Solving Techniques
Learn to solve any Sudoku puzzle with these techniques, organised from easiest to most advanced.
Basic Techniques
Master these first — they solve most puzzles.
| Technique | Difficulty | Description |
|---|---|---|
| Naked Single | Easy | One candidate left in a cell |
| Hidden Single | Easy | Only place for a digit in a unit |
| Naked Pair | Easy | Two cells with same two candidates |
| Naked Triple | Easy | Three cells with three candidates |
| Naked Quad | Medium | Four cells with four candidates |
| Hidden Pair | Medium | Two digits confined to two cells |
| Hidden Triple | Medium | Three digits confined to three cells |
| Hidden Quad | Medium | Four digits confined to four cells |
| Pointing Pair/Triple | Medium | Box candidates aligned in a row/column |
| Box/Line Reduction | Medium | Row/column candidates confined to one box |
Intersection Techniques
The fish family — patterns formed by row and column intersections.
Basic Fish
| Technique | Difficulty | Description |
|---|---|---|
| X-Wing | Hard | Two rows and two columns forming a rectangle |
| Swordfish | Hard | Three rows and three columns |
| Jellyfish | Expert | Four rows and four columns |
| Squirmbag | Expert | Five rows and five columns (5-fish) |
| Whale | Expert | Six rows and six columns (6-fish) |
| Leviathan | Expert | Seven rows and seven columns (7-fish) |
Finned Fish
| Technique | Difficulty | Description |
|---|---|---|
| Finned X-Wing | Expert | X-Wing with extra candidates in a fin |
| Finned Swordfish | Expert | Swordfish with extra candidates in a fin |
| Finned Jellyfish | Expert | Jellyfish with extra candidates in a fin |
| Finned Squirmbag | Expert | Squirmbag with extra candidates in a fin |
| Finned Whale | Expert | Whale with extra candidates in a fin |
| Finned Leviathan | Expert | Leviathan with extra candidates in a fin |
Sashimi Fish
| Technique | Difficulty | Description |
|---|---|---|
| Sashimi X-Wing | Expert | Finned X-Wing with missing base candidate |
| Sashimi Swordfish | Expert | Finned Swordfish with missing base candidate |
| Sashimi Jellyfish | Expert | Finned Jellyfish with missing base candidate |
| Sashimi Squirmbag | Expert | Finned Squirmbag with missing base candidate |
| Sashimi Whale | Expert | Finned Whale with missing base candidate |
| Sashimi Leviathan | Expert | Finned Leviathan with missing base candidate |
Franken Fish
| Technique | Difficulty | Description |
|---|---|---|
| Franken X-Wing | Expert | X-Wing with boxes in base or cover sets |
| Franken Swordfish | Expert | Swordfish with boxes in base or cover sets |
| Franken Jellyfish | Expert | Jellyfish with boxes in base or cover sets |
Mutant Fish
| Technique | Difficulty | Description |
|---|---|---|
| Mutant X-Wing | Expert | X-Wing with mixed unit types |
| Mutant Swordfish | Expert | Swordfish with mixed unit types |
| Mutant Jellyfish | Expert | Jellyfish with mixed unit types |
Bent Set Techniques
The wing family — patterns formed by connected bi-value cells.
| Technique | Difficulty | Description |
|---|---|---|
| Chute Remote Pair | Medium | Bi-value cells in the same chute create eliminations |
| Y-Wing | Hard | Three bi-value cells in a hinged pattern |
| XYZ-Wing | Hard | A tri-value pivot with two bi-value wings |
| WXYZ-Wing | Expert | Four cells containing exactly four distinct digits |
Uniqueness Techniques
Based on the fact that valid Sudoku puzzles have exactly one solution.
| Technique | Difficulty | Description |
|---|---|---|
| BUG | Expert | Force the solution when almost bi-value |
| Unique Rectangle | Hard | Avoid deadly patterns with multiple solutions |
| Avoidable Rectangle | Hard | Prevent deadly patterns using solved cells |
| Extended Unique Rectangle | Expert | 2×3 deadly patterns with three digits |
| Hidden Unique Rectangle | Expert | Use strong links to prevent deadly patterns |
| Tridagon | Expert | Cyclical parity violations across four boxes |
Chaining Techniques
Advanced techniques that follow chains of logical implications.
Single-Digit Chains
| Technique | Difficulty | Description |
|---|---|---|
| Simple Colouring | Expert | Track conjugate pairs with two colours |
| Skyscraper | Hard | Two parallel strong links forming a skyscraper |
| Two-String Kite | Hard | Perpendicular strong links connected through a box |
| Turbot Fish | Hard | Two strong links for one digit connected through a box |
| X-Chain | Expert | Discontinuous chain of strong links for a single digit |
| X-Cycles | Expert | Chains of alternating strong and weak links |
| Grouped X-Cycles | Expert | X-Cycles with grouped nodes |
Multi-Digit Chains
| Technique | Difficulty | Description |
|---|---|---|
| Rectangle Elimination | Expert | Rectangular patterns with strong and weak links |
| 3D Medusa | Expert | Multi-digit colouring chains |
| XY-Chain | Expert | Chains through bi-value cells using alternating digits |
| Twinned XY-Chains | Expert | Two parallel XY-chains forming a locked set |
| Alternating Inference Chains | Expert | Multi-digit chains combining bi-value and bi-location links |
| Digit Forcing Chain | Expert | ON and OFF chains for convergent conclusions |
| SK Loops | Expert | Locked sets around four solved cells |
Forcing Chain Variants
| Technique | Difficulty | Description |
|---|---|---|
| Nishio Forcing Chain | Expert | Test candidate validity by following implications to contradiction |
| Cell Forcing Chain | Expert | Chain from all candidates in a cell |
| Unit Forcing Chain | Expert | Chain from all positions of a digit in a unit |
Advanced AIC Variants
| Technique | Difficulty | Description |
|---|---|---|
| AIC with Groups | Expert | AICs using grouped nodes for box/line interactions |
| AIC with ALSs | Expert | AICs incorporating Almost Locked Sets |
| AIC with URs | Expert | AICs incorporating Unique Rectangle logic |
Exotic Strategies
Rare and complex techniques for the most difficult puzzles.
| Technique | Difficulty | Description |
|---|---|---|
| Almost Locked Sets | Expert | N cells with N+1 candidates |
| Sue-de-Coq | Expert | AAALS with block and aligned cells |
| Death Blossom | Expert | Stem cell connected to ALS petals |
Difficulty Levels
- Easy — Look for these first; solve most newspaper puzzles
- Medium — Required for harder puzzles; still straightforward to spot
- Hard — Need practice to recognise; solve most "hard" rated puzzles
- Expert — Complex patterns; required for the toughest puzzles
Getting Started
If you're new to Sudoku solving:
- Start with Naked Single and Hidden Single
- Learn Naked Pair for harder puzzles
- Progress through techniques as needed
Check the Glossary for term definitions.