Sudoku Glossary

This glossary is the canonical vocabulary reference for VeyraPlay Sudoku.

Use it when a Guide, solver message, or interface label introduces a term you do not recognize. Definitions are intentionally shorter than full technique Guides: the glossary tells you what a term means, while the dedicated Guide explains how the proof works.

Sudoku vocabulary is not perfectly standardized across books, apps, forums, and solvers. Where several names exist, VeyraPlay uses one preferred public term and keeps important aliases discoverable.

Our default choices include:

• box rather than block for the 3×3 region;
• unit in beginner-facing explanations and house when advanced solver terminology benefits from it;
• clue with given retained as a common alias;
• candidate for a logically possible digit and pencil mark/note for its visible notation.

How to use this Sudoku glossary

The terms below fall into several recurring groups:

• grid vocabulary — cell, row, column, box, house, peer, band, stack;
• candidate vocabulary — candidate, bivalue, conjugate pair, pencil mark;
• deduction vocabulary — placement, elimination, reservation, implication, contradiction;
• technique vocabulary — Singles, subsets, Fish, Wings, Coloring, Chains, uniqueness;
• puzzle/theory vocabulary — clue, solution, minimal puzzle, difficulty, symmetry, generation;
• notation — rNcM, candidate sets, Strong/Weak Link symbols.

For a complete introduction to the physical grid, see Sudoku Grid Explained. For the logic behind candidates and deductions, see Sudoku Candidates and Sudoku Logic.

A

AIC — Alternating Inference Chain

An advanced chain built by alternating Strong and Weak inference relationships.

AIC is a broad language for expressing many chain deductions. VeyraPlay covers ordinary Alternating Inference Chains and extends the model with Grouped AIC.

Algorithm X

A recursive algorithm for solving exact cover problems. Sudoku can be encoded as exact cover, making Algorithm X one complete-search approach for finding or counting solutions.

It is commonly paired with Dancing Links (DLX) as an efficient data structure implementation.

ALS — Almost Locked Set

A set of N cells in one house containing exactly N+1 different candidates in total.

An ALS is not itself an elimination. Advanced techniques use relationships between ALS structures to create Strong/Weak inferences and candidate eliminations.

ALS-XZ

An expert technique using two Almost Locked Sets connected by a Restricted Common Candidate (X) and another shared candidate Z. The RCC relationship forces Z into one of the sets, allowing Z eliminations from cells that see all relevant Z occurrences.

Almost Locked Set

See ALS.

Avoidable Rectangle

A uniqueness pattern related to Unique Rectangles in which already solved digits participate in a configuration that could otherwise permit a second solution.

It belongs to the advanced uniqueness family.

B

Backtracking

A systematic search algorithm that chooses a possibility, propagates consequences, and returns to an earlier choice when the branch fails.

Software commonly uses backtracking or equivalent complete-search methods for solution finding and uniqueness testing. A human-solving curriculum can still focus on explainable deductions rather than branch search.

Band

A horizontal group of three 3×3 boxes.

A classic 9×9 Sudoku has three horizontal bands.

Base set

In Fish terminology, one of the source houses used to define the Fish.

In a row-based X-Wing, for example, the two source rows are the base sets and the candidate positions are contained within two cover columns.

Bivalue cell

An unsolved cell with exactly two candidates.

Bivalue cells are central to patterns such as:

• XY-Wing;
• W-Wing;
• Remote Pair;
• XY-Chain.

Block

A common alias for a 3×3 box.

VeyraPlay normally uses box in public copy.

Box

One of the nine 3×3 regions in classic 9×9 Sudoku.

Every completed box contains digits 1–9 exactly once.

Box-Line Reduction

VeyraPlay's public title for the Claiming direction of Locked Candidates.

If all remaining positions for a digit in a row or column lie inside one box, that digit can be eliminated from the other cells of the box.

Also called:

• Claiming;
• Locked Candidates Type 2.

BUG — Bivalue Universal Grave

A uniqueness structure in which every unsolved cell is bivalue and candidate occurrences form a binary pattern capable of supporting multiple solutions.

The related BUG+1 technique uses one exceptional candidate to prevent that state.

BUG+1

A uniqueness technique in which the grid is almost a Bivalue Universal Grave except for one extra candidate. The exceptional candidate can often be placed to avoid the non-unique BUG state.

C

Candidate

A digit that can still legally occupy an unsolved cell given the current grid state.

A candidate is a possibility, not a guess and not necessarily the final answer.

Candidate elimination

Removing a candidate because a logical deduction proves that the digit cannot occupy that cell.

An elimination is genuine progress even if no digit is placed immediately.

