How to Solve Sudoku
A complete step-by-step guide from your very first puzzle to expert-level techniques.
Before You Begin
Sudoku is one of the world's most popular logic puzzles — and also one of the most misunderstood. Many beginners believe Sudoku requires mathematical ability or numerical intuition. In reality, Sudoku is purely a logic puzzle. The digits 1–9 are used only as labels; you could equally use letters A–I or any nine distinct symbols. What matters is constraint satisfaction: ensuring no symbol repeats in any row, column, or box.
This guide walks you through every solving technique in order of difficulty, from the basic grid rules to advanced chain techniques used by expert solvers. Each step builds on the previous one. Whether you are picking up Sudoku for the first time or looking to crack Hard and Expert puzzles, this guide gives you the complete logical framework.
For hands-on, interactive practice alongside this guide, the MySudokuWorld Academy offers 20 structured lessons with live puzzle boards, step-by-step tutorials, and an AI Coach that explains each technique in real time on a real puzzle.
Step-by-Step Solving Guide
Understand the Grid Structure
A standard Sudoku is played on a 9×9 grid containing 81 cells. The grid is divided into nine 3×3 boxes (also called blocks or regions). The puzzle begins with some cells already filled in (called "givens" or "clues"). Your goal is to fill every empty cell with a digit from 1 to 9.
Each cell belongs to three units simultaneously: its row (one of nine horizontal lines), its column (one of nine vertical lines), and its box (one of nine 3×3 squares). This triple membership is what creates the rich web of constraints that makes Sudoku uniquely challenging.
Apply the Three Core Rules
Sudoku has exactly three rules: (1) Each row must contain the digits 1–9 exactly once. (2) Each column must contain the digits 1–9 exactly once. (3) Each 3×3 box must contain the digits 1–9 exactly once.
These three rules interact at every cell. When you place a digit, it simultaneously blocks that digit from 8 other cells in its row, 8 other cells in its column, and 8 other cells in its box — up to 24 constraint effects from a single placement. Well-constructed puzzles always have exactly one solution that satisfies all three rules simultaneously.
Start with Cross-Hatching (Scanning)
The first solving technique to learn is scanning, also called cross-hatching. Pick any digit from 1 to 9. Find every row and column that already contains that digit — those rows and columns create "blocks" that prevent the digit from appearing at their intersections within any box.
For each 3×3 box that does not yet contain your chosen digit, eliminate every cell that is blocked by rows or columns containing the digit. If only one cell remains unblocked in the box, place the digit there. Work through all 9 digits and all 9 boxes in this way. This scan alone can fill 20–40 cells on an Easy puzzle.
Find Naked Singles (Single Candidate Cells)
A Naked Single is a cell where only one digit is legally permitted — all other eight digits from 1–9 have been blocked by its row, column, or box constraints. These are the simplest possible placements and require no advanced logic.
To find Naked Singles, examine near-complete units (rows, columns, or boxes with 7 or 8 digits already placed). The remaining empty cells have very few candidates. Work out which digits are forbidden by the existing placements, and if only one digit remains, place it immediately.
Find Hidden Singles
A Hidden Single is a digit that can only go in one specific cell within a unit, even though the cell appears to have multiple candidates. Unlike Naked Singles (spotted by looking at a cell), Hidden Singles require you to look at the digit's available positions within an entire unit.
For example, if digit 4 can only appear in one cell within a given row — because every other empty cell in the row is blocked by 4s elsewhere in its column or box — that cell must contain 4. Scanning every digit in every unit for this pattern is the most productive intermediate technique and handles the majority of Medium-difficulty placements.
Use Intersection Techniques
Pointing Pairs: if a digit in a 3×3 box can only appear in cells that all lie on the same row or column, eliminate that digit from the rest of that row or column. Box-Line Reduction: if a digit in a row or column can only appear within cells of the same box, eliminate that digit from the rest of the box.
These intersection techniques bridge the gap between basic singles and the more advanced pair strategies. They are standard tools for Hard puzzles and frequently unlock a cascade of Hidden Singles after each elimination.
Apply Naked Pairs and Hidden Pairs
A Naked Pair is two cells in the same unit that both contain exactly the same two candidates — eliminate those two digits from every other cell in the unit. A Hidden Pair is two digits confined to the same two cells within a unit — eliminate every other candidate from those two cells.
These pair techniques are usually the first that require full pencil-mark candidate tracking. After applying a pair, the resulting eliminations often reveal Naked Singles or Hidden Singles that were previously obscured. Pairs can be extended to triples (Naked Triples, Hidden Triples) with the same logic applied to three cells and three digits.
