How to play Sudoku

Sudoku looks like a maths puzzle but there is no arithmetic in it at all: it is pure logic, and the digits could just as well be nine animals. This guide teaches the game from zero with a diagram for every idea, the same way our sister site Chess2ez teaches chess. When you are ready, you can play a free puzzle online or print one for paper.

1. The goal, and the one rule

A Sudoku is a 9x9 grid divided into nine 3x3 boxes. Some cells start out filled in; these are the givens and they never change. Your job is to fill every empty cell with a digit from 1 to 9 so that:

• every row contains 1 to 9 exactly once,
• every column contains 1 to 9 exactly once,
• every 3x3 box contains 1 to 9 exactly once.

That is the whole game. No adding, no guessing: every proper puzzle has exactly one solution you can reach step by step with the techniques below.

2. What a conflict looks like

A conflict is the same digit appearing twice in one row, one column or one 3x3 box. It means at least one of those two digits is wrong. Everything in Sudoku flows from avoiding conflicts: a digit is proven correct precisely when every other digit in that cell would cause one.

The same clash is illegal down a column or inside a box. When you play online on ChalkBee, the Auto-check setting paints conflicts red for you exactly like this.

3. Scanning: start where the grid is fullest

The easiest deductions live in the rows, columns and boxes that are already nearly complete. A unit with eight digits filled has exactly one digit missing, so the empty cell fills itself: run through 1 to 9, see which digit is absent, and write it in.

Scanning also works one digit at a time: pick a digit, say 7, and look at each box. Every row and column that already contains a 7 is blocked for that digit, and often only one legal cell in the box remains. Sweep every digit this way before reaching for anything fancier; easy puzzles solve completely on scanning alone.

4. Pencil marks: write down what is still possible

When no cell fills itself immediately, stop trying to hold the puzzle in your head. Pencil marks (also called notes or candidates) are small digits written in a corner of an empty cell listing every value its row, column and box still allow.

As you fill neighbouring cells in, cross the placed digit out of the pencil marks in the rest of its row, column and box. The moment a cell's marks shrink to a single digit, that digit goes in, which erases more candidates elsewhere, and the grid unravels one elimination at a time. The online player has a Notes mode (and an auto-fill option) that manages exactly this for you.

5. Obvious singles: one candidate left

An obvious single is a cell where eight of the nine digits are already ruled out by its row, column and box together. Only one candidate survives, sitting in plain sight, so it must be the answer. This is the workhorse deduction of Sudoku: most cells you fill in any puzzle are obvious singles.

6. Hidden singles: one cell left for a digit

A hidden single flips the question around. Instead of asking “what can this cell be?”, ask “where in this box can this digit go?”. A cell may have several candidates on its own, but if one of those digits has no other legal home in the row, column or box, it is forced all the same. The single is “hidden” among the other candidates.

Obvious and hidden singles are the same rule seen from opposite ends: one narrows a cell down to one digit, the other narrows a digit down to one cell. Harder puzzles need further techniques (pairs, triples and beyond, covered in the strategy quick reference), but singles carry you through every easy and medium puzzle.

7. Beginner tips

• Start with the fullest units. Rows, columns and boxes with six or more givens are where the first digits fall.
• Work digit by digit. Sweep the grid for all the 1s, then the 2s, and so on. It is far less overwhelming than staring at empty cells.
• Never guess. A proper Sudoku never needs it. A guess that happens to work teaches you nothing, and one that fails quietly poisons the whole grid.
• Use notes for anything uncertain. If a digit is not proven, pencil it. Committing a maybe as a definite is how solves go wrong.
• Re-scan after every placement. Each digit you place blocks a row, a column and a box, which usually unlocks a fresh single nearby.
• Pick the right difficulty. Easy puzzles have more givens and solve on scanning alone; save the harder levels for when singles feel automatic.