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

Getting Started

If you're new to Sudoku solving:

  1. Start with Naked Single and Hidden Single
  2. Learn Naked Pair for harder puzzles
  3. Progress through techniques as needed

Check the Glossary for term definitions.