How to play Sudoku, with tips from Olive the owl

The puzzle behind Sudoku: Sudoku

Sudoku in its modern form is usually credited to Howard Garns, an American puzzle maker whose grids appeared in Dell Magazines in 1979 under the name Number Place. In the 1980s the Japanese publisher Nikoli took it up and called it sudoku, short for a phrase meaning that each number must stay single. It became a favourite around the world in the mid 2000s.

Also known as Number Place.

The rules are the classic ones. Before the 9 by 9 board, Easy starts with 4 by 4 boards (numbers 1 to 4, boxes of 2 by 2) and 6 by 6 boards (numbers 1 to 6, boxes of two rows by three columns). Every box is a den: fill one and a sleepy friend wakes up. A wrong number costs one of three hearts, and notes are always free.

How to play Sudoku

Olive the owl tucks one of each number into every row, column and den.

• Every row, every column and every box holds each number exactly once.
• Each box is a den. Fill a den and a sleepy friend wakes up.
• A wrong number costs one of your three hearts. Lose all three and the puzzle starts again.
• Relaxed mode (in Settings) has no hearts and checks nothing until the grid is full.
• Three stars for a puzzle with no hearts lost and no hints. A hint or two caps it at two stars, and lots of hints at one.

What you can never do

• No number twice in a row, column or den.
• A given number never changes.

Controls with Olive the owl

• Tap a square, then a number.
• Turn on Notes to pencil in ideas. Auto fills them in for every empty square, for free.
• With a keyboard: arrow keys move, Space selects, a number fills, Shift and a number writes a note, N switches notes, Backspace clears, Ctrl and Z undoes.

Strategies for beginners

Start on a small board

If sudoku is new to you, the first 60 levels are 4 by 4 and 6 by 6 boards. They follow the same rules with fewer numbers, so you learn to spot the patterns before the full 9 by 9.

Scan one number across the dens

Pick a number, say 5, and look at where the 5s already are. Each one rules out its own row and column. If a den has only one square left that no 5 can see, the 5 goes there. Players call this cross-hatching, and it solves most easy puzzles.

Check rows and columns the same way

Every row and column needs each number once too. When only one square in a row can take a missing number, that is its spot, even if the square itself could hold other numbers. This is called a hidden single.

Count what a square can't be

Pick one empty square and list the numbers already in its row, column and den. On a 9 by 9 board, if eight numbers are taken, the ninth is the answer. This is called a naked single.

Use notes when the singles run out

Notes are the small numbers that might still fit a square, also called pencil marks or candidates. Turn on Notes to write them yourself, or tap Auto to fill them in for every empty square. Notes and auto notes are free and never count as hints.

See where a number points

If a number's notes inside one den all sit in the same row, that number must go in that row within the den. So you can rub it out of the rest of the row in the other dens. The same works for columns, and the other way round.

Spot pairs

When two squares in the same row, column or den can each only be the same two numbers, those two numbers belong to them. Rub both out of every other square in that row, column or den. Hidden pairs and triples work on the same idea.

Learn the big patterns last

The hardest Expert and Master puzzles bring X-wings, XY-wings and swordfish, patterns that link several rows or columns at once. You never need anything harder, and you never need to guess. When you are stuck, a hint shows the next step and why it works.

Quick tips from the game

• Look for a row, column or box that is nearly full: the missing number often has only one place to go.
• Small boards come first: 4 by 4, then 6 by 6, then the classic 9 by 9.

Words to know

Given

A number printed on the board at the start. Givens never change.

Den

Our name for a box: the blocks marked out by thicker lines, 3 by 3 on a 9 by 9 board. Each den holds every number once.

Candidate

A number that could still go in a square. Notes are how you write candidates down; many players call them pencil marks.

Unit

Any row, column or den. Each unit holds every number exactly once. Some players call it a house.

Single

A square with only one possible number (a naked single), or a number with only one possible square in a unit (a hidden single).

Pair

Two squares in a unit that share the same two candidates, or two numbers that fit only the same two squares of a unit.

X-wing

An advanced pattern: a number that fits only two squares in each of two rows, lined up in the same two columns. It rules that number out of the rest of those columns.

Questions about Sudoku