Candidate set

The complete set of digits currently legal in one unsolved cell.

Example:

{2,5,7}

Cell

One square in the Sudoku grid.

Classic Sudoku contains 81 cells.

Cell-first search

A solving viewpoint that starts from the candidate set inside individual cells and small groups of cells.

Naked Singles, Naked Subsets, and many Wings are naturally found this way.

Chain

A sequence of connected logical implications.

Introductory chains use Strong and Weak Links. Some chains stay on one digit; others move between digits or more complex nodes.

Claiming

A Locked Candidates direction in which all positions for a digit in a row or column are confined to one box.

The digit can then be removed from the rest of that box.

See Box-Line Reduction.

Clue

A digit supplied before solving begins.

Also called a given.

Color Trap

A Simple Coloring elimination.

If an uncolored candidate sees one candidate of each color from the same connected coloring component, one of those colors must be true, so the uncolored candidate must be false.

Color Wrap

A Simple Coloring contradiction.

If two candidates of the same color see each other, that color cannot represent the true polarity. All candidates of that color can be eliminated.

Coloring

A method that propagates two alternating truth states through connected Strong Links for one candidate.

Simple Coloring then uses contradictions or visibility relationships to make eliminations.

Column

One vertical house of nine cells.

A completed column contains digits 1–9 exactly once.

Conjugate pair

Exactly two remaining positions for the same digit within one house.

Those two candidate positions form a Strong Link: if one is false, the other must be true.

Constraint

A condition a valid solution must satisfy.

Classic Sudoku's main structural constraints are the row, column, and box requirements.

Contradiction

An impossible consequence used as proof that an earlier assumption or candidate state cannot be true.

Examples include:

• a duplicate solved digit in a house;
• a cell with no legal candidate;
• a house with no possible location for a required digit;
• an impossible implication state.

Cover set

In Fish terminology, one of the houses that collectively contain every relevant candidate position from the base sets.

For a row-based X-Wing, the cover sets are columns.

Crosshatching

A visual scanning method that uses solved instances of a digit in intersecting rows/columns to block positions inside another box or unit.

Crosshatching commonly reveals Hidden Singles.

D

Dancing Links (DLX)

A linked-list technique designed to make cover/uncover operations efficient in exact-cover search. In Sudoku discussions, DLX usually refers to an implementation of Algorithm X over the Sudoku exact-cover matrix.

Deadly pattern

A candidate structure that would permit more than one solution if completed.

The classic example is the two-digit rectangle behind Unique Rectangle techniques.

Digit

One of the symbols 1–9 used in classic Sudoku.

Sudoku uses them as labels; arithmetic value is not part of the classic rules.

Digit-first search

A solving viewpoint that follows one digit across houses rather than starting from one cell's full candidate set.

Hidden Singles, Locked Candidates, Fish, Strong-Link patterns, and Coloring are naturally found this way.

Difficulty

The amount and type of human solving work a puzzle requires or appears to require.

Difficulty can depend on technique depth, recognition burden, dependency structure, and solver conventions—not just clue count.

Difficulty model

A system for converting a puzzle's analyzed solve path and/or player data into a rating, score, or label such as Easy, Hard, or Expert.

E

Elimination

See candidate elimination.

Empty Rectangle

A single-digit pattern using candidate geometry inside one box plus a Strong-Link connection outside it to produce an elimination.

It belongs to the same broad advanced neighborhood as Turbot Fish, Skyscraper, Two-String Kite, and X-Chains.

Endpoint

A candidate or node at one end of a chain or pattern.

Many chain deductions eliminate a candidate that sees both endpoints when at least one endpoint must be true.

Exact cover

A mathematical formulation in which a solution selects options so that every required constraint is satisfied exactly once.

Classic Sudoku can be encoded as an exact-cover problem, which is useful for algorithmic solvers.

F

False candidate

A candidate that is still written or displayed but can be logically eliminated from the current state.

Fish

A family of single-digit candidate patterns based on matching base sets and cover sets.

Basic Fish include:

• X-Wing — size 2;
• Swordfish — size 3;
• Jellyfish — size 4.

Finned Fish

A Fish that contains one or more extra candidate positions—fins—outside the clean basic-Fish cover structure.

The fin changes where eliminations are valid.

Finned X-Wing

A size-2 Finned Fish based on X-Wing structure plus one or more fins.

Floor

A specialist alias sometimes used for a horizontal chute/band of three boxes.

VeyraPlay prefers band in normal public copy.

Forcing Chain

A deduction that examines every alternative in a selected starting set and proves a common consequence or a contradiction. VeyraPlay distinguishes structured Forcing Chains from unsupported guessing and from more general branching Forcing Nets.

