Sudoku Rules: What First-Timers Need to Know

Sudoku is a puzzle where you fill a 9 × 9 grid with digits. It appears in newspapers, puzzle magazines and on phones all over the world. You need a pencil and nothing else. No arithmetic and no general knowledge.

This post is for people who have never played. It covers the rules, the points about the rules that people often get wrong, and how to go about a first puzzle.

The rules

There are three.

Fill each empty cell of the 9 × 9 grid with one digit from 1 to 9.
No digit may appear twice in any row, any column, or any of the nine 3 × 3 boxes marked by thick lines.
The digits already printed in the grid stay as they are.

That is all. A row has nine cells, so does a column, so does a box, and there are nine digits. “No digit twice” therefore means the same as “every digit from 1 to 9 exactly once”.

Names for the parts of the grid

These words come up in every guide, so here they are.

Row: a line of nine cells running across. Counted from the top.
Column: a line of nine cells running down. Counted from the left.
Box: one of the nine 3 × 3 squares with thick borders. Also called a block, region or nonet.
Clue or given: a digit printed in the grid at the start.
Candidate: a digit that could still go in an empty cell.

Every cell belongs to exactly one row, one column and one box at the same time. Placing a digit means checking all three.

Common misunderstandings

It is not a maths puzzle. It uses digits, but there is no adding or multiplying. The digits 1 to 9 are just nine different symbols. The same puzzle would work with nine colours or nine pictures. That is why people who dislike numbers can enjoy it. Each row, column and box does add up to 45, but only because it holds 1 to 9 once each. You never need that fact to solve.

Diagonals do not count. In standard sudoku, the same digit can appear twice on a diagonal. There are variants, such as diagonal sudoku or Sudoku X, where the two long diagonals must also hold 1 to 9, but those are different puzzles with an extra rule. Unless the instructions say so, ignore diagonals.

There is no order inside a box. As long as 1 to 9 are all there, any digit can be in any position.

It is not a game of luck. A well-made puzzle has exactly one solution. That means every cell can be decided by a reason from the digits around it. You never have to guess.

Seeing the rule in a single row

Here is the simplest possible case, in a row I made up. A dot is an empty cell.

3 7 . | 9 1 4 | 6 2 8

Of the digits 1 to 9, only 5 is missing from this row. So the empty cell is 5.

Every sudoku technique grows out of this idea. In a row, a column or a box, rule out the digits that cannot go somewhere, and when one is left, write it in. In a real puzzle you combine what the row, the column and the box tell you to narrow a cell down to one.

Where the name comes from

The puzzle in its modern form is generally traced to 1979, when Dell Magazines in the United States printed it under the name “Number Place”. The setter is thought to have been Howard Garns.

In Japan, the puzzle company Nikoli introduced it in 1984 with a long name that means roughly “the digits must be single”. That was shortened to sūdoku, “single digits”. Sudoku is a Nikoli trademark in Japan, so other Japanese publishers usually call it nanpure, short for Number Place. Elsewhere it took the Japanese name and spread widely from around 2004, when British newspapers began to print it (Wikipedia: Sudoku).

So a puzzle first published in America under an English name became known to the world by its Japanese one. I find that a nice small twist.

Your first puzzle

For the first puzzle, I would pick the easiest level you can find. In an easy puzzle, cells that can be decided without writing any notes keep turning up.

A rough way to start:

Pick a digit that appears often among the clues.
Pick a box that does not have that digit yet.
Rule out the rows and columns of that box that already have the digit elsewhere. If only one cell in the box is left, write the digit there.

On paper, keep an eraser handy. When you get stuck, check for a digit or a box you have not looked at yet. For the next steps, in the order I would learn them, see How to Solve Sudoku: The First Techniques Beginners Should Learn.

Playing on Sudoku365

Sudoku365 is a sudoku app I make for iPhone, iPad and Android. It has four difficulties, Easy, Medium, Hard and Expert, with 300 puzzles each, 1,200 in total.

How to Play on the home screen covers the rules in four pages: fill the blanks with 1 to 9, and each row, each column and each 3 × 3 box holds every digit once.

Selecting a cell during a game highlights its row, its column, its box and every cell with the same digit. The idea of checking all three at once becomes something you can see on screen. With Show incorrect numbers on in settings (the default), a digit that breaks the rules shows up at once and counts as a mistake. Three mistakes end the game.

For a first game I would choose Easy. All 300 Easy puzzles have been checked with a solver, and every one can be finished without notes, only by ruling out digits through rows, columns and boxes. All 1,200 puzzles have also been checked to have exactly one solution.

The app is free with ads, and a one-time Remove Ads purchase turns them off. For getting set up, see Getting Started with Sudoku365. For streaks and stats, see Sudoku365 Tips.

The rules of sudoku fit in three lines, and yet those three lines give every puzzle its own path. One digit and one box is a good place to begin.