pointing pairs.

Common mistakes

• Placing a digit by guessing. One wrong digit can ruin the whole grid, so use notes and eliminate first.
• Forgetting to update your notes after placing a digit.
• Scanning only rows. Always check columns and boxes as well.

Origin

Modern Sudoku was published in the United States in 1979 under the name Number Place, and became a worldwide craze after it was popularised in Japan, where it got the name Sudoku, and then in newspapers around the world in the 2000s.

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