Forcing Net

A forcing structure in which implications branch rather than remaining a single chain. Forcing Nets are deliberately outside the first V2 freeze.

Full House

A direct placement where one house has exactly one unsolved cell remaining, so the missing digit must occupy that cell.

Also commonly described as Last Digit.

It is the simplest member of the Singles family.

G

Group node

A set of candidate positions treated as one logical node because the group as a whole participates in a valid Strong or Weak inference. Box-line intersections are a common source of group nodes.

Grouped AIC

An Alternating Inference Chain that allows one or more logical nodes to represent candidate groups instead of only single candidates. The alternation rules remain the same as ordinary AIC.

Given

A common alias for a starting clue.

H

Hidden Pair

Two digits whose remaining positions within one house are restricted to the same two cells.

Other candidates can be removed from those two cells.

Hidden Quad

Four digits whose remaining positions in one house are restricted to the same four cells.

The four digits are reserved there, so other candidates can be removed from those cells.

Hidden Rectangle

An advanced uniqueness pattern related to Unique Rectangles. Its candidate structure creates a Strong-Link-based uniqueness deduction without matching the simplest Type 1 shape.

Hidden Single

A digit that has exactly one legal position remaining in a row, column, or box, even if the target cell still displays several candidates.

Hidden Subset

A set of N digits restricted to exactly N cells in one house.

Those digits are reserved for those cells, so all other candidates can be removed from the cells.

Hidden Pair, Hidden Triple, and Hidden Quad are Hidden Subsets.

Hidden Triple

Three digits whose possible positions in one house are restricted to the same three cells.

House

A specialist umbrella term for a group governed by an exactly-once digit constraint.

In classic Sudoku, the standard houses are:

• 9 rows;
• 9 columns;
• 9 boxes.

That gives 27 standard houses.

VeyraPlay often uses unit in beginner-facing copy and house when advanced solver language benefits from it.

I

Implication

A logical relationship of the form:

if this candidate/state is true or false, another candidate/state must become true or false.

Strong and Weak Links are the basic implication language for many advanced techniques.

Intersection

The cells shared by two houses, such as the three cells where a row passes through a box.

Locked Candidates exploit row/box or column/box intersections.

Invalid puzzle

A starting puzzle that fails an intended validity requirement—for example because it has no solution, conflicting clues, or (under the usual classic-Sudoku quality expectation) more than one solution.

J

Jellyfish

A size-4 basic Fish.

Four base rows (or columns) restrict one Fish digit to four cover columns (or rows), allowing eliminations in the cover sets outside the bases.

L

Last Digit

See Full House.

Latin square

An arrangement in which each symbol appears exactly once in every row and column.

A completed classic Sudoku grid is a constrained 9×9 Latin square with an additional 3×3 box requirement.

Link

A logical relationship between candidates or more complex inference nodes.

The two foundational link types are Strong Link and Weak Link.

Locked Candidates

An intersection technique where candidate positions for one digit are confined by the overlap between a box and a row or column.

The two directions are:

• Pointing — box → row/column;
• Claiming / Box-Line Reduction — row/column → box.

M

Minimal puzzle

A unique Sudoku in which removing any one clue destroys uniqueness.

A minimal puzzle does not necessarily have the globally minimum possible number of clues.

Minimum-clue puzzle

A unique puzzle using the smallest possible clue count for the puzzle class under discussion.

For classic 9×9 Sudoku, no unique 16-clue puzzle exists; unique 17-clue puzzles do exist.

Multi Coloring

An extension of Coloring that reasons across more than one disconnected Strong-Link coloring component for the same digit.

N

Naked Pair

Two cells in one house whose combined candidates are exactly the same two digits.

Those digits are reserved for the pair, so they can be eliminated from other cells in the house.

Naked Quad

Four cells in one house whose combined candidate union contains exactly four digits.

Those four digits are reserved for the four cells.

Naked Single

An unsolved cell with exactly one legal candidate remaining.

Naked Subset

A set of N cells in one house whose combined candidates contain exactly N digits.

Those digits are reserved for those cells and can be removed from the rest of the house.

Naked Triple

Three cells in one house whose combined candidates contain exactly three digits.

Nishio

A contradiction-based advanced technique that follows the consequences of one candidate being true, often through single-digit forcing-chain logic, and eliminates the candidate if that assumption reaches an impossible state.

Note

A visible annotation written or displayed in a cell.

A note may represent a candidate, but candidate is the logical state while note describes the notation/interface.

P

Peer

A cell that shares a row, column, or box with another cell.

Two different peer cells cannot contain the same solved digit.

