Sudoku Rules: A 3-Minute Guide

What does a Sudoku grid look like?

A Sudoku grid is nine cells across and nine cells down, for a total of 81 cells. A horizontal line is a Row, a vertical line is a Column, and each group of three cells across and three down enclosed by bold lines is a 3×3 box. Each grid has nine rows, nine columns and nine boxes.

In this article, you will see cell positions written as coordinates. Rows run from 1 to 9 from top to bottom, and columns from 1 to 9 from left to right. The cell in row 3, column 5 is r3c5. Boxes are numbered 1 to 9 from left to right, starting at the top left and continuing on the next line.

A number already filled in at the start is a given. You cannot change the givens; your goal is to fill the remaining empty cells.

There are just three rules

1. Each row contains the numbers 1 to 9 exactly once.
2. Each column also contains the numbers 1 to 9 exactly once.
3. Each box also contains the numbers 1 to 9 exactly once.

Together, these rules mean that a number you enter must be absent from all three of the cell's row, column and box. The numbers are simply symbols in a sequence, so you do not need arithmetic such as addition or multiplication.

A valid Sudoku has exactly one solution: this property is called uniqueness. DailySudoku checks uniqueness when generating puzzles, so the original givens determine exactly one number for every cell. The techniques you need to find those numbers, however, vary from puzzle to puzzle.

Finding your first number ① — pick a cell and check all three areas

Your first approach is to pick an empty cell and gather all the numbers already in its row, column and box. Look at r3c3 in the example below.

c1c2c3c4c5c6c7c8c9

r1r2r3r4r5r6r7r8r9

3

5

9

7

4

3

9

5

6

9

8

5

3

4

2

4

2

9

7

1

3

2

6

5

6

4

8

3

7

9

2

1

2

4

6

7

8

3

2

4

• Row 3 contains 6, 9, 8, 5, 3, 4 and 2.
• Column 3 contains 5, 7, 9, 6, 2 and 3.
• Box 1 contains 3, 5, 6, 7 and 9.

Together, these three areas already contain every number from 2 to 9. Only 1 remains, so r3c3 must be 1.

Finding your first number ② — pick a number and find its place

If you cannot spot a cell using ①, change your approach. Pick a number, then count how many cells in one row, column or box can hold it. Look for 2 in row 1 of the same example. Row 1 has six empty cells: r1c2, r1c4, r1c5, r1c6, r1c7 and r1c8.

• r1c2 cannot be 2 because column 2 already has a 2 at r4c2.
• r1c5 cannot be 2 because column 5 has a 2 at r5c5, and r1c6 cannot be 2 because column 6 has a 2 at r7c6.
• r1c7 and r1c8 cannot be 2 because box 3 already has a 2 at r3c9.

Only r1c4 remains, so row 1's 2 must go in r1c4.

When these methods are not enough

You can often finish an easy puzzle with just these two methods. As difficulty rises, though, most empty cells may still have two or more possibilities after you check all three areas, and you may struggle to find just one place for a number in a row. Instead of keeping everything in your head, write the possible numbers, or candidates, in small figures in each cell. This can help you see your next move.

Common mistakes

• You check the box but overlook the row and column. Even if a number is missing from the box, you cannot enter it if it is already in the same row or column. Always check all three areas together.
• You repeat a number in the same line. Having the same number twice in a row, column or box breaks the rules. If you enable “Mistake limit” in the game settings, the game ends when you reach the set number of mistakes.
• You guess without being sure. If your guess is wrong, the cells you fill in afterward can go wrong too. When you get stuck, use Hint instead of guessing. It reveals one cell's answer, and you have a limited number of uses per puzzle.

Practice puzzle

c1c2c3c4c5c6c7c8c9

r1r2r3r4r5r6r7r8r9

5

4

2

7

3

5

6

6

7

8

4

9

2

8

3

2

8

9

5

6

4

6

8

1

9

2

8

6

5

3

4

2

9

3

5

4

1

6

8

5

What number goes in r3c2? As in “Finding your first number ①,” check row 3, column 2 and box 1 together.

Show answer

1. Row 3 contains 6, 7, 8 and 4; column 2 contains 3, 2, 6 and 9; and box 1 contains 3, 4, 5, 6 and 7. Together, they contain every number from 2 to 9, so only 1 remains.