Rules
It’s simple
You are given a 9x9 grid. Some cells contain digits, others are empty.
Fill all empty cells with digits from 1 to 9.
Each digit must appear only once in each row, column and 3x3 block.
Details and examples
Grid
Sudoku grid is logically split into 3x3 blocks. There are 9 such blocks. Each cell belongs to exactly one row, one column and one block.
See Example 1. The highlighted cell belongs to the 4th row, 6th column and 5th block. Blocks are numbered from top to bottom and left to right, similar to normal text reading order. However, you don’t really use this numbering when solving Sudoku. You only need it to understand hints.
Givens
Each Sudoku puzzle starts with some pre-filled digits on the grid, known as givens. The remaining empty cells need to be filled with digits from 1 to 9.
A common misconception about Sudoku is that its difficulty is determined by the number of empty cells. This is not true. You may find a Sudoku with only 20 givens that is very easy, while another with as many as 50 givens might be very difficult.
Example 2 shows a typical Sudoku puzzle.
Constraints
Each digit must appear only once in each row, column and 3x3 block.
See Example 3. It shows you a row, column and block filled with digits so that the uniqueness constraint it met.
Don’t be confused by slightly different definitions of Sudoku rules. There are multiple ways to describe the uniqueness constraint. For example, one might say that each row, column and block must contain every digit from 1 to 9, or that digits in each row, column and block can not repeat. All these wordings are equivalent.
Solving Sudoku
Every valid Sudoku has exactly one solution. You solve Sudoku by filling the cells one by one until the grid is fully solved. A cell can be filled with a digit if you can logically conclude that either:
- this cell cannot contain any other digit; or
- this cell is the only one in row, column or block that can contain this digit.
In other words, you fill a cell with a digit if you can logically conclude that it must be there. A common beginner mistake is to fill a cell with a digit when it may be there, rather than when it must be there. Don’t do that - never guess! There is always a logical way to find and fill the next cell.
Example 4 shows the solution of the Sudoku puzzle shown in Example 2.
Let's get to solving
Solving Sudoku is the best way to understand the rules. Ready to try? Play your first Sudoku: