Sudoku 9×9 is one of the world’s most loved logic puzzles, blending reasoning, pattern recognition, and patience.
While anyone can fill numbers in a grid, true mastery comes from understanding the techniques and strategies behind every successful solution.
This reference guide gathers all the major solving concepts, organized from beginner to expert level, including extreme logical methods and hybrid visual approaches. These strategies and techniques make Sudoku more fun — they keep you thinking logically instead of guessing.
Why Learn Sudoku Techniques?
Sudoku attracts many types of solvers:
- Beginners who want to learn how to solve Sudoku 9×9 systematically.
- Intermediate players seeking better accuracy and faster solving times.
- Advanced enthusiasts exploring refined techniques to tackle hard or diabolical puzzles.
- Experts and analysts studying logical structures and algorithmic solving.
- Learners or professionals aiming to boost focus, memory, and problem-solving ability through daily brain training.
Whether you’re just starting or pushing toward the most complex logic chains, each strategy below sharpens your reasoning and makes solving more enjoyable.
This guide aims to be a truly comprehensive source — bringing together all known Sudoku solving techniques and strategies for every skill level, from beginners to expert solvers, in one reliable place.
Beginner Sudoku Techniques and Strategies
Naked Singles
Or also called obvious single occurs when a cell has only one possible number remaining.
It’s the most basic Sudoku 9×9 technique and the first step in every solve.
Always scan for naked singles to build momentum and establish a logical foundation.
Hidden Singles
A hidden single appears when a number can go in only one cell within a row, column, or box, even if that cell lists other candidates.
Finding hidden singles uncovers placements invisible at first glance.
It’s a core beginner-to-intermediate bridge technique.
Last possible number
This method applies when a unit (row, column, or box) has eight filled numbers and only one remains unused.
The remaining digit is the only valid placement for the empty cell.
It is a fundamental deduction step that ensures each unit contains all digits from 1 to 9 exactly once.
Last free cell
When a row, column, or box contains only one empty cell, that position must take the missing number from that unit.
It requires no candidate analysis, only simple counting.
This is typically one of the first observations used to progress an easy Sudoku grid.
Sudoku notes (Candidate marking)
Notes record all possible candidates for each unsolved cell, usually written in small numbers.
They allow solvers to visualize eliminations and interactions across the grid.
Maintaining accurate notes is essential for applying intermediate and advanced solving strategies.
Intermediate / Advanced Sudoku Techniques and Strategies
Naked Pairs
Also called obvious pairs are two cells in a unit contain the same two candidates; therefore, no other cells in that unit can contain those numbers.
Recognizing naked pairs refines elimination accuracy.
This method encourages organized pencil marking and candidate management.
Hidden Pairs
Hidden pairs occur when two numbers appear only in two specific cells within a unit, even though those cells may list more options.
By identifying them, you can remove all other candidates from those cells.
This promotes precision and tighter logical control.
Naked Triples
Also called obvious triples happen when three cells in a row, column, or box share exactly three candidates, those digits can be removed from all other cells in that unit.
It strengthens spatial reasoning.
Naked triples are less frequent but very effective in breaking stagnation.
Hidden Triples
Hidden triples happen when three numbers appear only in three particular cells but are mixed with other candidates.
Spotting them demands detailed note tracking.
It’s a rewarding skill that deepens awareness of pattern distribution.
Pointing Pairs / Box-Line Reduction
If a number in a 3×3 box appears only in one row or column, it can be eliminated from the same row or column outside that box.
This interplay between box and line reduces clutter.
It’s a simple yet powerful logical link connecting grid regions.
X-Wing
An X-Wing pattern occurs when two rows (or columns) each have a candidate in exactly two matching columns (or rows).
Visualizing the X shape helps remove that candidate from all intersecting units.
It’s often the first “aha moment” for solvers learning structured visual logic.
Swordfish
A Swordfish extends the X-Wing to three rows and three columns.
It demands careful grid scanning and visualization.
This technique efficiently cuts through puzzles that resist simpler eliminations.
XY-Wing
Same as Y-Wing. Check the following explanations.
Y-Wing
The Y-Wing technique also known as XY-Wing connects three cells forming a logical relationship between shared candidates.
No matter which value the pivot cell takes, one specific candidate in the overlapping area can always be eliminated.
It’s an advanced strategy helping solvers make key breakthroughs in medium to hard Sudoku puzzles.
XYZ-Wing
The XYZ-Wing builds on the XY-Wing by introducing a pivot cell containing all three digits (X, Y, Z).
