Sudoku Techniques Glossary: Every Pattern Name in Plain Terms
A Sudoku techniques glossary groups pattern names into logical families, from basic singles to advanced chains. This organized list explains each term in plain language and when it appears in a puzzle. Understanding these categories helps you learn faster and solve more efficiently, as each family of techniques solves a specific type of logical impasse. Our hint engine finds that players who learn techniques in these logical groups progress much more quickly than those who tackle them in a random order. This guide will walk you through the main families, using a real puzzle to illustrate foundational concepts like singles.
Singles and Subsets: The Foundation
The most basic techniques involve finding cells that can only be one number or small sets of numbers that limit others. A Naked Single is a cell with only one possible candidate digit left. This is the simplest placement and often appears right after filling in pencil marks. For instance, in our example puzzle, cell r1c4 is a classic Naked Single; after simple eliminations, only the digit 7 can go there. A Hidden Single occurs when a digit has only one possible cell left in a row, column, or box. This is another fundamental placement. In the same puzzle, the digit 9 in row 3 is a Hidden Single, placing it in r3c7 because all other cells in that row are blocked for 9.
Beyond singles, subsets like Naked Pairs, Triples, and Quads involve two, three, or four cells in a unit that collectively contain the same two, three, or four candidates. These patterns let you eliminate those candidates from all other cells in the unit. Hidden Pairs, Triples, and Quads work in reverse: two, three, or four digits have their possible positions limited to the same two, three, or four cells in a unit, allowing you to remove all other candidates from those cells. These subset techniques are essential for solving puzzles of Easy to Medium difficulty and are a natural progression from singles. You can see a practical sequence of These Techniques in Order in many standard puzzles.
- Naked Single: A cell with only one possible candidate.
- Hidden Single: A digit with only one possible cell in a row, column, or box.
- Naked Pair/Triple/Quad: A set of 2-4 cells in a unit containing exactly the same 2-4 candidates.
- Hidden Pair/Triple/Quad: A set of 2-4 digits that can only go in the same 2-4 cells in a unit.
Intersection or 'Locked' Candidate Techniques
These strategies use the overlap between a box and a row or column to limit where a candidate can go. A Pointing Pair (or Triple) happens when all candidates for a digit within a box are confined to a single row or column. Because the digit must be placed within that box, it can be eliminated from the rest of that row or column outside the box. For example, if in a box all possible 5s are in the same row, you can remove 5 as a candidate from the rest of that row. This is a powerful early-to-mid game elimination. You can learn more about spotting this in our dedicated Pointing Pairs Guide.
The converse is a Claiming Pair (or Triple). This occurs when all candidates for a digit within a row or column are confined to a single box. Since the digit for that row/column must be placed within that box, you can eliminate that digit from all other cells in that box. These intersection techniques are often the key to revealing more singles and are critical for Medium-difficulty puzzles. They rely entirely on the geometry of the 9x9 grid and the rule that each digit must appear once per row, column, and box.
- Pointing Pair/Triple: All instances of a candidate in a box are in one row/column; eliminate it from the rest of that row/column.
- Claiming Pair/Triple: All instances of a candidate in a row/column are in one box; eliminate it from the rest of that box.
Fish Patterns: X-Wing, Swordfish, Jellyfish
Fish are advanced patterns that generalize the idea of a pair across multiple rows and columns. An X-Wing involves two rows where a candidate appears only in two columns, and these positions line up. This alignment forces the candidate into one of two diagonal pairs, allowing you to eliminate it from all other cells in the affected columns. A Swordfish extends this to three rows and three columns, and a Jellyfish to four. These patterns become necessary in Hard and Expert puzzles when simpler techniques stop yielding progress.
The logic is based on a cover set principle: if a candidate must appear once in each row (or column), and its possible positions are perfectly aligned across a set of rows and columns, then eliminations can be made in the intersecting units. Learning to spot Fish requires practice in candidate notation. Our resource on Sudoku Fish Patterns breaks down the visual patterns and the logic behind them. While our example puzzle solves with only singles, many harder grids will require an X-Wing or Swordfish to break a deadlock.
- X-Wing: A candidate is limited to two cells in each of two rows (or columns), and these cells share the same two columns (or rows).
