Catalog of Logic

Sudoku Solution Strategies

Hidden Single

When a number is the only candidate left for a specific cell within a row, column, or box.

Naked Single

A cell where only one number is possible because all others are eliminated.

Hidden Pair

Two numbers appear as candidates in only two cells within a unit.

Intersection (Box/Line)

When a candidate in a row or column is restricted to a single box, it eliminates that candidate from the rest of the box.

Intersection (Pointing)

When candidates in a box are restricted to a single row or column, they point outwards.

Naked Pair

Two cells in a unit contain only the same two candidates, meaning those numbers must go there.

Naked Triple

Three cells in a unit contain combinations of only three candidates, meaning those numbers must go there.

BUG Type 1 (BUG+1)

When only one cell has 3 candidates and all others have 2, the extra candidate must be the solution.

Hidden Quad

Four numbers find a secret hiding spot in four cells, locking out all other candidates.

Hidden Triple

Three numbers are "hidden" as candidates in only three cells, forming a secret alliance that eliminates everything else.

Naked Quad

Four cells in a unit contain combinations of only four candidates.

X-Wing (Col)

A rectangular pattern formed by a candidate appearing twice in two columns.

X-Wing (Row)

A rectangular pattern formed by a candidate appearing twice in two rows.

Y-Wing

A pattern involving three cells with bi-value candidates (Pivot and two Wings).

2-String Kite

Two strong links (one row, one column) connected in a box, eliminating candidates from the intersection.

Finned X-Wing (Col)

A Column X-Wing with an extra "Fin" that allows for localized eliminations.

Finned X-Wing (Row)

A Row X-Wing with an extra "Fin" that allows for localized eliminations.

Remote Pairs

A chain of cells containing the same pair of numbers. If the chain is long enough, the ends eliminate candidates.

Sashimi X-Wing (Col)

Column-based Sashimi X-Wing.

Sashimi X-Wing (Row)

A degenerate Finned X-Wing where a corner is missing.

Skyscraper (Col)

Two vertical columns linked by a base row, forming two "towers" of different heights.

Skyscraper (Row)

Two horizontal rows linked by a base column, forming two "towers" lying on their sides.

Swordfish (Column)

A 3x3 pattern where a candidate appears in only three columns, restricted to the same three rows.

Swordfish (Row)

A 3x3 pattern where a candidate appears in only three rows, restricted to the same three columns.

Unique Loop Type 1

Eliminate candidates from a single rescue cell to prevent a deadly pattern in a loop of 4 or more cells.

Unique Rectangle (Type 1)

Use the "Deadly Pattern" rule to eliminate candidates that would cause the puzzle to have two valid solutions.

Unique Rectangle (Type 2)

A variation of the Unique Rectangle where two corners have the same extra candidate.

Unique Rectangle (Type 3 Hidden)

A variation of UR Type 3 using hidden subsets.

Unique Rectangle (Type 3)

When extra candidates in the "roof" cells form a Naked Subset with neighboring cells.

Unique Rectangle (Type 4)

When one UR candidate is "locked" in a row or column, the other candidate can be eliminated.

W-Wing

A fan-favorite "secret shortcut" using two identical pairs connected by a Strong Link.

XY-Chain

An advanced chain strategy using multiple bivalue cells to connect a number from start to finish.

XYZ-Wing

A more advanced version of the Y-Wing that involves three cells and an extra candidate in the pivot.

Alternating Inference Chain (AIC)

A powerful chain technique that alternates strong and weak links to prove which candidates can be eliminated.

BUG Type 2

When multiple BUG cells share the same extra candidate, eliminate it from cells that see all of them.

BUG Type 3

When BUG cells' extras form a Naked Subset with other cells in a shared region, eliminate subset values from the region.

BUG Type 4

When a common value is locked to BUG cells in a shared region, eliminate other candidates from them.

Unique Loop Type 2

When multiple loop cells share the same extra candidate, eliminate it from cells that see all of them.

Unique Loop Type 3

Eliminate candidates when loop extras form a Naked Subset with other cells in a shared region.

