Sudoku Glossary: Every Term Explained

Sudoku has its own vocabulary, and knowing the correct terms makes it much easier to learn new techniques, follow solving guides, and discuss strategies with other players. This glossary covers every important sudoku term, from basic vocabulary that every beginner needs to advanced terminology used by expert solvers and competitive players. Terms are organized by category for easier reference, starting with the fundamentals and progressing to advanced concepts.

Basic Sudoku Terms

Cell

A single square in the sudoku grid. A standard 9x9 sudoku has 81 cells arranged in 9 rows and 9 columns. Each cell holds exactly one digit (1 through 9) in the completed puzzle. Empty cells are what you fill in during solving.

Given (or Clue)

A digit that is already placed in the grid at the start of the puzzle. Givens are the starting information from which you deduce all other values. The number of givens varies by difficulty — easy puzzles might have 36 or more, while the hardest known puzzles have only 17. Givens are also sometimes called "clues" or "initial digits."

Row

A horizontal line of 9 cells spanning the full width of the grid. There are 9 rows in a standard sudoku, typically numbered 1 (top) through 9 (bottom). Each row must contain every digit from 1 to 9 exactly once.

Column

A vertical line of 9 cells spanning the full height of the grid. There are 9 columns, typically numbered 1 (left) through 9 (right). Each column must contain every digit from 1 to 9 exactly once.

Box (or Block, Region, Square)

One of the nine 3x3 sub-grids outlined by thicker lines in the puzzle. Boxes are typically numbered 1 through 9, reading left to right and top to bottom. Each box must contain every digit from 1 to 9 exactly once. The term "block" and "region" are common alternatives.

Band

A horizontal group of three boxes spanning the full width of the grid. There are three bands in a standard sudoku: top (boxes 1-3), middle (boxes 4-6), and bottom (boxes 7-9). Rows within the same band can be swapped without invalidating the puzzle.

Stack

A vertical group of three boxes spanning the full height of the grid. There are three stacks: left (boxes 1, 4, 7), middle (boxes 2, 5, 8), and right (boxes 3, 6, 9). Columns within the same stack can be swapped while preserving validity.

Peers

All cells that share a constraint with a given cell — that is, all cells in the same row, same column, and same box. Every cell has exactly 20 peers. If a cell contains the digit 5, none of its 20 peers can contain 5. Understanding peers is fundamental to every solving technique.

Candidate

A digit that could potentially go in an empty cell based on current information. When you start solving, each empty cell might have several candidates. Solving techniques work by eliminating candidates until only one remains. Candidates are also called "possibilities" or "potential values."

Notation and Marking Terms

Pencil Marks

Small numbers written in empty cells to track candidates. On paper, solvers write tiny digits in the corners or center of cells. In digital sudoku apps like Sudoku Royale, pencil marks are typically entered through a dedicated notes mode. Effective use of pencil marks is essential for solving anything harder than easy puzzles. See our complete guide to pencil marks.

Snyder Notation

A pencil marking system popularized by Thomas Snyder (a multiple-time World Sudoku Champion). In Snyder notation, you only write pencil marks for candidates that appear exactly twice within a box. This produces far fewer marks than full notation while still capturing the most useful information for finding pairs and singles. Many competitive speed solvers use Snyder notation because it is faster to write and easier to scan.

Full Notation

Writing all possible candidates in every empty cell. This is more thorough than Snyder notation and is required for advanced techniques like X-Wing and Swordfish, which need complete candidate information across rows and columns. Full notation takes longer to write but provides the information needed for any technique.

Center Marks vs. Corner Marks

Two conventions for where to write pencil marks within a cell. Corner marks place candidates in the corners of the cell (typically used in Snyder notation). Center marks place all candidates in the center of the cell, written small. Some apps support both modes, letting solvers use corner marks for Snyder notation and center marks for full notation in the same puzzle.

Basic Solving Techniques

Naked Single

A cell that has only one remaining candidate after eliminating all other possibilities based on the digits present in its row, column, and box. If a cell's peers already contain the digits 1, 2, 3, 4, 5, 6, 7, and 8, then the cell must contain 9. Naked singles are the simplest and most fundamental solving technique. Every easy puzzle can be solved with naked singles alone.

Hidden Single

A candidate that appears in only one cell within a row, column, or box, even though that cell may have multiple candidates. For example, if the digit 7 can only go in one cell within box 5, that cell must be 7 regardless of what other candidates it has. Hidden singles are the second most important technique and, combined with naked singles, solve the vast majority of easy and medium puzzles. Learn more in our hidden singles guide.

Scanning (Cross-Hatching)

A visual technique for quickly identifying where a digit can go within a box by checking which rows and columns already contain that digit. You mentally "cross out" rows and columns that pass through the box and already have the digit, leaving only valid placement positions. Scanning is the fastest way to find naked and hidden singles and is the primary technique used by speed solvers.