If the pivot’s value triggers a contradiction, linked candidates can be eliminated.
It’s a favorite among solvers who enjoy complex conditional logic.
Pointing triples
Pointing Triples occur when three instances of the same candidate are confined within a single box and all lie along one shared row or column.
In that case, the candidate can be eliminated from all other cells in that same row or column outside the box.
This technique is an advanced extension of the Pointing Pair logic — slightly rarer and more challenging to spot, suitable for upper-intermediate solvers.
45 rule
The 45 Rule is based on the mathematical fact that the sum of digits 1 through 9 is always 45. Therefore, every row, column, and 3×3 box in Sudoku must total 45. This property allows logical deductions — if the sum of several cells is known, the remaining cell(s) can be calculated. The 45 Rule is particularly useful in Sudoku variants like Killer Sudoku, where cage totals are used to determine missing values.
Skyscraper
Skyscraper is an advanced visual Sudoku technique that tracks candidates across two rows (or columns) to identify a “tall building” pattern. If a candidate appears in exactly two cells in one row, and the corresponding cells form a logical link with another row, the candidate can be safely eliminated from other intersecting cells. This method is effective in medium to very hard Sudoku puzzles and requires precise visualization of relationships between rows, columns, and boxes.
Block/Block Interaction
Block/Block Interaction is an advanced Sudoku technique that uses relationships between two 3×3 blocks to eliminate candidates. If a candidate can only occupy a specific portion of one block, and the corresponding cells in a neighboring block contain the same candidate, it can be eliminated from other cells in that neighboring block. The method requires visualizing inter-block relationships and is effective in medium to very hard Sudoku puzzles.
Expert-Level Sudoku Techniques and Strategies
Jellyfish
A four-row-by-four-column pattern mirroring the logic of X-Wing and Swordfish.
It’s rare but critical for very hard puzzles.
Identifying a Jellyfish proves advanced pattern-visualization mastery.
Nishio
Nishio is an advanced Sudoku technique based on controlled logical trial. It is used when there are two possible positions for a specific digit. The solver temporarily assumes one placement, continues solving, and observes whether a contradiction arises. If it does, the initial choice is eliminated, confirming the other option. Although it resembles trial-and-error, it remains a logical and structured method rather than random guessing.
X-Cycles
X-Cycles are an advanced chain-based logic technique focusing on a single candidate digit. They use alternating strong and weak links between occurrences of that candidate across rows, columns, and boxes. When a closed loop (cycle) is formed, the solver can confirm certain values or eliminate candidates that lead to logical contradictions. This technique combines visualization and structured reasoning, making it a favorite among high-level solvers.
XY-Chain
An XY-Chain is an advanced Sudoku technique built from a sequence of bivalue cells (each containing exactly two candidates). These cells are linked together through shared candidates, forming a logical chain. If the first and last cells in the chain contain the same candidate, that candidate can be eliminated from any cell that “sees” both endpoints. The XY-Chain provides powerful logical eliminations without guessing and is a favorite among experienced solvers.
Extended Unique Rectangle (EUR)
The Extended Unique Rectangle (EUR) is an advanced variation of the Unique Rectangle technique, used to prevent multiple solutions in Sudoku. EUR examines specific configurations of four or more cells where candidate combinations could create dual solutions. By applying this method, solvers can safely eliminate certain candidates or confirm values while maintaining uniqueness. It is particularly useful for very difficult grids where standard Unique Rectangle logic is insufficient.
Hidden Unique Rectangle
Hidden Unique Rectangle is an advanced variation of the standard Unique Rectangle technique. It deals with cases where the potential rectangle pattern is not immediately visible because some cells contain extra candidates. The goal is to uncover these hidden configurations that could cause a non-unique solution and eliminate surplus candidates to maintain uniqueness. This method requires careful candidate tracking and precise logical reasoning.
Empty Rectangles
Empty Rectangles is an advanced visual Sudoku technique focused on candidate elimination using empty areas within a block. If a candidate is missing in a particular row or column and appears only in specific cells of another block, that candidate can be eliminated from other parts of the grid. This method requires strong visualization skills and careful tracking of logical relationships between cells, and is typically applied in difficult Sudoku puzzles.
Finned Fish
A finned fish adds an extra “fin” candidate disrupting the perfect symmetry of the base fish pattern.
Depending on whether the fin is true or false, certain eliminations become valid.
This hybrid reasoning blends structure with conditional deduction.
