Sudoku Rules: How to Play

The grid and the rule

A Sudoku grid has 9 rows and 9 columns, which makes 81 cells. Thicker lines divide it into nine boxes of 3 × 3 cells. Some cells contain a digit from the start; these are the givens.

The rule: fill every empty cell with a digit from 1 to 9 so that each row, each column and each box contains every digit exactly once.

The digits are only nine different symbols. Nothing is added or multiplied; letters or colours would work as well.

Words that players use

What makes a puzzle fair

A proper Sudoku has exactly one solution. With too few givens, or badly placed ones, several different grids fit the givens and the player is forced to guess.

It has been shown by a complete computer search that a puzzle with 16 givens never has exactly one solution; the smallest possible number of givens is 17. Puzzles with that few givens are rare and hard to find. The daily puzzles on this site have between 22 and 39 givens.

The number of different completed grids is 6,670,903,752,021,072,936,960, so puzzles do not run out.

The number of givens does not decide alone how hard a puzzle is. What matters is which kind of reasoning is needed to find the next digit.

A worked example

Take a row that looks like this, where a dot is an empty cell:

The row contains 1, 2, 3, 5, 6, 7 and 9. The digits 4 and 8 are missing, so the cells in columns 2 and 6 hold 4 and 8 in some order.

Now suppose that column 2 already contains an 8 in another row. Then the cell in column 2 of our row cannot be 8. It is 4, and the cell in column 6 is 8.

Both digits were found without trying anything out. Each step used the rule directly: a digit that is already in a unit cannot appear in it again.

The two basic questions

Almost all of an easy puzzle is solved by asking one of two questions again and again.

• Which digits can go into this cell? If only one digit is left after you remove the digits of its row, column and box, the cell is decided.
• Where in this unit can this digit go? If only one cell of a row, column or box can take the digit, it goes there.

Players call the results of these questions singles. The techniques page shows both with examples and continues with the methods that medium and hard puzzles need.

• Sudoku solving techniques
• Play the daily Sudoku

Where the puzzle comes from

The puzzle in its present form was published in 1979 in the United States by Dell Magazines under the name Number Place. The Japanese publisher Nikoli introduced it in Japan in 1984; the name Sudoku comes from there and refers to digits that stay single.

Common mistakes

• Forgetting the boxes. A digit can be new to its row and column and still be in the box already.
• Writing a digit because it is possible. A digit belongs in a cell only when nothing else is possible there, or when the digit has no other place in a unit.
• Continuing after a contradiction. If a unit shows a digit twice, an earlier digit is wrong. Go back with undo or use the check instead of repairing around it.
• Guessing between two digits. It looks like a shortcut, but a wrong guess shows up many moves later and everything since then has to be removed.