Intermediate Solving Techniques

Naked Pair

Two cells in the same row, column, or box that have exactly the same two candidates and no others. For example, if two cells in a row both have candidates {3, 7}, then 3 and 7 must go in those two cells (in some order), and you can eliminate 3 and 7 from all other cells in that row. Naked pairs are one of the most commonly needed intermediate techniques. See our detailed naked pairs tutorial.

Hidden Pair

Two candidates that appear in exactly the same two cells within a row, column, or box, even though those cells may contain additional candidates. If 4 and 9 only appear in cells A and B within a row, then cells A and B must contain 4 and 9, and you can eliminate all other candidates from those two cells. Hidden pairs are harder to spot than naked pairs but equally powerful.

Naked Triple

Three cells in the same row, column, or box whose combined candidates include exactly three digits. The individual cells do not each need to contain all three digits — for instance, cells with candidates {2, 5}, {2, 8}, and {5, 8} form a naked triple for the digits 2, 5, and 8. Those three digits can be eliminated from all other cells in the shared unit. The same logic extends to naked quads (four cells, four digits).

Hidden Triple

Three candidates that appear in exactly three cells within a row, column, or box. All other candidates can be eliminated from those three cells. Hidden triples are significantly harder to spot than naked triples because the cells usually contain additional distracting candidates. Like hidden pairs, they require careful examination of candidate distributions.

Pointing Pair (Pointing Candidates)

When a candidate within a box is confined to a single row or column, that candidate can be eliminated from the rest of that row or column outside the box. For example, if the digit 6 can only appear in row 2 within box 1, then 6 cannot appear in row 2 within boxes 2 or 3. This is also called a "locked candidate" (type 1). See our pointing pairs and box-line reduction guide.

Box-Line Reduction (Claiming)

The inverse of pointing pairs. When a candidate within a row or column is confined to a single box, that candidate can be eliminated from the rest of that box. If the digit 3 in row 4 can only appear within box 4, then 3 can be eliminated from all other cells in box 4 that are not in row 4. This is also called a "locked candidate" (type 2).

Advanced Solving Techniques

X-Wing

A pattern involving a single candidate that appears in exactly two cells in each of two different rows, and those cells share the same two columns (forming the corners of a rectangle). The candidate can be eliminated from all other cells in those two columns. The same logic applies with rows and columns swapped. X-Wing is often the first advanced technique that solvers learn and is named for the X-shaped pattern formed by the elimination lines. Our X-Wing visual guide explains this in detail.

Swordfish

An extension of X-Wing to three rows and three columns. A candidate appears in two or three cells in each of three rows, and those cells are confined to exactly three columns. The candidate can be eliminated from all other cells in those three columns. Swordfish patterns are harder to spot than X-Wings because the pattern is larger and may not form a clean rectangular shape. See our Swordfish technique guide.

Jellyfish

The further extension of the X-Wing family to four rows and four columns. A candidate is confined to at most four cells in each of four rows, and those cells occupy exactly four columns. Eliminations occur in the four columns outside the pattern cells. Jellyfish patterns are rare in well-graded puzzles and extremely difficult to spot manually. Most solvers never need this technique for standard puzzles.

XY-Wing

A pattern involving three cells, each with exactly two candidates. A pivot cell shares one candidate with each of two wing cells. The wing cells share a common candidate that is not in the pivot. Any cell that sees both wing cells can have that common candidate eliminated. For example, if the pivot has {3, 5}, one wing has {3, 7}, and the other has {5, 7}, then 7 can be eliminated from any cell that sees both wings. XY-Wing is a powerful technique for expert-level puzzles. Learn more in our advanced strategies guide.

XYZ-Wing

A variation of XY-Wing where the pivot cell has three candidates instead of two. The pivot contains all three digits involved in the pattern (e.g., {3, 5, 7}), while the wings each share two digits with the pivot. The common digit among all three cells can be eliminated from cells that see all three pattern cells. XYZ-Wing eliminations are more restricted than XY-Wing because the candidate must see all three cells, not just the two wings.

Simple Coloring

A technique that uses two-coloring on a single candidate to find eliminations. Start with a conjugate pair (two cells in a unit that are the only places for a candidate) and assign alternating colors along chains of conjugate pairs. If two cells with the same color see each other, that color is false and all cells of that color can be eliminated. If a cell without coloring sees cells of both colors, that cell can be eliminated. Coloring is a visual and intuitive approach to chain-based logic.

Multi-Coloring

An extension of simple coloring that considers multiple independent coloring chains for the same candidate. When two separate chains interact (a cell in one chain sees a cell in another), additional eliminations become possible. Multi-coloring is more powerful than simple coloring but also more complex to apply.

