Terminology

The Sudoku community has developed its own terminology. Most of the basic terms are now widely accepted, but some concepts are known by many different names. Here is an alphabetic list of the most commonly used terms.

0-9

3D Medusa

A coloring technique for multiple digits.

45 rule

A rule stating that the sum of the cells in a house must be 45. This is most applicable to Killer Sudoku.

A

Advanced Coloring

An alias used for 3D Medusa.

AIC

An acronym used for Alternating Inference Chain.

Aligned Pair Exclusion

A solving technique that examines the possible configurations for a pair of cells in an intersection.

Aligned Triple Exclusion

A solving technique that examines the possible configurations for a triple of cells in an intersection.

Almost Locked Set

A set of N cells with candidates for N+1 digits.

ALS

An acronym used for Almost Locked Set.

Alternating Inference

See: Inference

Alternating Inference Chain

A chain with alternating strong and weak inference.

APE

An acronym used for Aligned Pair Exclusion.

Ariadne's Thread

A metaphore used for backtracking.

Asymmetric Puzzle

A puzzle is asymmetric if its particular geometric shape is such that rotations or reflections do not result in the same bit pattern of clues. Essentially all of the different digits in the clue are converted into a single bit which is on if the clue for that position was given and off if there is no clue for that position.

ATE

An acronym used for Aligned Triple Exclusion.

Automorphic solution grids

Sometimes all the possible permutations for a solution grid creates duplicate permutations. A permutation which has duplicates is an automorphic solution grid.

B

B/B Plot

A diagram showing strong links.

Backdoor

Placement of a digit from the solution into a cell which reduces the difficulty level of the remaining puzzle.

Backtracking

Return to an earlier position in the solving path, after a contradiction or a dead end has been reached.

Band

An alias used for floor.

Bifurcation

A limited form of Trial & Error where only constraints with 2 remaining candidates are considered.

Big Number

Collective term for given and placed digits, as opposed to little number for pencilmarks.

Bilocal Unit

A unit constraint with only 2 candidates left.

Bivalue Cell

A cell with only 2 candidates left.

Bivalue Universal Grave

A pattern in which all cells have 2 candidates, which causes the Sudoku to have 0 or 2 solutions.

Block

An alias used for box.

Block-Block Interaction

An alias used for Locked Candidates type 2.

Bowman Bingo

A solving technique that does a systematic analysis of all implications for a move.

Box

A group of 9 cells in a 3x3 formation. In a Sudoku grid, boxes usually have a thicker border.

Box Exclusion

A method by which hidden singles can be found by excluding candidates within a box using non-duplication with rows and columns; an alias for Cross-Hatching

Box-Line Reduction

An alias used for Locked Candidates type 2.

Boxcol

The intersection of a box and a column.

Boxrow

The intersection of a box and a row.

Braid Analysis | Braiding

A solving technique that analyzes the way digits are organized in a chute.

Bridge

A weak link that connects 2 clusters in a coloring technique.

Broken Wing + Guardians

A solving technique that uses Turbot Fish patterns and Guardians to make eliminations.

Buddy

An alias used for peer.

BUG

An acronym used for Bivalue Universal Grave.

BUG Lite

A deadly pattern that is between Unique Rectangle and BUG.

C

C

Short for Column.

Cage

Isolated part of the grid in a Killer Sudoku, with the sum of all caged cells in the top left corner.

Candidate

A possible digit that may be placed into a cell. Candidates are represented by pencilmarks.

Candidate elimination cell

A cell that contains a candidate capable of causing a contradiction in a fish pattern.

Canonical form

A standard form of presentation which will identify if two puzzles are scrambled duplicates.

Cell

A small square in a Sudoku grid that can contain a single digit.

Cell Set

An alias used for house.

Chain

A series of linked cells or candidates.

Chute

A part of the grid which is either a floor or a tower.

Claiming

An alias used for Locked Candidates type 2.

Clue

An alias used for given.

Cluster

A group of candidates which are all interconnected with strong links. Used in Coloring.

