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Start with the three overlapping rules
A classic Sudoku has 81 cells arranged in nine rows and nine columns. The thicker borders divide it into nine 3 × 3 boxes. Complete the grid with the digits 1 through 9 so that each digit appears exactly once in every row, every column, and every box. The printed starting clues stay fixed.
A row runs horizontally; a column runs vertically. Each cell belongs to one of each, plus one box, so every placement must satisfy all three groups at the same time. Diagonals impose no extra rule in classic Sudoku. The digits identify nine different symbols: solving does not require addition, multiplication, or a calculator.
To describe a position, use r for row and c for column, counting from the top left. For example, r4c5 is the cell in row 4, column 5, inside the central box. This notation helps you explain a move and return to it later.
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List what a cell can still contain
A candidate is a digit not yet ruled out for an empty cell. Begin with 1 through 9, then remove every digit already placed in that cell's row, column, or box. The remaining digits are possibilities, not confirmed answers. Pencil notes keep those possibilities separate from filled cells.
The following is an illustrative local position, not a complete puzzle. Row 4 already contains 1, 3, 4, 6, 7, and 9. You are examining r4c5. Column 5 contains a 2, and the central box contains an 8; neither contains a 5. Other filled cells remove no additional candidates from the row's missing set.
| Check | Reason | Candidates left |
|---|---|---|
| Row 4 | The six placed digits exclude 1, 3, 4, 6, 7, and 9 | 2, 5, 8 |
| Column 5 | A 2 is already in this column | 5, 8 |
| Central box | An 8 is already in this box | 5 |
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Naked Single: one cell has one candidate
The example leaves only 5 in r4c5. This is a Naked Single: every other digit is excluded, so 5 is forced. The exclusions can come from several groups; the row does not need to be almost complete. Before entering the answer, make sure your candidate list included every possibility and that the existing placements are correct.
After placing 5, remove 5 from notes in the same row, column, and box. One of those cells may now have only one candidate, giving you the next move. A candidate elsewhere in the grid is unaffected unless it shares one of those three groups.
The simplest single
A row reads 1, 2, 3, 4, 5, 6, 7, 8, blank. Its last cell must be 9. If that cell's column or box already contains 9, the position has a contradiction: recheck an earlier entry instead of choosing another digit.
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Keep notes and answers consistent
A digit fitting one cell is not enough to prove it belongs there. Several digits may fit without immediately breaking a rule. Enter a confirmed answer only when you can explain what rules out the alternatives, or what prevents that digit from going anywhere else in its group.
- Check the box as well as the row and column. A placement can satisfy two groups while duplicating a digit in the third.
- Do not mistake a partly written note list for a complete candidate list. One note is not proof of a single if other possibilities were never recorded.
- Refresh affected notes after each placement. An outdated candidate can hide a deduction or suggest a false choice.
- Treat a duplicate digit, an empty cell with no candidates, or a group with nowhere for a missing digit as a reason to review recent entries.
- Keep starting clues unchanged. Use undo to revisit your own moves when the reasoning no longer fits.
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Repeat a small, reliable solving routine
Begin with a row, column, or box that has several clues. Identify its missing digits, inspect the relevant empty cells, and look for either kind of single. After every placement, return to the three groups it affects before scanning the rest of the board. This is more manageable than repeatedly staring at all 81 cells.
When a pass finds nothing, check whether your notes are complete and switch perspective: scan cells for a single candidate, then scan each missing digit for a single location. These two techniques are a useful foundation, but they do not solve every Sudoku. Harder positions can require other deductions. Being unable to find a single does not prove the puzzle has no solution.
Explain one move before making the next
Say, 'This cell must be 5 because its row excludes six digits, its column excludes 2, and its box excludes 8.' After entering 5, check those same three groups again. Practicing a short explanation helps distinguish a deduction from a plausible guess.
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Practice on a difficulty that leaves room to learn
Open Sudoku in Logic & Number Puzzles and choose an introductory difficulty. Use Pencil notes to record candidates, then try to justify a placement before asking for a hint. The service offers unlimited play and multiple difficulty levels, so you can begin another puzzle when you want more practice. Difficulty names describe the service's own ratings; they are not a universal measure across puzzle sites.
A fresh puzzle may be generated with randomness, but deductions concern the fixed clues already on its board. That is different from predicting an independent random draw. The related lottery-odds guide explains why previous draw results do not reveal the next winning numbers; Sudoku's constraints supply information that those results do not.
Sources and further reading
These references support the definitions and limits discussed in this guide. Worked scenarios labeled as examples are illustrative.
- Nikoli: Sudoku rulesThe puzzle publisher's rules for digits, rows, columns, and 3 × 3 boxes.
- Sudoku.coach: Naked SingleThe teaching site's explanation of a cell with one remaining candidate.
- Sudoku.coach: Hidden SingleThe teaching site's explanation of a digit with one possible location in a group.
- 4ool Puzzle: SudokuThe live Sudoku game, rules, difficulty controls, pencil notes, and hints.