Sudoku

Sudoku is played on a grid of 9 rows and 9 columns, split into nine 3×3 boxes. Some cells start with a digit (the clues). You fill in the rest.

You never need arithmetic: the digits are just nine different symbols.

• Each row holds the digits 1 to 9, each exactly once.
• Each column holds the digits 1 to 9, each exactly once.
• Each 3×3 box holds the digits 1 to 9, each exactly once.
• The clues can't be changed. The puzzle is solved when every cell is filled and no digit repeats in a row, column or box.

An easy puzzle here starts with 36 to 41 clues and can be finished with the two simplest steps alone: the naked single and the hidden single. At every moment there are several cells you can fill for certain, so you never get stuck for long.

Medium uses the same two steps with fewer clues, so the next sure cell is harder to spot. Hard and expert need the techniques described on their own pages.

Hidden single: pick a digit, say 5, and a box that has no 5 yet. Look along the rows and columns that cross the box. Every 5 already in one of those lines rules out the cells of the box on that line. When only one cell of the box is left for the 5, it goes there. The same works for a row or a column.

Naked single: pick an empty cell and list what its row, column and box already contain. If eight different digits are there, the ninth is the only one left for the cell.

Start with the digits that appear most often in the clues: each one rules out many cells, so they finish first. A row, column or box with one empty cell left is the easiest of all.

Tap or click a cell, then a number below the grid. On a keyboard, the arrow keys move between cells, 1 to 9 fill a cell, and Backspace or Delete clears it.

Notes turns the number buttons into pencil marks: small digits that remind you what can still go in a cell. Press N to switch on a keyboard, or hold Shift while you type a digit. When you place a digit, it is taken out of the notes in its row, column and box.

Undo takes back as many steps as you like. Hint first points out any wrong digit, then shows the next step a person could find, with the technique and why it works; press Hint again to fill it in. "Show mistakes" marks a wrong digit in red as soon as you enter it; switch it off to check your own work. Your game is saved in this browser, so you can close the page and come back.

Latin squares, grids where each symbol appears once per row and column, were studied by mathematicians for centuries. The puzzle with the extra rule for boxes first appeared in an American puzzle magazine in 1979 under the name Number Place; it is usually credited to Howard Garns, a retired architect.

A Japanese puzzle publisher brought it to Japan in 1984 and gave it the name Sudoku, short for a phrase meaning that each digit must stay single. In Japan that name is a trademark, so many puzzle books there still call the game Number Place. The puzzle spread around the world after British newspapers began printing it in 2004.