Column Exclusion

A method by which hidden singles can be found by excluding candidates within a column using non-duplication with rows and boxes; a process similar to Cross-Hatching but within a column.

Color Trap

A coloring technique that eliminates candidates outside a single cluster.

Color Wing

A coloring technique that eliminates candidates using multiple clusters.

Color Wrap

A coloring technique that eliminates candidates inside a single cluster, by means of contradiction.

Coloring

A solving technique that uses colors to identify conjugate pairs. Can be simple (single or one chain) or multi- (two chains). Also described as Magnetism by some authors.

Column

A vertical line in the grid, containing 9 cells.

Common Peer Elimination

If all cells in a particular constraint contains a particular digit as a candidate sees another cell, then that digit can be eliminated from the latter cell. This is a basic technique used in Sudoku Variants with irregular groups of cells.

Conflict

An alias used for contradiction.

Conjugate pair

The last 2 candidates for a particular digit in a single house. Used in Coloring.

Connected pair

A pair of candidates which cannot both be false at the same time.

Constraint

A restriction derived from the rule. Sometimes used as an alias for house.

Contradiction

The state of the grid in which the puzzle no longer complies with the rule.

Cross-Hatching

A method by which hidden singles can be found.

Crossover

A basic technique for Sudoku-X, which looks at eliminating common peers of diagonal cells.

D

Deadly pattern

A pattern that would cause a Sudoku to have multiple solutions.

See also: Unavoidable Set

Diagonal

A group of 9 diagonally connected cells. In Sudoku-X and other variants, the diagonals must also contain digits 1 through 9.

DIC

An acronym used for Double Implication Chain.

Digit

A number between 1 and 9 which can be placed into a cell.

Disjoint Subset

An alias used for subset.

Division

A method by which the cells in the grid are divided into 9 houses. All rows together form a division and so do all columns and all boxes.

Double Implication Chain

A chain that propagates implications in both directions.

E

Eliminate

Removing a candidate from the grid.

Empty Rectangle

A solving technique that uses a strong link and grouped candidates.

Equivalence Marks

A solving technique that uses marks to represent parity instead of colors.

See also: GEM | Graded Equivalence Marks

Equivalent

A term which indicates that a group of candidates must be true or false together.

ER

The acronym for Empty Rectangle.

Error

An alias used for contradiction or conflict.

Eureka | Eureka notation

A notation system for chains and loops.

Exclusion

The process of removing a candidate from the grid

F

Family

An alias for peer

Fillet-O-Fish

See: Finned Fish

Fin

The additional candidate(s) in the box constraint that belongs to a Finned Fish

Finned Fish

A variety of fish that uses an additional box constraint.

Fish

A set of solving techniques that compares sets of unit constraints for a single digit.

Fishy Cycle

A loop formed by candidates for a singe digit.

See also: Turbot Fish

Fixed Digit | Number | Value

An alias used for given.

Floor

A part of the grid containing 3 rows and 3 boxes.

Floor Minlex

The result of Box Canonicalization of a Floor. There are 416 essentially different floor minlexes (minimum lexicographic).

Forced Digit

An alias used for Naked Single.

45 rule

A solving technique in Killer Sudoku making use of the knowledge that the digits in each house add to 45.

Franken Fish

A variety of fish that uses multiple additional box constraints.

Full House

A house with only a single empty cell.

G

Gattai

A puzzle with 2 or more overlapping Sudokus.

GEM

An acronym used for Graded Equivalence Marks

Given | Given Digit | Given Number

A digit placed in a cell by the puzzle setter. It cannot be changed by the player.

Graded Equivalence Marks

A solving technique that uses marks in the pencilmark grid to represent different grades of parity.

See also: Equivalence Marks

Gerechte Design

A special design of a Latin square where the n × n Latin square grid is also divided into n regions, with n cells in each.

Grid

81 cells organized in 9 rows and 9 columns.

Group

An alias used for house, which includes rows, columns and boxes and extra houses for Sudoku Variants.

Guardian

See: Broken Wing

Guess

A digit placed into a cell without a logical reason.

