Sudoku Glossary

This glossary is the canonical vocabulary reference for VeyraPlay Sudoku.

Use it when a Guide, Learn lesson, solver message, or interface label introduces an unfamiliar term. Definitions are intentionally concise; each technique's full proof remains in its dedicated Guide.

Where Sudoku communities use several names for the same idea, VeyraPlay chooses one preferred public term and keeps important aliases discoverable. That lets the product stay consistent without pretending that the wider Sudoku community uses only one vocabulary.

How to read the glossary

Terms fall into four useful groups:

• grid vocabulary — cell, row, column, box, peer, unit;
• candidate vocabulary — candidate, pencil mark, bivalue, conjugate pair;
• technique vocabulary — Singles, subsets, Fish, Wings, Chains;
• puzzle/theory vocabulary — clue, unique solution, minimal puzzle, difficulty, symmetry.

For beginner-facing copy, prefer plain terms such as box, clue, and unit. Solver-community aliases such as block, house, and given remain here because players will encounter them elsewhere.

A

AIC — Alternating Inference Chain

A general chain that alternates Strong and Weak inference relationships between candidates.

VeyraPlay treats full AIC solving as Expert expansion, after the introductory Sudoku Chains material.

B

Backtracking

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

VeyraPlay may use backtracking for correctness and uniqueness validation, but the Learn curriculum focuses on human-readable deductions.

Band

A horizontal group of three 3×3 boxes.

A classic 9×9 Sudoku contains three bands.

Base set

In Fish terminology, a row or column chosen as one of the source units whose candidate positions are covered by a corresponding set of rows or columns.

For a row-based X-Wing, the two source rows are the base sets.

Bivalue cell

An unsolved cell containing exactly two candidates.

Bivalue cells are especially important in:

• XY-Wing;
• W-Wing;
• XY-Chains.

Block

A common alternative to box.

VeyraPlay prefers box in public copy.

Box-Line Reduction

The Claiming direction of Locked Candidates.

A row or column restricts one digit to a single box, allowing that digit to be removed from the rest of the box.

Also called Claiming or Locked Candidates Type 2.

Box

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

Each box must contain digits 1–9 exactly once when the puzzle is complete.

C

Candidate

A digit that can still legally fit in an unsolved cell based on the current grid.

Candidates are often displayed as small numbers inside the cell.

Candidate set

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

Example:

{2,5,7}

Candidate elimination

Removing a digit from a cell's candidate set because a logical deduction proves that digit cannot be placed there.

An elimination is a valid solving move even when it does not immediately place a digit.

Cell

One square in the Sudoku grid.

Classic Sudoku contains 81 cells.

Chain

A sequence of logical implications connecting candidates.

Introductory chains are built from Strong and Weak Links.

Claiming

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

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

VeyraPlay's dedicated public page is titled Box-Line Reduction, with Claiming as an alias.

Clue

A digit supplied by the puzzle before solving begins.

Also called a given.

Color Trap

A Simple Coloring elimination where an uncolored candidate sees opposite colors from the same connected coloring component.

Because one color polarity must be true, the uncolored candidate is false.

Color Wrap

A Simple Coloring contradiction where two same-color candidates see each other.

That color polarity cannot be true, so candidates carrying that color in the component can be eliminated.

Coloring

A one-digit inference method that alternates two states across a connected network of Strong Links.

See Simple Coloring.

Column

A vertical line of nine cells.

Each completed column contains digits 1–9 exactly once.

Conjugate pair

Two candidate positions for the same digit that are the only remaining positions for that digit within a row, column, or box.

They form a Strong Link.

Cover set

In Fish terminology, a row or column that covers the candidate positions supplied by the base sets.

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

Contradiction

A proof that a temporary candidate assumption is impossible because valid implications lead to an invalid state.

Contradiction reasoning is not the same as accepting an unsupported guess.

Crosshatching

A beginner scanning method that uses existing digits in rows and columns to rule out positions inside a box.

D

Deadly pattern

In uniqueness terminology, a candidate configuration that could permit multiple interchangeable completions.