A classic 9×9 cell has 20 distinct peers.

Pencil mark

A small written/displayed note used to track candidates or selected possibilities inside an unsolved cell.

Pincer

One of the outer cells in a Wing pattern such as XY-Wing or XYZ-Wing.

Pivot

The central cell that connects the pincers in patterns such as XY-Wing or XYZ-Wing.

Placement

A logical move that proves one digit must occupy one cell.

Pointing

A Locked Candidates direction where all remaining positions for a digit inside one box lie in a single row or column.

That digit can be eliminated from the same row/column outside the box.

Also called Locked Candidates Type 1.

Pointing Pair

A common name for a Pointing configuration with two candidate positions inside the box.

The same logic also works when three positions align, so Pointing is the more general family name.

R

RCC — Restricted Common Candidate

A candidate shared between two Almost Locked Sets under restrictions that prevent it from being true in both ALS structures simultaneously.

RCC relationships are foundational to several ALS techniques.

Region

A generic term for a group of cells governed by a uniqueness constraint.

In classic Sudoku, box is the clearer public term for the nine 3×3 regions. In variants, regions may have other shapes.

Remote Pair

A chain of bivalue cells that all contain the same pair of digits and are connected through peer relationships.

Alternating the two values along the chain can eliminate those digits from cells that see appropriately opposite endpoints.

Row

One horizontal house of nine cells.

A completed row contains digits 1–9 exactly once.

S

Sashimi Fish

A Fish variant in which the underlying basic-Fish structure has a missing expected candidate position and one or more fins alter the elimination geometry.

Scanning

A broad search habit that visually checks rows, columns, and boxes for missing digits, restrictions, and forced positions.

See / sees

Two cells see each other if they are peers—meaning they share a row, column, or box.

Simple Coloring

A single-digit Strong-Link technique that assigns two alternating colors through one connected conjugate-pair network and then searches for Color Trap, Color Wrap, or related contradictions.

Single

A direct placement where one digit is forced.

The core Singles are:

• Full House / Last Digit;
• Naked Single;
• Hidden Single.

Snyder notation

A selective pencil-mark system commonly used on paper in which a digit is often noted when it has exactly two candidate positions inside a box.

It is a notation discipline, not a Sudoku rule, and does not replace full candidate notation in every puzzle state.

Solution

A complete assignment of digits that satisfies all required constraints of the puzzle.

Solution count

The number of complete valid solutions consistent with the starting clues.

For a classic published Sudoku, the expected count is normally exactly one.

Solution grid

A complete valid 9×9 Sudoku grid before clues are removed to form a puzzle.

Solution path

A sequence of solving steps that progresses from the starting clues to the completed grid.

Different human-style solvers can find different valid paths through the same puzzle.

Stack

A vertical group of three boxes.

A classic grid has three stacks.

Strong Link

An inference stating that two candidate states cannot both be false.

For simple candidate links:

if A is false, B must be true; if B is false, A must be true.

A conjugate pair is the standard single-digit example.

Subset

A reservation relationship between a small set of cells and the same-sized set of digits inside one house.

Subsets are commonly divided into Naked and Hidden forms.

Swordfish

A size-3 basic Fish.

Three base houses restrict one digit to three cover houses, allowing eliminations in those covers outside the bases.

Symmetry

A structural relationship preserved under a transformation.

In puzzle construction, the word often refers to clue-layout symmetry—for example rotationally symmetric clue positions. Such visual symmetry is a design choice, not a basic Sudoku rule.

T

Technique

A repeatable logical pattern or proof used to place a digit or eliminate a candidate.

A technique is different from a broader strategy, which organizes when and where to search.

Tower

A specialist alias sometimes used for a vertical chute/stack of three boxes.

VeyraPlay prefers stack.

Trivalue cell

An unsolved cell with exactly three candidates.

Turbot Fish

A short single-digit chain pattern built from two Strong Links connected by a Weak Link. Skyscraper and Two-String Kite can be understood within this broader family of short alternating inference structures.

Two-String Kite

A single-digit pattern built from a conjugate pair in one row and another in one column, with one endpoint from each pair interacting inside the same box.

U

Unique solution

A puzzle has a unique solution when exactly one completed grid satisfies all starting clues and constraints.

Unique Rectangle

A uniqueness family based on four cells occupying exactly two rows, two columns, and two boxes. The family prevents candidate states that would allow two interchangeable completions.

Uniqueness technique

A deduction that uses the additional premise that the puzzle has exactly one solution.

Unique Rectangle and BUG+1 are examples.

Unit

A group of cells that must contain digits 1–9 exactly once in classic Sudoku.