H

Hatching

An alias used for Cross-Hatching.

Hidden Single

A unit constraint with only a single candidate remaining. The digit can be placed in the candidate's cell.

Hidden Subset - Hidden Pair | Hidden Triple | Hidden Quad

A solving technique that isolates a group of cells and digits from the remainder of a house.

Hinge

An alias used for Empty Rectangle.

Hint

An alias used for given. True from the perspective of puzzle makers, but players may have a different concept in mind when asking for a hint.

House

A group of 9 cells that must contain digits 1 through 9. A house can be a row, a column or a box in standard Sudoku.

I

Implication

Effect on a candidate caused by the true or false state of another candidate.

Improper puzzle

An alias used for invalid.

Inference

Interaction between the true or false states of 2 linked candidates.

Initial Digit | Number | Value

An alias used for given.

Innie

In Killer Sudoku, a cell that does not belong to any of the selected cages, but lies inside the tested house(s).

Innie-outie difference

In Killer Sudoku, the difference between the innies and outies may be used to eliminate candidates.

Intersection

A part of the grid where 2 houses share one or more cells. Mostly used for intersections between a box and a row or column.

Intersection Removal

An alias used for Locked Candidates.

Invalid

A Sudoku is invalid if it has no solutions or multiple solutions.

Irreducible puzzle

An alias used for Minimal Puzzle

Isomorphic Puzzles

Two puzzles (puzzles or solution grids) are isomorphic if they can be converted into one another through renumbering or allowed geometrical transformations. There are 6,670,903,752,021,072,936,960 different solution Sudoku grids, but only 5,472,730,538 of these grids are essentially different. Thus there are on average about 1.218 x 10^12 isomorphic Sudoku solutions per unique solution.

J

Jellyfish

A fish of size 4.

Jigsaw Sudoku

A Sudoku Variant that has irregularly shaped regions.

K

K9

A way to reference Sudoku cells, by using a letter for the row and a number for the column.

Killer Sudoku | Killer

A Sudoku variant where givens are replaced by cages labeled with the sum of the digits to be placed inside them.

Killer Convention

In Killer Sudoku, the convention that all digits in each cage is distinct.

Killer Subset

An extension of the Subset technique that is applicable to Killer Sudoku.

Kraken Fish

A fish pattern with indirect connections to a candidate which can be eliminated.

L

Last Digit

The last placement of a digit.

Last Value

: An alias used for Last Digit

Law of Leftovers

A solving technique used for jigsaw Sudokus.

Line

A house that is either a row or a column.

Line-Box Interaction

An alias used for Locked Candidates.

Link

Connection between 2 cells or candidates. See also: Strong link and Weak link.

Little Number

An alias used for pencilmark.

Locked Candidates

A solving technique that uses the intersections between lines and boxes.

Locked Pair

A Naked Pair located in a single intersection.

Locked Triple

A Naked Triple located in a single intersection.

Locked Set

An alias used for subset.

LoL

An acronym used for Law of Leftovers

Loop

A loop of linked cells or candidates.

M

Magic Cell

An alias used for backdoor.

Mark | Markup

An alias used for pencilmark. Also the act of placing them in the grid.

Mathematically equivalent

Puzzles which are essentially the same. By permutating rows, columns and digits, one can be mapped to the other.

Maximal

A puzzle is maximal if it has the maximum number of clues possible, and yet there is a unique solution. In regular Sudoku the maximum number of clues is 81-3 (=78).

MC

An acronym used for Multi-Colors

Mini-col

An alias used for boxcol.

Minimal

A puzzle P is minimal if it has one and only one solution and if every given is necessary. In other words, if any one of the givens is deleted, then the puzzle obtained has more than one solution.

Mini-row

An alias used for boxrow.

Minlex-Puzzle

A puzzle in its canonical form.

Multi-Colors

A coloring technique that uses more than 2 colors, forming multiple clusters.

Mutant Fish

A fish pattern with an odd mixture of rows, columns and boxes.

N

Naked Single

A cell with only a single candidate remaining. It can be placed in the cell.

