Sudoku is a number-placement puzzle played on a 9×9 grid: fill every row, column and 3×3 box with the numbers 1 through 9, each used exactly once. No math is involved, only logic.
The puzzle starts with some cells already filled in. Those are called “givens.” Your job is to work out what belongs in the empty cells using the clues the givens provide, not by guessing. Below are the rules, two starter strategies, and a small 4×4 puzzle to try the ideas on before moving to a full grid.
What are the rules of sudoku?
A standard sudoku grid is 9 cells by 9 cells, split into nine 3×3 boxes (Encyclopaedia Britannica). Each row, each column and each 3×3 box must contain the numbers 1 to 9 with no repeats.
The numbers are just labels. Britannica notes the game “is based entirely on logic, without any arithmetic involved,” so you could swap the digits for letters or colors and the puzzle would play the same way. This guide covers the classic 9×9 grid and basic techniques only. It doesn’t cover variant grid sizes, killer sudoku, or advanced solving methods like X-Wing or swordfish.
How do you solve a sudoku puzzle?
You solve sudoku by eliminating possibilities until only one number can go in a cell. Two starting techniques cover most easy and medium puzzles: scanning and pencil marks.
Scanning means checking a row, column or box to see which numbers are missing, then checking the other rows, columns and boxes that overlap it to rule out where those missing numbers can’t go. If a box is missing a 7, and two of its rows already have a 7 elsewhere, the 7 in that box has to go in the one remaining row.
Pencil marks means writing the small candidate numbers in a cell’s corner when more than one number could still fit. As you fill in more cells, some candidates get ruled out. When a cell ends up with only one candidate left, that’s the answer. This section covers scanning and pencil marks only. It doesn’t cover pattern-based techniques used in harder puzzles.
Why does sudoku build logic skills?
Sudoku exercises the kind of step-by-step deduction used in logic and math, though the research on lasting benefit is still limited. A 2026 systematic review in Frontiers in Neuroimaging found that sudoku consistently activates brain regions tied to executive control and working memory, but the reviewers cautioned that the small number of studies “preclude firm conclusions” about whether playing it actually improves those skills over time.
What sudoku does teach clearly, activity by activity, is elimination: ruling out wrong answers until one option is left. That’s useful practice for word problems and geometry proofs, both of which also rely on ruling out what can’t be true. This isn’t a claim that sudoku raises test scores or IQ. It doesn’t cover that.
Can you practice on a smaller grid?
Yes. A 4×4 sudoku uses the numbers 1 to 4, split into four 2×2 boxes, and follows the same rule: each row, column and box gets every number exactly once. It’s a fast way to try scanning before tackling a full 9×9 grid.
| 1 | 2 | 3 | |
| 1 | |||
| 2 | 4 | ||
| 4 | 1 |
Try filling in the blanks using only scanning: for each empty cell, check which numbers already appear in its row, column and 2×2 box, and rule those out. This puzzle has exactly one solution.
Show answer and reasoning
Solution:
| 1 | 2 | 3 | 4 |
| 3 | 4 | 1 | 2 |
| 2 | 1 | 4 | 3 |
| 4 | 3 | 2 | 1 |
Row 1 is missing 4, and since column 4 has no 4 yet, it goes in the top-right cell. Row 2’s box (top-right) already has 1 and 4 from row 1’s column, and the box needs 2 and 3. Column 4 already has a 4, so column 4 gets 2, leaving 3 for the remaining cell in that box. Row 2’s bottom-left box needs 3 and 4, but column 1 already has 1, 2 and 4, so column 1 gets 3, and 4 fills the last cell. From there, each remaining row and column has only one missing number, and each fits without conflict. Every row, column and 2×2 box contains 1, 2, 3 and 4 exactly once.
Ready for a full grid? Our learning games hub links to other logic and strategy games, and the math games section has more number-based puzzles if scanning and pencil marks clicked for you. If you’d rather practice arithmetic directly, see our math worksheets and homeschool worksheet resources.
Sources
- Encyclopaedia Britannica. Sudoku
- Frontiers in Neuroimaging. Neural correlates of Sudoku play: a systematic review of brain imaging studies (2026)