How to Play Sudoku

The rules take about a minute to learn. Getting good takes longer, but not as long as most people expect, and none of it involves maths.

The one rule

A sudoku grid is 9 squares across and 9 down, divided into nine 3×3 boxes. Some cells already have numbers in them; those cannot be changed. Fill every empty cell with a digit from 1 to 9 so that:

• each row holds 1–9 with no repeats,
• each column holds 1–9 with no repeats,
• each 3×3 box holds 1–9 with no repeats.

That is the entire rule. Everything else is a consequence of it.

There is no arithmetic

People assume sudoku is a numbers puzzle because it is made of numbers. It is not. Nothing is ever added, subtracted, or compared. The digits are simply nine symbols that have to be arranged without collisions, swap them for nine colours and the puzzle would be exactly the same. This is worth knowing if you have been avoiding sudoku on the grounds of being bad at maths.

Three techniques that actually work

1. Start where the grid is fullest

Scan for the row, column, or box that already has the most numbers. If a box has eight digits and one blank, the missing digit is forced, there is only one number it can be. Two blanks, and you often only need one other clue to break it open. Beginners tend to start at the top left and work across; it is far more productive to start wherever the puzzle has already done the work for you.

2. Work one digit at a time

Pick a digit that already appears several times on the grid, say, 7. Every row and column containing a 7 is now closed to another 7. Look at a box with no 7 in it and cross off every row and column that already has one. Frequently only a single cell survives. Then move to the next digit and do it again.

This is the technique that turns a grid from intimidating into methodical, and it is the one most self-taught solvers arrive at last.

3. Pencil in the candidates

When a cell narrows to two or three possibilities, write them small in the corner. It feels like admitting defeat, but it is not: as other cells resolve, those candidates get eliminated one by one, and the answer falls out on its own. Hard puzzles are essentially unsolvable without this.

On screen the number pad handles this for you. On paper you need room to write, which is worth knowing before you print: a grid squeezed six to a page leaves no space for candidates. If you want to practise the notation on its own, print a blank sudoku grid one or two per page and copy a puzzle into it by hand.

Solving a puzzle step by step

Rules are one thing; watching them work is another. Here is how the first few moves of a real grid actually go.

Step 1: find the fullest box

Scan the nine boxes and pick the one with the most numbers already in it. Say a box has 1, 3, 4, 6, 7, 8, 9 filled and two blanks. Only 2 and 5 are missing. Now look at the rows and columns those two blank cells sit in. If one of them already contains a 2 somewhere else, then 2 cannot go there, so that cell must be 5. The box is finished, and you have not guessed anything.

Step 2: chase a single digit

Pick a digit that appears often, say 7. Go box by box. In each box without a 7, cross out every row and column that already has one. Frequently a single cell survives, and that is where the 7 goes. Place it, then keep going: the 7 you just placed closes another row and column, which may force the next one.

This is the technique that turns a grid from intimidating into mechanical, and it is the one most self-taught solvers arrive at last.

Step 3: write the maybes down

When neither trick moves, start pencilling. A cell that could only be 2 or 8 gets a small "2 8" in the corner. Do that across a row or a box. Now look for a digit that appears as a candidate in only one cell of that unit: it has to go there, whatever else that cell could have been.

Step 4: repeat until it collapses

Every number placed removes candidates elsewhere. What felt stuck at twenty blanks tends to unravel at ten, and the last five usually fall in under a minute. That collapse is the whole pleasure of the thing.

You never need to guess

Every proper sudoku has exactly one solution, reachable by logic alone. If you find yourself guessing, you have missed a deduction somewhere . The guess, if wrong, will not reveal itself for another twenty cells, by which point the grid is ruined. When stuck, go back and re-scan rather than gambling.

Where to start practising

If the rule is new to you, a smaller grid removes the intimidation without changing anything about the logic:

Once the pattern clicks, move to a full 9×9 grid with plenty of givens:

Frequently asked questions

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