The classic Unique Rectangle {X,Y} four-corner state is a common example.

Difficulty model

The algorithm or heuristic used to convert a puzzle's solving features into a product difficulty label or score.

A good model can consider required techniques, total effort, dependency structure, and later player data.

Digit

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

Sudoku uses digits as labels; arithmetic is not required.

Difficulty

A rating intended to describe how challenging a puzzle is.

Difficulty is not determined reliably by clue count alone. Systems may consider required solving techniques, the number of steps, dependencies between steps, and other features.

E

Elimination

See candidate elimination.

Endpoint

The first or last candidate node in a chain.

Some chain deductions prove that at least one of two endpoints is true, allowing an elimination from candidates that see both.

F

Exact cover

A mathematical formulation in which a valid solution must satisfy a collection of requirements exactly once.

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

Fish

A family of single-digit patterns based on candidate restrictions across matching sets of rows and columns.

Examples:

• X-Wing;
• Swordfish;
• Jellyfish.

Finned Fish

A Fish variation containing additional source candidates — the “fin” — that changes where eliminations are valid.

Finned Fish belong to a later Expert expansion.

G

Given

A starting clue placed in the puzzle before the player begins.

VeyraPlay may use given and clue, with clue preferred in beginner-facing explanatory copy where it reads more naturally.

H

Hidden Pair

Two digits that can appear only in the same two cells of one unit.

Other candidates can be removed from those two cells.

Hidden Single

A digit that has only one possible position in a row, column, or box, even if the target cell contains several candidates.

Hidden Subset

A family including Hidden Pairs, Triples, and Quads.

N digits are restricted to N cells inside one unit.

Hidden Triple

Three digits restricted to the same three cells in a unit.

Other candidates can be removed from those three cells.

House

A solver-community term for a row, column, or box.

VeyraPlay prefers unit in public educational copy, but may mention house in the glossary because it appears in advanced Sudoku resources.

I

Invalid puzzle

A starting grid that fails the intended publishing requirements — for example because it has no solution, multiple solutions when uniqueness is required, contradictory givens, or unsupported product metadata.

Intersection

The cells shared by two units, most commonly where a box overlaps a row or column.

Locked Candidates use box-line intersections.

J

Jellyfish

A size-4 basic Fish using four base sets and four cover sets.

Deferred to Expert expansion.

L

Latin square

An n × n arrangement of n symbols where each symbol appears exactly once in every row and column.

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

Link

A logical relationship between two candidate possibilities.

See Strong Link and Weak Link.

Locked Candidates

A family of intersection eliminations.

Two main directions:

• Pointing: box → row/column;
• Claiming: row/column → box.

M

Minimal puzzle

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

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

Minimum-clue puzzle

A puzzle at the smallest possible clue count for its Sudoku class while retaining a unique solution.

For classic 9×9 Sudoku, the proven minimum is 17 clues.

N

Naked Pair

Two cells in the same unit whose combined candidate set contains exactly two digits.

Those digits can be removed from other cells in the unit.

Naked Single

A cell with exactly one remaining candidate.

Naked Subset

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

Examples:

• Naked Pair;
• Naked Triple;
• Naked Quad.

Naked Triple

Three cells in one unit whose candidate union contains exactly three digits.

Note

A small candidate mark entered by the player.

See pencil mark.

P

Peer

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

Two peer cells cannot contain the same solved digit.

Pencil mark

A small note showing a candidate digit for an unsolved cell.

Pincer

One of the outer cells in a Wing pattern.

In XY-Wing:

• pivot {X,Y};
• pincers {X,Z} and {Y,Z}.

Pivot

The central cell of a Wing pattern.

In XY-Wing the pivot is bivalue {X,Y}.

In XYZ-Wing the pivot contains {X,Y,Z}.

Placement

Entering a solved digit into a cell because logic has reduced it to one valid value.

Pointing

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

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

Pointing Pair

A common name for Pointing when the source intersection contains two candidate cells.