Rows, columns, and boxes are the 27 standard units/houses.

VeyraPlay often uses unit in accessible explanatory copy.

W

Weak Link

An inference stating that two candidate states cannot both be true.

For candidates A and B:

if A is true, B must be false.

Both may still be false.

Wing

A family of candidate patterns that often links bivalue or near-bivalue cells around a pivot/pincer structure or an external Strong Link.

Examples include XY-Wing, XYZ-Wing, and W-Wing.

W-Wing

A pattern using two separated bivalue cells with the same pair {X,Y} plus an external Strong Link on one of those digits. The structure proves the other digit occurs at one endpoint and enables eliminations from cells that see both endpoints.

WXYZ-Wing

An advanced Wing/subset-style pattern involving four cells and four candidates under a restricted shared-candidate relationship.

It is covered in the V2 Sudoku Wings family and its dedicated WXYZ-Wing Guide.

X

X-Chain

A chain that follows one candidate digit through alternating Strong and Weak Links and starts and ends with a Strong inference on that digit.

X-Cycle

A closed single-digit alternating-link structure. Depending on how the cycle closes, it can produce eliminations or placements.

X-Wing

A size-2 basic Fish.

Two base rows (or columns) restrict one digit to the same two cover columns (or rows), enabling eliminations in the covers outside the bases.

XY-Chain

A chain of bivalue cells whose internal candidate relationships provide Strong Links and whose peer relationships connect successive cells. The chain starts and ends on the same candidate digit, enabling eliminations from cells that see both ends.

XY-Wing

A three-cell Wing with:

• pivot {X,Y};
• one pincer {X,Z};
• another pincer {Y,Z}.

At least one pincer must contain Z, so Z can be eliminated from cells that see both pincers.

XYZ-Wing

A three-cell Wing with a trivalue pivot {X,Y,Z} and two related pincers {X,Z} and {Y,Z}. The target must see all relevant Z positions, including the pivot.

Y

Y-Wing

A common alias for XY-Wing.

Numbers and notation

3D Medusa

A multi-digit coloring technique that propagates two opposite truth states through a connected candidate network using Strong relationships such as conjugate pairs and bivalue cells.

Unlike Simple Coloring, the network can move between different digits.

rNcM

Row/column cell notation.

Example:

r5c2

means row 5, column 2.

Multiple row or column numbers may be compressed in specialist notation. For example, r57c2 refers to r5c2 and r7c2.

{2,5,7}

Candidate-set notation.

The cell currently allows digits 2, 5, and 7.

= in chain notation

Often used to represent a Strong Link or strong inference.

Exact notation varies between communities and software.

- in chain notation

Often used to represent a Weak Link or weak inference.

<> or ≠

Common notation meaning a cell/candidate is not a particular value.

= digit

Common shorthand indicating a placement or true candidate state.

FAQ

What is a house in Sudoku?

A house is a solver-community umbrella term for a row, column, or box. Classic 9×9 Sudoku therefore has 27 standard houses.

Is a Sudoku box the same as a block?

Yes in classic Sudoku. Both names usually refer to one 3×3 region. VeyraPlay prefers box in public-facing explanations.

What is the difference between a candidate and a pencil mark?

A candidate is a digit that remains logically possible in a cell. A pencil mark or note is a visible way of recording that information. A digital interface can maintain candidates even when they are not displayed.

What does it mean when two cells see each other?

They are peers: they share a row, column, or box. Two peer cells cannot contain the same solved digit.

What is a bivalue cell?

An unsolved cell with exactly two candidates. Bivalue cells create especially useful Strong-Link relationships inside the cell and appear in many Wings and Chains.

Why do Sudoku techniques have different names on different sites?

Sudoku terminology developed across books, forums, puzzle publishers, and software, so aliases are common. A technique may have a family name, an older community name, and a solver-specific label. The proof matters more than the branding.

Does this glossary include every named Sudoku technique?

No. It prioritizes vocabulary used by the VeyraPlay corpus plus important terms required to understand planned expert expansion. Extremely niche named patterns should be added only when they become editorially useful.

Vocabulary principles used by VeyraPlay

When several terms are valid, consistency matters more than pretending only one vocabulary exists.

Our general rules are:

• teach the clearest mainstream term first;
• preserve important aliases for search and interoperability;
• distinguish logical state from UI notation;
• distinguish strategy from technique;
• distinguish a basic Sudoku constraint from an additional puzzle-quality premise such as uniqueness;
• avoid assigning universal difficulty levels to techniques when solver taxonomies differ.

As the expert library expands, new terms should be added here only when they are used meaningfully elsewhere in the corpus.