Finned X-Wing
Finned X-Wing is an advanced extension of the X-Wing technique where a “fin” creates an additional candidate outside the main X-Wing pattern. This fin allows the solver to eliminate candidates that would otherwise remain unaffected by a standard X-Wing. It is used in medium to very hard Sudoku puzzles and requires precise visualization of row, column, and box relationships.
Finned Swordfish
Finned Swordfish is an advanced extension of the Swordfish technique. It includes an extra “fin” outside the main three-row, three-column pattern, allowing eliminations of candidates that would otherwise remain unaffected by a standard Swordfish. This method combines visual scanning with logical deduction and is mainly applied in very hard Sudoku puzzles where standard techniques fail.
Finned Jellyfish
Finned Jellyfish is an advanced extension of the Jellyfish technique, including an extra “fin” outside the main four-row, four-column pattern. This fin allows eliminations of candidates that would otherwise remain unaffected by a standard Jellyfish. The technique combines visual scanning with logical deduction and is suitable for very hard or competitive Sudoku puzzles.
Simple Coloring
Simple Coloring also called Multi-Coloring type 1, uses two colors to mark cells containing the same candidate that are connected through strong links. If two cells of the same color see each other (i.e., share a row, column, or box), that color represents a false set and all candidates of that color can be eliminated. This technique is powerful for exposing hidden logical contradictions and serves as the foundation for Multi-Coloring and other advanced visual strategies.
Multi-Coloring
Multi-Coloring also called Multi-Coloring type 2, multi-coloring technique or advanced coloring is an extension of Simple Coloring, used in advanced Sudoku solving.
Coloring techniques rely on creating logical chains by assigning two alternating colors (often Blue/Green) to candidates of the same digit.
In Multi-Coloring, you expand beyond one such chain — you track multiple separate coloring chains for the same digit simultaneously.
This allows cross-comparisons between different color networks.
- Choose a specific digit (e.g., all 7s in the grid).
- Find separate, unconnected chains of that digit using strong links (when a digit can only appear in two cells of a unit).
- Assign alternating colors (e.g., blue/green, red/orange, etc.) to each chain.
- Apply these rules:
- ❌ If two cells of the same color “see” each other → that color is false everywhere.
- ✅ If a cell sees two different colors → that digit can be eliminated from that cell.
- ✅ If one color causes a contradiction → the opposite color must be true.
Multi-coloring allows you to handle disconnected inference chains that cannot be connected into a single continuous loop (like AICs or Nice Loops).
It’s a visual inference technique, bridging logical deduction and visualization.
Forcing Chains
Forcing Chains are an advanced Sudoku technique based on if–then logic. The solver follows the logical consequences of an assumption — if one candidate is true, another must be false — creating a chain of linked deductions. If all possible branches lead to the same conclusion (such as confirming or eliminating a candidate), that result is logically guaranteed. This method forms the foundation for more complex techniques like Forcing Nets and specialized chains (Cell, Unit, or Digit Forcing Chains).
ALS (Almost Locked Set)
An ALS is a group of N cells containing N + 1 candidates.
Because only one number can vary, strong links emerge between ALSs.
This concept powers several elite-level techniques, including Death Blossom.
Sue de Coq
This elegant pattern occurs at intersections of boxes and lines where candidates interact through restricted cells.
It enables multiple eliminations via precise logical reasoning.
Sue de Coq represents the artistry of pure Sudoku logic.
Unique Rectangle
The Unique Rectangle technique ensures that a Sudoku puzzle maintains a single valid solution. When four cells form a rectangle sharing the same two candidates, a risk of multiple solutions arises. By applying this method, solvers can eliminate candidates or confirm values to preserve uniqueness. It is commonly used in medium to very hard Sudoku puzzles.
Unique Loop
Unique Loop is a technique based on Sudoku’s requirement for a single unique solution. When cells form a closed loop pattern that could produce multiple valid solutions, the Unique Loop logic allows solvers to eliminate risky candidates. It is an extension of the Unique Rectangle concept, applied in more complex grids to preserve puzzle uniqueness.
Bivalue Universal Grave (BUG) + 1
In a near-completed grid with only bivalue cells plus one extra candidate, a BUG + 1 pattern appears.
Identifying it instantly reveals the correct resolution.
It’s a precise and satisfying endgame move.
