Sudoku Solving Techniques

Last Remaining Cell is the simplest and most intuitive Sudoku solving technique, making it the perfect starting point for beginners. The idea is straightforward: when eight of the...

Cross-Hatching is a visual scanning technique used to find where a specific digit can be placed within a 3x3 box. It works by drawing imaginary lines through the box along the rows...

Pencil Marking is the essential practice of writing small candidate numbers in empty cells to track which digits are still possible in each position. While not a solving technique...

Naked Singles is one of the most fundamental Sudoku solving techniques and the natural next step after Last Remaining Cell. A Naked Single occurs when an empty cell has only one po...

Hidden Singles is a powerful beginner technique that approaches Sudoku solving from the opposite direction of Naked Singles. Instead of asking "what digit can go in this cell?", yo...

Pointing Pairs and Pointing Triples is an intersection technique that exploits the overlap between a 3x3 box and a row or column. When a candidate digit within a box is confined to...

Box/Line Reduction is the complement of Pointing Pairs and applies the same intersection logic in the opposite direction. While Pointing Pairs looks at a candidate confined within...

Naked Pairs is one of the most fundamental intermediate Sudoku techniques and often the first subset strategy that solvers learn after mastering basic elimination and hidden single...

Hidden Pairs is a powerful intermediate technique that complements Naked Pairs by taking the opposite perspective on candidate subsets. While a Naked Pair involves two cells that c...

Naked Triples extends the Naked Pairs concept to three cells and three candidates. A Naked Triple occurs when three cells in the same row, column, or box collectively contain exact...

Hidden Triples is the three-candidate extension of Hidden Pairs. A Hidden Triple occurs when three candidate digits appear in exactly three cells within a row, column, or box, but...

Naked Quads is the four-cell extension of the Naked Pairs and Naked Triples techniques. A Naked Quad occurs when four cells in the same row, column, or box collectively contain exa...

Hidden Quads is the rarest and most challenging of the hidden subset techniques. A Hidden Quad occurs when four candidate digits appear in exactly four cells within a row, column,...

The X-Wing is one of the most well-known advanced Sudoku techniques. It occurs when a particular candidate digit appears in exactly two cells in each of two different rows, and tho...

The Finned X-Wing is a variation of the standard X-Wing where one of the two rows has the candidate in additional cells beyond the two X-Wing columns. These extra cells are called...

The Swordfish is a natural extension of the X-Wing pattern, scaled up from a 2x2 grid alignment to a 3x3 configuration. It occurs when a candidate digit appears in two or three cel...

Simple Coloring is an advanced Sudoku technique that uses the concept of conjugate pairs to build chains of logical implications for a single candidate digit. A conjugate pair exis...

The Skyscraper is an advanced Sudoku technique that can be understood as a special case of both Turbot Fish and X-Chains. It involves a single candidate digit that forms two conjug...

The 2-String Kite is an advanced Sudoku technique that uses two conjugate pairs for the same candidate digit connected through a shared box. Unlike a Skyscraper, where the two conj...

The Y-Wing, also known as XY-Wing, is a powerful advanced Sudoku technique that uses three bivalue cells (cells with exactly two candidates each) arranged in a specific logical con...

The XYZ-Wing is an extension of the Y-Wing technique that involves a pivot cell with three candidates instead of two. The pattern uses one trivalue pivot cell and two bivalue wing...

Remote Pairs is an advanced Sudoku technique based on chains of bivalue cells that all contain the same two candidates. When multiple cells each have exactly the same pair of candi...

Jellyfish is one of the most complex fish-pattern techniques in Sudoku, extending the logic of X-Wing and Swordfish to encompass four rows and four columns simultaneously. Just as...

Finned Swordfish is one of the rarest and most advanced fish-pattern techniques in Sudoku. It extends the logic of the standard Swordfish by allowing one of the pattern's corners t...

The W-Wing is an elegant expert-level Sudoku technique that combines bivalue cells with strong links to achieve candidate eliminations. The pattern involves two bivalue cells that...

Unique Rectangles is a powerful Sudoku solving technique that exploits one of the fundamental rules of valid Sudoku puzzles: every well-formed puzzle must have exactly one solution...

BUG, which stands for Bivalue Universal Grave, is a uniqueness-based Sudoku technique that leverages the fundamental principle that every valid Sudoku puzzle has exactly one soluti...

X-Cycles are an advanced Sudoku technique that involves building alternating chains of strong and weak links for a single candidate digit, forming a closed loop or cycle across the...

XY-Chains are a sophisticated Sudoku solving technique that links together a series of bivalue cells (cells with exactly two candidates) to form a logical chain whose endpoints for...

The Complete Solver is the capstone lesson of the entire Sudoku curriculum. Rather than introducing a new technique, this lesson challenges you to apply every technique you have le...