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Rules: three constraints meet in every cell

The grid is divided three ways at once: nine rows, nine columns and nine 3×3 boxes. Any digit you place must satisfy the row, column and box it belongs to, so each cell is effectively competing with up to 20 neighbours (8 in its row, 8 in its column and 4 more in its box).

Digits printed at the start are called givens and cannot be changed. Every QuizLab puzzle is checked by computer to have exactly one solution before it is published. If a grid allowed two answers, you would eventually be forced to guess, and a forced guess is not logic.

The numbers are never added or multiplied. Nine colours or nine symbols would work just as well, which is why people who dislike arithmetic still enjoy Sudoku.

Controls: finish a whole grid without touching the mouse

• Select a cell: click or tap it, or move one cell at a time with the arrow keys.
• Enter a digit: press 1–9 on the keyboard or use the number pad under the grid.
• Clear a cell: Backspace, Delete or 0.
• Toggle pencil marks: press M. While it is on, digits go into the corner of the cell as small candidates.
• Open help: H or the question-mark key.
• Undo is unlimited, so you can test a hypothesis and roll back to where you were.

Strategy: follow a digit, not an empty cell

Beginners tend to stare at one empty cell and ask what could go there. It is usually faster to pick a digit and sweep the whole grid for it. If 7 already appears six times, there are only three boxes left that need a 7, and one of them often has a single legal spot.

Next, finish the units that are almost full. A row or box with seven digits has only two or three candidates left, so it is the cheapest place to check. Each cell you fill there removes candidates from the crossing rows and columns and opens new placements.

When a medium or harder grid stalls, start writing candidates. Only with complete pencil marks will you notice a pair of cells in one unit that share the same two candidates; once you see that pair, those two digits can be erased from every other cell in the unit. Sloppy notes lead to wrong eliminations, so fill them in one box at a time.

History: born in an American magazine, named in Japan

The idea of placing each symbol once per row and column goes back to the Latin squares studied by the 18th-century mathematician Leonhard Euler. The modern puzzle, however, first appeared in 1979 in Dell's puzzle magazines under the name Number Place, and is credited to Howard Garns, a retired architect.

In 1984 the Japanese publisher Nikoli introduced it with a long title meaning 'the digits must remain single', and the abbreviation Sudoku became the global name. After The Times in the UK began printing it in late 2004, it spread through newspaper puzzle pages across Europe and North America the following year.

Mathematicians took it seriously too. A 2005 computation counted about 6.67×10²¹ distinct completed grids, and in 2012 an exhaustive computer search proved that a uniquely solvable puzzle needs at least 17 givens; any grid with only 16 has more than one solution.

Questions that come up while solving Sudoku

I am completely stuck. Is this a grid where I have to guess?

No. QuizLab's generator only lets through grids with exactly one solution, so somewhere there is always a cell that logic can settle. If you are stuck, you have usually missed a candidate in your notes or left one that should have been erased. Rewriting the notes box by box usually reveals the way forward.

Can I solve on paper with a pencil?

Yes. The Sudoku print page lets you choose a difficulty and print it on a single A4 sheet. Large-print grids and answer sheets are available too, which helps when solving with older relatives or children who find long screen time tiring.

Does the daily puzzle change difficulty by weekday?

Yes. Each weekday has a fixed difficulty, light at the start of the week and harder towards the weekend. Everyone gets the same grid on the same day, so clear times on the leaderboard can be compared directly.