- Swordfish: The same pattern across three rows and three columns.
- Jellyfish: The same pattern across four rows and four columns.
Wings and Chains: Forcing Logical Paths
This family uses stronger logical dependencies between cells, often involving bi-value cells (cells with only two candidates). A Y-Wing (or XY-Wing) uses three bi-value cells arranged in a pivot-and-pincers shape. If the pivot cell sees both pincers, a candidate common to the pincers can be eliminated from any cell seen by both. An XYZ-Wing is similar but uses a pivot cell with three candidates. These are common in Hard puzzles.
Chains are more general. An X-Chain (or Simple Coloring) follows a strong link on a single candidate through alternating colors, allowing eliminations. An XY-Chain connects a series of bi-value cells, where the start and end share a candidate that can be eliminated from cells seen by both ends. These techniques force conclusions by exploring the logical consequences of placing a digit in a particular cell. They represent a significant step up in deductive reasoning for Sudoku.
- Y-Wing (XY-Wing): Three bi-value cells where the pivot sees two pincers; eliminates a candidate common to the pincers.
- XYZ-Wing: A three-cell pattern where the pivot has three candidates and the pincers are bi-value.
- X-Chain/XY-Chain: A sequence of strong links or bi-value cells that forces an elimination at a distance.
Uniqueness Arguments
These advanced techniques rely on the assumption that a valid Sudoku puzzle has only one solution. They identify patterns that would create multiple solutions (a 'deadly pattern') and use that to make eliminations that preserve uniqueness. The most common is the Unique Rectangle (UR). If a rectangle of four cells across two rows and two boxes contains the same two candidates and nothing else, and three of the cells are bi-value, then you can often remove candidates from the fourth cell to avoid the deadly pattern.
Other variants include Unique Rectangle Type 1, 2, 3, etc., and Extended Unique Rectangles. These are typically last-resort techniques for the most extreme Expert and Diabolical puzzles. It's important to understand that these are not purely logical deductions from the standard rules, but arguments based on the puzzle's designed uniqueness. They are powerful tools for human solvers facing seemingly impossible grids.
- Unique Rectangle (UR): A rectangular pattern of four cells sharing two candidates; used to avoid a multiple-solution scenario.
- Uniqueness-based techniques assume the puzzle has one solution to justify eliminations.
Key Facts
- ▪A Naked Single is a cell with only one remaining possible digit.
- ▪A Hidden Single occurs when a digit has only one possible cell left in a row, column, or box.
- ▪A Naked Pair is two cells in a unit that contain the same two candidates, allowing those digits to be removed from other cells in the unit.
- ▪A Pointing Pair eliminates a candidate from a row or column because all its instances in a box are aligned in that line.
- ▪An X-Wing is a pattern where a candidate is confined to two rows and two columns, forming a rectangle, enabling eliminations.
- ▪A Y-Wing uses three bi-value cells to eliminate a candidate from cells seen by two 'pincer' cells.
- ▪A Unique Rectangle technique uses the puzzle's single-solution guarantee to avoid patterns that would create multiple solutions.
Frequently Asked Questions
What is the simplest Sudoku technique?
The simplest is the Naked Singles, where a cell has only one possible number left. It's the first technique used after basic pencil marking.
What is the difference between a Naked Pair and a Hidden Pair?
A Naked Pair is two cells with only the same two candidates, obvious in notation. A Hidden Pair is two digits that can only go in two specific cells, but those cells have other candidates that must be removed first.
When should I look for an X-Wing?
Look for an X-Wing in Hard puzzles when simpler techniques like singles, pairs, and pointing/claiming no longer give you any new placements or eliminations.
Are uniqueness techniques like Unique Rectangle always valid?
They are valid for puzzles guaranteed to have one solution. In a properly constructed published puzzle, you can safely use them. They are not deductions from the core rules alone.
What is a 'bi-value' cell?
A bi-value cell is a cell with only two possible candidates. Many advanced techniques like Y-Wings and XY-Chains specifically rely on bi-value cells to create forcing chains of logic.
How do I know which technique to try next?
Follow a logical order: start with all singles, then subsets (pairs/triples), then intersection techniques, then fish, then wings and chains. Our guide on technique order details this progression.