Use Fish Techniques: X-Wing and Swordfish
X-Wing: if a digit appears in exactly two cells in each of two rows, and those pairs align in the same two columns, eliminate the digit from the rest of those two columns. Swordfish extends this to three rows and three columns.
Fish techniques are powerful because they can eliminate candidates from many cells at once. X-Wing is typically the first advanced technique beginners encounter after pairs. Recognizing the rectangular pattern (two rows × two columns for X-Wing) takes practice but becomes second nature with experience.
Use Coloring and XY-Wing for Expert Puzzles
Coloring traces alternating conjugate pairs (cells where a digit has exactly two positions in a unit) to prove which cells must or cannot contain a digit. XY-Wing uses three bi-value cells arranged in a Y-shape to eliminate a shared candidate from cells that see both "wing" cells.
These techniques represent the transition from advanced to expert solving. Mastering Coloring builds the intuition for Alternating Inference Chains (AICs), which are the most general and powerful logical technique available to human solvers.
Verify and Complete
Once you have placed all 81 digits, verify your solution: every row should contain 1–9 exactly once, every column 1–9 exactly once, and every 3×3 box 1–9 exactly once. A valid solution satisfies all three constraints simultaneously with no repetitions.
If you find an error, do not panic. Common sources of mistakes include: a stale pencil mark that was not erased after a placement, a scanning error where a digit was missed in a unit, or a logical error in applying a technique. Trace backward from the error to find where the inconsistency first appeared.
Common Mistakes to Avoid
✗ Guessing instead of deducing
✓ Every correct Sudoku has a logical path to the solution. If you feel the urge to guess, you have missed a deduction. Go back and re-scan using a technique from a higher step.
✗ Not updating pencil marks after placements
✓ Stale candidate lists cause cascading errors. After every placement, immediately erase that digit from all candidates in the same row, column, and box.
✗ Scanning too quickly
✓ A thorough scan of all 9 digits before making any moves takes 60 seconds but saves many minutes of backtracking. Speed comes after accuracy.
✗ Skipping techniques in order
✓ Applying X-Wing before exhausting all Hidden Singles wastes time — Hidden Singles are always faster to find and more common. Work through your technique checklist in order.
✗ Not labeling your technique
✓ When you spot a move, name the technique that produced it. This builds conscious pattern recognition that carries over to future puzzles.
✗ Giving up when stuck
✓ Being stuck means the next technique is something new to you. Use the MySudokuWorld AI Coach to identify which technique applies — then learn it in the Academy before continuing.
Frequently Asked Questions
How long does it take to solve a Sudoku?
Easy puzzles typically take 5–15 minutes for beginners, 2–5 minutes for experienced solvers. Medium puzzles take 15–30 minutes for intermediates. Hard puzzles can take 30–60 minutes or more. Expert puzzles are typically timed in hours, even for experienced solvers.
Do I need to be good at math to solve Sudoku?
No. Sudoku requires zero arithmetic. The digits 1–9 are used as labels — you could replace them with letters or symbols and the puzzle would be identical. What Sudoku requires is logical deduction, pattern recognition, and systematic thinking.
What is the hardest Sudoku in the world?
The "Platinum Blonde" puzzle by Arto Inkala is often cited as one of the hardest puzzles ever constructed, requiring advanced AIC chains for a pure-logic solution. Diabolical and Extreme-rated puzzles on MySudokuWorld test similar techniques.
Can every Sudoku be solved without guessing?
Any Sudoku with a unique solution can theoretically be solved without guessing using advanced enough logical techniques. However, some extreme puzzles require techniques so complex (very long AICs) that even expert human solvers resort to hypothesis testing. Standard published puzzles in Easy through Hard difficulty are always solvable without guessing.
Is there a Sudoku solving algorithm?
Yes — computers typically use backtracking algorithms to solve Sudoku in milliseconds. Human-style logical algorithms implement all the named techniques (Naked Singles, X-Wing, AICs, etc.) in sequence. MySudokuWorld's AI Coach uses a human-style logical solver to provide educationally meaningful hints.
What's the difference between Sudoku difficulty levels?
Difficulty is determined by which techniques are required to reach the unique solution. Easy = Naked Singles + scanning. Medium = adds Hidden Singles and Pointing Pairs. Hard = adds Naked/Hidden Pairs and X-Wing. Expert = adds Swordfish, Coloring, XY-Wing, and chains. The number of given clues also affects difficulty but is not the primary factor.
Learn Interactively with the Academy
Every technique in this guide has a dedicated interactive lesson with a live puzzle board.