Extreme Logic & Other Advanced Strategies
WXYZ-Wing
The WXYZ-Wing is an extension of the Y-Wing and XYZ-Wing patterns. It involves four cells sharing the candidates W, X, Y, and Z, with one pivot cell connected to all others. Depending on which candidate in the pivot is true, logical relationships allow certain eliminations elsewhere in the grid. This technique demands a deep understanding of candidate interactions and advanced visualization skills.
VWXYZ-Wing
The VWXYZ-Wing is an extension of the WXYZ-Wing pattern, involving five cells and five candidates — V, W, X, Y, and Z. A single pivot cell links to all others, forming complex logical relationships among candidates. Regardless of which candidate in the pivot proves true, specific eliminations can be made elsewhere in the grid. This advanced technique requires exceptional visualization and a deep grasp of high-level Sudoku logic patterns.
Phistomefel Ring
The Phistomefel Ring is a highly advanced Sudoku technique that leverages the inherent symmetry of the grid. It focuses on a ring of cells that are interlinked through rows, columns, and boxes in a balanced pattern. By analyzing these logical dependencies, solvers can confirm certain digits or eliminate candidates without guesswork. This strategy appears almost exclusively in extremely hard or competition-level puzzles where conventional logic methods fail.
3D Medusa
3D Medusa is an extremely advanced Sudoku technique based on multi-layer coloring of candidates. Instead of using a single digit or two-color system, it tracks complex logical connections among candidates across the grid, often involving several digits simultaneously. When contradictions appear (same color seen in one row, column, or box), specific candidates can be eliminated or confirmed. This highly visual and intricate method is reserved for elite-level solvers who enjoy deep logical exploration.
Fireworks
Fireworks is an advanced visual Sudoku technique based on a combination of candidate chains and coloring logic. It forms a distinctive “firework” shape where pivot cells influence multiple rows, columns, and boxes, allowing eliminations or confirmations of candidates. The method requires strong visualization skills and the ability to track logical links among multiple candidates simultaneously. Fireworks is mainly applied to very difficult or competition-level puzzles.
SK Loops
SK Loops (Sudoku Killer Loops) are an advanced technique based on forming closed logical loops of candidates. They are used to identify eliminations or confirmations when cells influence each other through chains of strong and weak links. The method is visually complex and requires careful tracking of interactions among multiple candidates across the grid. SK Loops are typically applied in extremely hard or competitive Sudoku puzzles.
Exocet
Exocet is a highly advanced, visually oriented Sudoku technique named after the missile-like shape it forms. It relies on specific candidate patterns distributed across two or more blocks, allowing eliminations and confirmations of values. The method focuses on key digits and uses inter-cell dependencies for logical solving. Exocet is applied mainly in extremely difficult or competitive Sudoku puzzles where standard techniques fail.
Grouped X-Cycles
Grouped X-Cycles are an advanced variation of the X-Cycles technique, where instead of single candidates, groups of cells (such as pairs or triples) are tracked as units. These groups form closed logical cycles, allowing eliminations or confirmations of candidates in other parts of the grid. The method requires careful analysis of the interactions between groups and is suitable for very difficult or competitive Sudoku puzzles.
Aligned Pair Exclusion (APE)
Aligned Pair Exclusion (APE) is an advanced visual technique focused on candidate elimination by analyzing pairs of cells that are “aligned” across blocks and rows/columns. If a candidate appears only in these aligned pairs, it can be eliminated from other cells that share a direct logical conflict. This method is effective in very difficult or competitive Sudoku puzzles where standard techniques fail.
Alternative Inference Chains (AIC)
Alternative Inference Chains (AIC) are an advanced technique based on chains of strong and weak links between candidates. They allow logical eliminations or confirmations when a closed loop or chain produces a contradiction. This is one of the most sophisticated pure logical solving methods in Sudoku.
Pattern Overlay Method (POM)
POM compares all valid pattern templates for each digit.
By overlaying possibilities, incompatible options are eliminated.
This technique merges human logic with computational precision.
Template Set Reduction
Each number has limited valid placement templates.
By contrasting and reducing overlapping templates, solvers remove impossibilities.
It’s systematic, data-driven reasoning useful for algorithmic analysis or extreme grids.
Contradiction Forcing (Trial & Error, T&E Limited)
A disciplined version of “what if” logic: assume a candidate, project consequences, and retract upon contradiction.
When used carefully, it verifies logical soundness rather than guessing.
Expert solvers use limited T&E only after all other logical avenues are exhausted.