The same logic also works with three aligned positions, sometimes called a Pointing Triple. VeyraPlay teaches the general concept as Pointing Candidates while retaining Pointing Pairs as the page title.

R

Region

A general term for a constrained group of cells.

In classic Sudoku, the 3×3 regions are normally called boxes.

Row

A horizontal line of nine cells.

Each completed row contains digits 1–9 exactly once.

S

Simple Coloring

A one-digit technique that assigns two alternating states across a connected conjugate-pair network.

The standard deductions covered here are Color Trap and Color Wrap.

Scanning

A broad beginner method of inspecting rows, columns, and boxes to find restricted positions or missing digits.

Single

A forced placement.

The two main beginner types are:

• Naked Single;
• Hidden Single.

Solution

A completed grid satisfying all puzzle clues and Sudoku constraints.

Solution count

The number of completed grids consistent with the starting clues and Sudoku constraints.

For standard VeyraPlay classic puzzles, the target is exactly one.

Solution grid

A fully completed valid 9×9 Sudoku grid.

A solution grid is not yet a puzzle; a puzzle is created by selecting clues from a solution grid and validating the resulting starting state.

Solution path

An ordered sequence of solving steps used to reach the solution.

A human-style solution path can also be used to estimate difficulty or generate training material.

Stack

A vertical group of three 3×3 boxes.

Classic Sudoku contains three stacks.

Strong Link

A relationship where two candidates cannot both be false.

Key inference:

A false → B true.

A conjugate pair is the most common example.

Subset

A candidate-reservation structure where N digits are confined to N cells.

Subsets can be Naked or Hidden.

Symmetry

A transformation or layout property that preserves or visually organizes Sudoku structure.

Examples include consistent digit relabeling and certain row/column/band/stack transformations. Clue-layout symmetry is an aesthetic construction choice, not a classic Sudoku rule.

Swordfish

A size-3 Fish using three base sets and three cover sets.

T

Technique

A repeatable logical pattern or method used to make a placement or candidate elimination.

Trivalue cell

An unsolved cell containing exactly three candidates.

Two-String Kite

A single-digit pattern built from one row Strong Link, one column Strong Link, and a connecting box.

U

Unique solution

A puzzle property meaning exactly one completed grid satisfies the clues and constraints.

Unique Rectangle

A family of techniques that uses the assumption that the puzzle has exactly one solution to avoid a local two-solution rectangle.

Uniqueness technique

Any solving technique that relies on a verified or assumed unique solution.

Uniqueness is not one of the three basic row/column/box rules.

Unit

A group in which a digit may appear only once.

In classic Sudoku:

• each row is a unit;
• each column is a unit;
• each box is a unit.

VeyraPlay prefers unit over house in educational copy.

W

Weak Link

A relationship where two candidates cannot both be true.

Key inference:

A true → B false.

Wing

A family of candidate patterns connecting a pivot and/or wing cells.

Examples:

• XY-Wing;
• XYZ-Wing;
• W-Wing.

W-Wing

Two matching bivalue cells connected indirectly through a Strong Link on one of their candidates.

X

X-Chain

A single-digit alternating inference chain.

X-Wing

A size-2 Fish where two base rows or columns restrict one candidate digit to the same two cover units.

XY-Chain

A chain built from bivalue cells where candidate values change as the inference passes from cell to cell.

XY-Wing

A three-bivalue-cell pattern with:

• pivot {X,Y};
• pincers {X,Z} and {Y,Z}.

The shared Z can be removed from cells that see both pincers.

XYZ-Wing

A Wing with:

• pivot {X,Y,Z};
• pincers {X,Z} and {Y,Z}.

The Z elimination target must see the pivot and both pincers.

Numbers and notation

rNcM

A coordinate notation.

For example:

r4c7 = row 4, column 7.

{2,5,7}

A candidate-set notation indicating that an unsolved cell can currently contain 2, 5, or 7.

=

May be used in advanced chain diagrams to represent a Strong Link.

-

May be used in advanced chain diagrams to represent a Weak Link.