Unique Loop Type 4

When one loop value is locked to rescue cells in a shared region, eliminate the other loop value from them.

3D Medusa

An advanced coloring strategy that links multiple candidates across the grid to find contradictions.

Aligned Pair Exclusion

A strategy that eliminates candidates by analyzing all possible combinations of values for two cells and excluding impossible ones.

Complex Logic (Trial and Contradiction)

Last resort strategy that tests candidates and eliminates those that lead to contradictions.

Jellyfish (Column)

A 4x4 pattern where a candidate appears in only four columns, restricted to the same four rows.

Jellyfish (Row)

A 4x4 pattern where a candidate appears in only four rows, restricted to the same four columns.

Region Forcing Chain

An advanced chain technique that explores all possible positions of a candidate in a region to prove an elimination or placement.

Simple Coloring

Use two colors to trace a single candidate across the grid. If a cell sees both colors, it can be eliminated.

X-Cycle (Continuous)

A continuous loop of strong and weak links for a single digit that validates the chain and eliminates peers.

X-Cycle (Discontinuous)

A single-digit chain that forms a loop with a contradiction, forcing an elimination.

XY-Cycle (Continuous)

A perfect loop of bivalue cells that turns weak links into strong links, causing eliminations outside the loop.

XY-Cycle (Discontinuous)

A chain through bivalue cells that loops back to contradict itself, forcing an elimination.

Y-Cycle (Continuous)

A continuous loop of bivalue cells that forms a stable logic ring, eliminating candidates from peers.

Y-Cycle (Discontinuous)

A chain of bivalue cells that forms a loop with a "break," proving the starting candidate is impossible.

The Ultimate Guide to Sudoku Solving Techniques

Whether you are just learning the basic rules or trying to conquer a fiendishly difficult grid, having a reliable Sudoku strategy makes all the difference. Guessing will only get you so far. To truly master the game, you need to rely on pure logic.

This catalog serves as your complete toolkit. We have compiled all the most effective Sudoku solving techniques—from the simplest beginner moves to the most complex patterns used by champions—organized by difficulty so you can learn at your own pace.

Finding the Right Sudoku Method for You

There is no single magic Sudoku method that solves every board instantly. Instead, solving requires a progression of skills. Here is how to use our comprehensive list of Sudoku solution strategies:

  • Start with the Basics (Easy & Medium): Build your foundation. These techniques teach you how to scan the board, spot Naked and Hidden Singles, and use basic pencil marks to find Pairs and Triples. You will use these Sudoku techniques on every single puzzle you play.
  • Move to Pattern Recognition (Hard): Once the basics stop working, it's time to learn how to look at the grid geometrically. You will start identifying visual shapes like the X-Wing or Swordfish to eliminate candidates.
  • Master the Grid (Expert & Extreme): For the top 1% of puzzles, you will need to learn advanced strategies for Sudoku. These include complex chaining methods (like XY-Chains), Coloring, and Unique Rectangles. These techniques teach you to see the hidden mathematical relationships across the entire board.

Every strategy page in our guide includes a real puzzle example. Don't just memorize the names—practice the logic, refine your intuition, and watch as previously "impossible" puzzles become entirely solvable.

Frequently Asked Questions About Sudoku Strategies

What is the best Sudoku solving technique?

There is no single "best" technique, as different puzzles require different approaches. However, the most fundamental and frequently used technique is the Naked Single (finding a cell that can only contain one possible number). For difficult puzzles, the X-Wing is widely considered the most essential advanced pattern to learn.

Is there a mathematical method to solve Sudoku?

Yes, Sudoku is entirely a game of logic and combinatorics, not math or guesswork. The most reliable Sudoku method is candidate elimination: writing down all possible numbers (pencil marks) for empty cells and systematically applying logical rules to cross them out until only the correct answers remain.

How do I learn advanced strategies for Sudoku?

The best way to learn advanced strategies is to master them one at a time. Start by thoroughly understanding how to find Pairs and Triples. Once you are comfortable tracking groups of candidates, move on to visual patterns like the Swordfish, and finally, practice logic chains like the XY-Chain.