Forcing Chain

A logical chain that starts with an assumption ("suppose this cell is X") and follows the consequences through a series of forced moves. If assuming both possible values for a cell leads to the same conclusion for another cell, that conclusion must be true. Forcing chains are powerful but computationally expensive for human solvers, and some purists consider them less elegant than pattern-based techniques.

Nice Loop

A type of chain that forms a closed loop through cells and candidates, with alternating strong and weak links. Strong links connect conjugate pairs (the only two places for a candidate in a unit), while weak links connect candidates within a cell. Nice loops generalize many other techniques — X-Wing, coloring, and XY-Wing can all be expressed as nice loops.

Unique Rectangle

A technique based on the principle that a well-formed sudoku puzzle has exactly one solution. If four cells in two rows and two columns form a rectangle where three corners have the same two candidates, the fourth corner must not be limited to those same two candidates (otherwise the puzzle would have two solutions — you could swap the digits and still have a valid grid). This allows eliminations from the fourth corner cell.

Competitive and Game Terms

Speed Solving

The practice of solving sudoku puzzles as fast as possible, often competitively. Speed solvers use optimized scanning patterns, minimal pencil marking (often Snyder notation), and deep pattern recognition to complete puzzles in minutes or even seconds. See our speed solving techniques guide.

Battle Royale (Sudoku)

A competitive format where multiple players solve the same puzzle simultaneously, with elimination between rounds. In Sudoku Royale's battle royale mode, up to 10 players compete on the same board through 3 rounds, with the lowest scorers eliminated after each round.

Duel

A head-to-head format where two players compete on the same puzzle. The player with the higher score at the end wins. Sudoku Royale offers a dedicated duel mode for 1v1 competition.

Bifurcation (Trial and Error)

The practice of guessing a value for a cell and seeing if it leads to a contradiction. If it does, the other candidate must be correct. While technically valid for reaching a solution, bifurcation is generally considered inelegant by serious solvers because it replaces logical deduction with trial and error. Well-crafted puzzles should always be solvable without bifurcation.

Backtracking

An algorithmic approach used by computer solvers that systematically tries values and reverses course when a contradiction is found. It is the computational equivalent of bifurcation. While essential for solver programs, backtracking is what human solvers aim to avoid through logical technique. Learn more in our guide to sudoku solvers.

Puzzle Construction Terms

Symmetry

The arrangement of givens in a puzzle. Most published puzzles use 180-degree rotational symmetry, meaning the pattern of given cells looks the same when the grid is rotated upside down. Diagonal symmetry, vertical symmetry, and full four-way symmetry are also used. Symmetry is an aesthetic choice that does not affect difficulty.

Minimal Puzzle

A puzzle where removing any single given would result in multiple solutions. Minimal puzzles have no redundant clues — every given is necessary. Not all published puzzles are minimal, but the concept is important in puzzle construction and the study of minimum clue counts.

Proper Puzzle

A puzzle with exactly one unique solution. This is the fundamental requirement for a valid sudoku puzzle. Puzzles with zero solutions (contradictory givens) or multiple solutions (insufficient givens) are considered improper. Quality puzzle generators always verify properness.

Equivalent Puzzles

Two puzzles that are identical after applying valid transformations (row swapping within bands, column swapping within stacks, band/stack swapping, transposition, or digit relabeling). Equivalent puzzles are structurally identical and have the same difficulty, even though they look different. The concept is important in counting distinct sudoku puzzles.

Isomorphism

The formal mathematical term for puzzle equivalence. Two puzzles are isomorphic if one can be transformed into the other through a sequence of valid operations. Determining whether two puzzles are isomorphic is a non-trivial computational problem related to graph isomorphism.

Variant-Specific Terms

Killer Sudoku

A variant that replaces some or all givens with "cages" — groups of cells whose values must sum to a specified total. Killer sudoku combines sudoku logic with arithmetic constraints. No digit can repeat within a cage. See our sudoku variants guide for more.

Diagonal Sudoku

A variant adding two extra constraints: both main diagonals must also contain the digits 1 through 9 exactly once. This additional constraint actually makes many placements easier to find, so diagonal sudoku puzzles can afford to have fewer givens.

Samurai Sudoku

A variant consisting of five overlapping 9x9 grids arranged in a cross pattern. The overlapping boxes must satisfy constraints from both grids they belong to, creating unique interactions. Samurai puzzles are larger and take longer to solve but use the same fundamental techniques.

Thermometer Sudoku

A variant where "thermometer" shapes are drawn across cells, and digits must increase along the thermometer from the bulb end to the tip. This adds ordering constraints that interact with standard sudoku logic.