Visual & Hybrid Sudoku Strategies
Digit Forcing Chains
Digit Forcing Chains are an advanced technique analyzing chains of logical relationships across multiple specific digits simultaneously. These chains combine X-Chains and other inter-cell links to allow eliminations that cannot be found when solving one digit at a time. The method requires strong visualization skills and is intended for very difficult or competitive Sudoku puzzles.
Nishio Forcing Chains
Nishio Forcing Chains combine the principles of Nishio (logical trial with contradiction testing) and Forcing Chains (conditional logic sequences). The solver assumes one candidate and traces all logical consequences throughout the grid. If both possible outcomes lead to the same conclusion — confirming or eliminating a candidate — that conclusion is logically certain. This is a highly powerful but complex technique, typically used in extremely hard Sudoku puzzles.
Cell Forcing Chains
Cell Forcing Chains are an advanced variation of Forcing Chains where the logical chain originates from an entire cell rather than a single candidate. The solver assumes each possible value of that cell in turn and traces the logical consequences across the grid. If all possible paths lead to the same outcome — such as eliminating a specific candidate elsewhere — that result is logically certain. This is a powerful high-level method capable of solving extremely difficult Sudoku puzzles without guessing.
Unit Forcing Chains
Unit Forcing Chains are an advanced variation of the Forcing Chains technique where the logical reasoning originates not from a single cell or digit but from an entire unit (row, column, or box). The solver explores what happens if a particular digit must or cannot appear in that unit, tracing the logical consequences throughout the grid. If all possible branches lead to the same result, the elimination or confirmation is logically certain. This is a powerful tool used in extremely difficult Sudoku puzzles.
Quad Forcing Chains
A Quad Forcing Chain is an ultra-advanced variation of the Forcing Chains technique involving four possible logical branches stemming from a single situation. The solver examines the consequences of all four scenarios (e.g., four candidates or combinations) and determines whether they all converge on the same conclusion — confirming or eliminating a candidate. If they do, that conclusion is logically guaranteed. This is an exceptionally rare yet powerful method, used mainly in the toughest or competition-level Sudoku puzzles.
Forcing Nets
Forcing Nets extend the logic of Forcing Chains into multi-branching logical networks. Instead of a single linear chain, they create an interconnected web of conditional relationships. If all possible branches lead to the same conclusion, a candidate can be safely confirmed or eliminated. This flexible and highly logical approach ranks among the most advanced Sudoku solving strategies.
Nice Loops (Type 1 – 6)
Nice Loops are an advanced Sudoku technique based on forming closed logical loops of candidates with alternating strong and weak links. When the loop closes and produces a contradiction or certainty, candidates can be safely eliminated or confirmed. This method enhances the solver’s ability to visualize complex logical relationships and is highly effective in difficult or competitive Sudoku puzzles.
Kraken Fish
A generalization of Fish patterns incorporating fins and chain links.
Kraken Fish uses overlapping logical “tentacles” to test consistency.
It’s among the hardest manual strategies, demanding both visualization and inference.
Death Blossom
A powerful expansion of ALS logic where multiple ALSs connect through shared candidates.
The interlocking relationships produce cascading eliminations.
Death Blossom exemplifies peak human logical construction in Sudoku solving.
ALS-XZ
ALS-XZ is an advanced Sudoku technique that leverages Almost Locked Sets (ALS) and their interactions to eliminate candidates. This method examines two ALS that share candidates X and Z; if one candidate must hold in one ALS, it logically affects the other ALS, allowing eliminations in other cells. ALS-XZ is an extremely challenging technique, suitable for very hard or competition-level Sudoku puzzles where standard methods fail.
Final Thoughts: From Learning to Mastery
Every Sudoku puzzle, from easy to evil, hides a logical story.
Understanding these techniques and strategies turns guesswork into reasoning and confusion into clarity.
For beginners, focus on naked and hidden singles; for intermediates, move through pairs, triples, and X-Wing patterns.
Advanced players will thrive with Wings, Fish, Coloring, and Chains, while experts explore ALS networks, Jellyfish, and Death Blossoms.
The path to mastery in Sudoku 9×9 solving is gradual but endlessly rewarding.
Each new strategy builds mental flexibility, pattern awareness, and satisfaction in pure logical deduction.
So pick up a fresh grid, apply what you’ve learned, and let logic guide every number into place. Sudoku has a positive effect on the human mind — it improves concentration, logical thinking, and overall mental well-being.
If you ever want to take a little break from Sudoku but still play with numbers, give Hidoku a try — it’s a fresh, relaxing twist on logic puzzles.