Naked Subset - Naked Pair | Naked Triple | Naked Quad

A solving technique that isolates a group of cells and digits from the remainder of a house.

Nishio

A limited form of Trial & Error where only candidates for a single digit are considered.

Node

A cell in a chain or loop.

Nonet

An alias used for box. This is the preferred term for Killer Sudoku.

NRC

Acronym used for the identification of a candidate. The letters stand for Number, Row and Column.

Number

An alias used for digit.

O

Opposite | Opposite Parity

Different parities in a single cluster. Only one of them can be true.

See also: Conjugate pair

Orbit

A group of cells which must all contain a given or be empty in order to preserve symmetry.

Outie

In Killer Sudoku, a cell that belongs to one of the selected cages, but lies outside the tested house(s).

P

Parity

Status of a candidate relative to other candidates. Parity is represented by a color or parity mark.

Pattern Overlay Method

A solving technique that examines possible ways to place remaining candidates in the grid.

Peer

A cell that shares a house with another cell.

Pencilmark

The representation of a candidate.

Pincer

One of the end cells in an XY-Wing or XYZ-Wing.

Pinned Digit

An alias used for Hidden Single.

Pivot

The central cell in an XY-Wing or XYZ-Wing.

Placement

Placing a candidate into an unsolved cell, thus changing it to a solved cell.

PM

The acronym for pencilmark.

Pointing Pair

An alias used for Locked Candidates.

POM

An acronym used for Pattern Overlay Method

Possibility

An alias used for candidate.

Proper puzzle

An alias used for valid puzzle.

Puzzle

Any incomplete Sudoku grid which follows the One rule. There may be one or more solutions.

R

R

Short for Row

Random Puzzle

For any given computer program which creates puzzles, a random puzzle essentially is a puzzle which is created chaotically, that is to say so randomly that the created puzzle would never (for all practical purposes) be created again.

Reducible puzzle

An alias used for a valid puzzle.

Region

An alias used for box, or extra houses for Sudoku Variants.

Remaining Possibilities

An alias for candidates.

Remote Pair

A solving technique that combines several Naked Pairs.

Restricted common

A digit which cannot be present in 2 Almost Locked Sets at the same time.

rncn

A way to reference Sudoku cells, by using a row number and a column number.

Rookery

A term for the pattern of 9 cells that a one digit could occupy in a completed Sudoku grid. A k-Rookery would be the pattern of cells that k-digits could occupy.

Row

A horizontal line in the grid, containing 9 cells.

Row Exclusion

A method by which hidden singles can be found by excluding candidates within a row using non-duplication with columns and boxes; process similar to Cross-Hatching but within a row.

Row Minlex

A particular canonical form which represents the set of isomorphic solution grids. It has the first row as the digits 1-9 in sequence, hence the name (see wiki page for more details).

While there are 416 minimal lexicographical configurations for the first 3 rows using 1-9 in box 1, there are over 35000 with 1-9 in row 1.

Row/Column-Block Interaction

An alias used for Locked Candidates type 1.

Rule

The one rule of Sudoku. Complete the grid in such a way that each row, column and box contain digits 1 through 9.

S

Samunamupure

Alias for Killer Sudoku. It is the Japanese form of "sum number"

Samurai

An variant with 5 overlapping Sudokus in an X pattern.

Sashimi Fish

A variety of fish where not all defining candidates are present.

SC

An acronym used for Simple Colors

Scramble

Create a mathematically equivalent grid from a given grid.

Seafood | Sealife

Aliases used for Fish.

See

Two cells see each other if they belong to the same constraint (row, column or box).

Sector

An alias used for house.

Segment

An alias used for intersection.

Set

An alias used for house.

Shaolin

A Gattai-25 Sudoku variant with 36 overlapping boxes.

Shi Doku

A NxN Sudoku variant played with a 2x2 box. Thus the grid is 4x4 and the digits 1-4 can be used.

Simple Colors

A coloring technique that is limited to 2 colors, using a single cluster.

