Sudoku

How to play Sudoku

Sudoku is a number placement puzzle. Fill the grid so that every row, every column and every box contains each digit exactly once. No arithmetic is involved — the digits are just symbols, and the whole puzzle is deduction.

Every puzzle here has exactly one solution, and can be reached without guessing.

The one rule

Each digit appears once in each row, once in each column, and once in each box. That is the entire rule set; everything else is a technique for applying it.

On the classic 9 x 9 the boxes are the nine 3 x 3 blocks. The other sizes work the same way with differently shaped boxes.

Grid sizes

• 4 x 4 — 2 x 2 boxes, digits 1 to 4. A gentle warm-up and genuinely good for children.
• 6 x 6 — rectangular 2 x 3 boxes, digits 1 to 6. Quick, but a proper puzzle.
• 9 x 9 — the classic newspaper Sudoku.
• 12 x 12 — 3 x 4 boxes, using A, B and C alongside 1 to 9 so every cell stays a single character. A serious sit-down puzzle.

Techniques, in the order you will need them

• Last one standing. A row, column or box with eight of its nine digits already placed leaves the ninth with nowhere else to go.
• Scanning. Take a digit and find every row, column and box it already occupies. Often that rules out all but one cell in some box.
• Pencil marks. Write the candidates into a cell and the puzzle starts telling you things. A cell with one candidate left is solved.
• Hidden singles. A digit that can go in only one cell of a box belongs there, even if that cell has several candidates of its own.
• Naked pairs. Two cells in a line sharing the same two candidates and nothing else must use those two between them, so both can be struck out everywhere else in that line.

Difficulty

Easy, Medium, Hard and Expert differ in how many digits you are given to start — from well over half the grid down to about a quarter. Fewer givens means longer chains of reasoning before the grid opens up.

Every difficulty is solvable by logic. Expert is a longer, more stubborn puzzle, not a puzzle that asks you to guess.

Exactly one solution

Puzzles are made by generating a complete, valid grid and then removing digits one at a time. After each removal a solver checks whether the puzzle still has exactly one solution — and if removing that digit would have allowed a second, it goes straight back.

That is why the uniqueness claim is worth something here: it is enforced during generation rather than hoped for afterwards. It also means every deduction you make is safe, because there is never a second answer for a chain of reasoning to lead you towards.

Hints that explain

The hint does not merely drop a digit into a cell. It names the reason — which row, column or box forces the placement — so a hint teaches you the technique rather than simply moving you forward. Used on a puzzle a step above your usual, it is the fastest way to improve.

The daily

One shared 9 x 9 a day, the same for every player, ramping through the week: easy on Monday and Tuesday, medium midweek, hard on Friday and Saturday, and expert on Sunday. Always 9 x 9, so times and streaks stay comparable.

It saves separately from free play, so a practice puzzle never costs you a half-finished daily.

Common questions

Do I ever have to guess?

No. Every puzzle has exactly one solution and can be reached by deduction. If you are guessing, there is a technique that will get you there instead.

Is there any maths in Sudoku?

None. The digits are symbols — you could play with nine colours and nothing would change.

What are pencil marks?

Small candidate digits noted in a cell. They are the working that most of the harder techniques are built on, and the puzzle keeps them for you.

Why does 12 x 12 use letters?

Twelve symbols are needed and two-digit numbers would not fit a cell cleanly, so it runs 1 to 9 and then A, B, C.