How to Solve Sudoku: Strategies for Every Difficulty Level

The Rules and What They Actually Mean

The Beginner Workflow

Technique 1: Cross-Hatching (Scanning)

Technique 2: Naked Singles

Technique 3: Hidden Singles

Using Pencil Marks

Technique 4: Naked Pairs

Technique 5: Hidden Pairs

Common Mistakes at Every Level

Difficulty Levels: What Changes

When to Use the Photo Scanner

Example cross-hatch walk-through

When to use pencil marks for naked singles

Hidden singles versus naked singles

Sudoku requires no mathematics — only systematic logical deduction. These techniques, applied in order, solve every Sudoku puzzle from easy to expert.

Every row, column, and 3×3 box must contain each digit from 1 to 9 exactly once. This means: if a digit already appears in a row, it cannot appear again in that row. Same for columns and boxes. The entire puzzle is solved by applying this constraint repeatedly until every cell is determined.

Importantly: Sudoku involves zero arithmetic. The digits are symbols, not numbers. You could replace them with nine different letters and the puzzle would work identically. This matters because it changes how you approach stuck situations — you're never calculating, always constraining. Thinking "where can the 7 go?" is more productive than any mathematical approach.

New Sudoku solvers benefit from a structured starting approach rather than scanning randomly. Follow this sequence for every puzzle until it becomes intuitive:

Cross-hatching is the foundation of Sudoku solving. For a given digit, scan all rows and columns that already contain that digit to find where it can go in each unsolved box. If a digit appears in two of the three rows passing through a box, it must go in the third row — and within that row, only one or two cells may be available after column elimination.

Work through digits 1-9 systematically. Some digits will have obvious placements immediately; others won't. Cross-hatching alone solves most easy Sudoku puzzles entirely. For medium puzzles, cross-hatching narrows the problem significantly before more advanced techniques are needed.

Imagine you're looking at the digit 3. The top-left box has a 3 in its middle row. The top-right box has a 3 in its top row. In the top-center box, the 3 must therefore go in the bottom row (the only remaining row not yet eliminated by cross-hatching). If the bottom row of the top-center box has only one empty cell, the 3's placement is forced immediately. If it has two empty cells, column elimination (checking which columns already contain 3) will narrow further.

A naked single is a cell where only one digit is possible. After eliminating all digits already present in the cell's row, column, and box, exactly one candidate remains. That candidate is the answer for that cell.

Finding naked singles requires checking each empty cell's row, column, and box for present digits. Cells with many neighbors already filled become naked singles first. Filling a naked single often creates more naked singles — when you fill a cell, it eliminates that digit from all cells in its row, column, and box, which may reduce some of those cells to single candidates. Work through naked singles in cascades before scanning for new ones.

For easy puzzles, naked singles are often found by visual inspection without writing candidates. For medium puzzles, writing all candidates in empty cells (pencil marks) before searching for singles makes the process faster and prevents missed singles. The practice of writing pencil marks is not a sign of weakness — it's the professional approach for anything above easy difficulty.

A hidden single exists when a digit can only go in one cell within a unit (row, column, or box), even though that cell has multiple candidates. The digit is "hidden" among other candidates. Scan each unit for digits that appear in only one cell's candidate list — those are hidden singles and should be placed immediately.

Hidden singles in boxes are often easier to spot than in rows and columns. If a digit can only go in one cell of a 3×3 box based on row and column elimination, place it regardless of what other candidates that cell might have. The box constraint alone is sufficient to force the placement.

The distinction confuses many beginners. A naked single has only one candidate in the cell. A hidden single has multiple candidates in the cell, but only one of those candidates can go anywhere in its unit (row, column, or box). Both result in immediate placements, but they're found by different scanning methods. Always check for hidden singles after exhausting naked singles.

For medium and hard puzzles, write small candidate digits in each empty cell showing all possibilities. Update candidates after each placement — remove the placed digit from all cells in the same row, column, and box. This transforms the puzzle from a memory challenge into a pure visual logic exercise. Professional Sudoku solvers use pencil marks for everything above easy difficulty — it's not a crutch, it's the correct approach.

Pencil mark discipline is critical: candidates must be accurate. An incorrectly written candidate (forgetting to remove a digit that's already placed in the same row) corrupts the logic chain that follows. After each placement, immediately erase that digit from all affected cells' candidate lists before moving on.

When two cells in the same unit contain exactly the same two candidates — and only those two — those two digits must go in those two cells (in some order). This means both candidates can be eliminated from all other cells in that unit. Naked pairs are the gateway to solving hard puzzles that resist basic scanning.

Example: cells A and B in the same row both contain only 3, 7'}. Neither 3 nor 7 can appear anywhere else in that row. You can remove 3 and 7 from all other cells in that row's candidate lists. This elimination often creates hidden singles or naked singles in other cells, cascading into further placements.

The complement of naked pairs: two digits that can only appear in exactly two cells within a unit, even though those cells have additional candidates. Those two digits must go in those two cells, meaning all other candidates in those cells can be eliminated. Hidden pairs require more careful scanning but appear frequently in medium-hard puzzles.

Finding hidden pairs: for each unit, check whether any two digits together appear as candidates in exactly two cells. If digits 4 and 9 both appear as candidates only in cells C and D within the same column, then C and D are a hidden pair for 4, 9'} — eliminate all other candidates from C and D.

Easy Sudoku puzzles are solved entirely with cross-hatching and naked singles. Medium puzzles require hidden singles and occasionally naked pairs. Hard puzzles require naked pairs, hidden pairs, and pointing pairs (see the Advanced Sudoku guide). Expert puzzles require X-Wings, Swordfish, and other advanced patterns. The techniques don't become harder — they become more pattern-recognition intensive.

The most important skill across all difficulty levels is candidate management. Accurate, up-to-date pencil marks make every technique faster and more reliable. Time spent maintaining pencil marks is always returned through faster pattern recognition.

PuzzleUnlock's Sudoku solver with photo scanning reads printed or digital Sudoku grids from photographs. Take a straight-on photo with good lighting and the AI fills the grid automatically — then solve instantly. This is particularly useful for newspaper and magazine puzzles where manual entry is slow and error-prone. The solver also confirms whether a puzzle is valid (has exactly one solution) — useful when you've entered a puzzle and the solver returns no solution, indicating a transcription error.

Stuck on today's Sudoku?

Step 1: Scan for the digit that appears most often in the given clues. Start cross-hatching with that digit — it will have the most constraints and produce the most immediate placements.

Step 2: Work through all digits 1-9 with cross-hatching. Note any forced placements but don't fill them in yet — complete the full scan first to avoid disrupting your analysis.

Step 3: Fill in all forced placements from the scan. Each placement may create new forced placements — scan the affected rows, columns, and boxes immediately after each fill.

Step 4: Check every empty cell for naked singles. This step is especially productive after multiple placements, as each new digit creates new single opportunities.

Step 5: Check each row, column, and box for hidden singles. Move to pencil marks if no singles remain.

Beginner: Forgetting that boxes, rows, and columns all constrain simultaneously. Only checking rows and columns without checking the 3×3 box, or vice versa.

Intermediate: Failing to cascade placements. After filling a cell, immediately re-check the affected row, column, and box for new singles before moving on.

Advanced: Sloppy pencil marks. Forgetting to remove a candidate after a placement creates false logic chains. Update pencil marks rigorously after every fill.

All levels: Guessing. If you're not sure where a digit goes, you haven't applied the right technique yet. Valid Sudoku puzzles always have a logical solution path — trust the techniques and don't guess.