Single

Elementary solving technique, using the fact that only a single candidate is left for a constraint.

Skinny Fish

See: Sashimi Fish

Skyscraper

A particular variety of Turbot Fish.

Solution

The answer to the puzzle. A grid where each cell contains a digit between 1 and 9 without violating the rule.

Solving path

A list of steps that shows how a particular puzzle is solved.

Square

An alias used for cell.

Squirmbag

A fish of size 5.

SSTS

Simple Sudoku Technique Set. The set of techniques supported by the Simple Sudoku program.

Stack

An alias used for tower, sometimes used as an alias for boxcol.

Strong Inference

see: Inference

Strong link

A link caused by a bivalue cell or bilocal unit.

Subgrid

An alias used for box.

Subset

A set formed by N cells and N digits, which are or can be isolated from the remaining cells and digits in a house.

Usually refers to Naked Subset or Hidden Subset.

Sudoku

A puzzle defined by a grid with givens and a unique solution, which can be found by completing the grid according to the rule.

Sudoku-X

A Sudoku variant where every diagonal must also contain the digits 1 to 9.

Sumo

A Gattai-13 Sudoku variant with 16 overlapping boxes.

Swordfish

A fish of size 3.

Symbol

An alias used for digit, especially when puzzle makers use alternative characters or pictures.

Symmetrical Puzzle

A puzzle is symmetric if its particular geometric shape is such that rotations or reflections result in the same bit pattern of clues. Essentially all of the different digits in the clue are converted into a single bit which is on if the clue for that position was given and off if there is no clue for that position.

T

Tabling

A form of Trial & Error where all candidates are tried.

Target Cell

A cell selected for analysis of remaining possibilities, to discover Naked Singles. These can also be found with pencilmarks.

Target Number

A number selected for analysis using techniques that seek to find the location of the number within a house.

Tower

A part of the grid that contains 3 columns and 3 boxes.

Traveling Pairs

An alias used for Braid Analysis.

Trebor's Tables

An alias used for tabling.

Trial & Error

A solving technique that eliminates candidates by proving that their placement leads to a contradiction.

Turbot Fish

A solving technique that uses loops of odd length for a single digit.

U

Unavoidable Set

A group of cells in the solution grid that requires at least one given.

Unique Rectangle

An Unavoidable Set with a rectangular shape.

See also: Deadly pattern

Unique Solution

The assumption that a Sudoku has a single solution. Subject of debate, especially when used in solving techniques.

Uniqueness Test

A series of solving techniques in which the solver avoids Unique Rectangles.

Unit

An alias used for house.

UR

An acronym used for Unique Rectangle

V

Valid

A Sudoku is valid if and only if it has a unique solution.

Value

Commonly used as an alias for digit, but in the context of a cell, its given or deduced value. An empty cell has no value, but there should be a value for it in the solution.

Veracity

See: Verity.

Verity

A statement which is true for all alternatives in a limited set.

W

Walkthrough | Walkthru

An alias used for Solving path.

Weak Inference

see: Inference

Weak link

A link between 2 peers or 2 candidates in a single cell.

Windoku | NRC-Sudoku | Hypersudoku | Sudoku Hyper

A Sudoku variant with 4 extra "windows", and each window must also contain the digits 1 to 9.

WXYZ-Wing

An extension of XYZ-Wing to 4 cells.

X

X-Cycle

A loop containing candidates for a single digit.

See also: Fishy Cycle

X-Wing

A fish of size 2.

XY-Chain

A chain of cells with 2 candidates each.

XY-Wing

A short XY-Chain with only 3 cells.

XYZ-Wing

A variation of XY-Wing that has an extra candidate in the pivot cell.

XYZW-Wing

Alias for WXYZ-Wing.

Y

Y-Wing

An alias used for XY-Wing.

External links

Other Sudoku Glossaries

• Glossary at www.suocue.net by Ruud van der Werf

• Glossary of Sudoku by Wikipedia®

• Lexicon of Sudoku at Sudoku Players Forum (http://www.playr.co.uk/sudoku)

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