How to play sudoku

Sudoku is a logic puzzle: no maths, no guessing. Learn the rules in a minute, then use the techniques below to solve anything from an easy sudoku to a master-level puzzle.

The rules

A sudoku is a 9×9 grid divided into nine 3×3 boxes. Some cells are already filled in. Your goal is to fill every empty cell with a digit from 1 to 9 so that:

• every row contains 1 to 9 exactly once,
• every column contains 1 to 9 exactly once,
• every 3×3 box contains 1 to 9 exactly once.

That's it. A well-made sudoku has exactly one solution, and you can always reach it with logic alone. Every puzzle in Sudoku Nonet is checked for this.

How to start a sudoku

1. Look for crowded areas. Rows, columns or boxes with six or more digits leave few options.
2. Scan one digit at a time. Pick a digit, say 5, and look at where it already appears. Each 5 rules out its row, column and box. Often only one cell is left for a 5 in some box.
3. Use pencil notes. When a cell is unclear, write down the candidates it could hold. In Sudoku Nonet, tap the pencil (or long-press a number) to add notes; they clear automatically when you place a digit nearby.
4. Never guess. If you're stuck, scan again for another digit or another box. There is always a logical next step.

Solving techniques

1. Naked single

A cell where only one digit is still possible, because the other eight already appear in its row, column or box. Fill it in.

2. Hidden single

A digit that can only go in one cell of a row, column or box, even if that cell has other candidates. This is the most common technique in easy and medium puzzles.

3. Naked pair

Two cells in the same row, column or box that both have only the same two candidates, for example {3, 7}. Those two digits must go in those two cells, so you can remove 3 and 7 from every other cell in that unit.

4. Pointing pair

If, within a box, a digit can only go in cells that share one row (or column), that digit must be in that row inside this box. Remove it from the rest of that row outside the box.

5. Hidden pair

Two digits that can only appear in the same two cells of a unit. Those cells must hold exactly those digits, so remove all other candidates from them.

6. Box/line reduction

The mirror image of a pointing pair: if, within a row (or column), a digit can only go in cells that share one box, it must be in that box on this row. Remove it from the other cells of that box.

7. Naked and hidden triples

The same idea as pairs, with three: three cells in a unit that together hold only the same three candidates, or three digits that fit in only the same three cells. The cells don't each need all three candidates.

8. X-Wing

For expert and master puzzles: if a digit can only go in two cells in each of two rows, and those cells line up in the same two columns, the digit must occupy two opposite corners of that rectangle. Remove it from the rest of those two columns.

9. Y-Wing

Three cells with two candidates each: a pivot {A, B} that sees one cell with {A, C} and another with {B, C}. Whichever digit the pivot gets, one of the other two must be C, so any cell that sees both of them can't be C.

10. Swordfish

An X-Wing with three rows: when a digit's possible cells in three rows all fall in the same three columns, it can be removed from the rest of those columns.

11. X-Chain

Follow one digit through the grid. Where a row, column or box has only two spots left for it, the two are strongly linked: if the digit isn't in one, it's in the other. Two spots that merely share a unit are weakly linked: if it's in one, it isn't in the other. Alternate strong and weak links, starting and ending with a strong one, and the digit must sit at one of the two ends, so it can be removed from every cell that sees both. The shortest X-Chains are known as the Skyscraper and the 2-String Kite.

12. XY-Chain

A Y-Wing that keeps going: a string of cells with exactly two candidates each, every cell sharing a digit with the next. If the first cell isn't Z, the chain forces the last one to be Z, so any cell that sees both ends can't be Z.

Stuck in Sudoku Nonet? A hint highlights the cells involved and names the technique, so you can see why the digit fits.

Tips for faster solving

• Finish the easy placements first; every new digit unlocks others.
• Keep your notes up to date; stale candidates cause mistakes.
• Turn on highlighting of identical numbers to spot hidden singles at a glance.
• Stuck for real? Take a hint, then look at why that digit fits. That's how you learn the next technique.