Mirrored from Sudopedia, the Free Sudoku Reference Guide

# 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

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.
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
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## B

B/B Plot
Backdoor
Placement of a digit from the solution into a cell which reduces the difficulty level of the remaining puzzle.
Backtracking
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

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 Variations with irregular groups of cells.
Conflict
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.
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

A pattern that would cause a Sudoku to have multiple solutions.
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.
Equivalent
A term which indicates that a group of candidates must be true or false together.
ER
The acronym for Empty Rectangle.
Error
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.
Fixed Digit | Number | Value
An alias used for given.
Floor
A part of the grid containing 3 rows and 3 boxes.
Floor Minlex
A minlex of a floor. There are 416 possible floor minlexes.
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.
A solving technique that uses marks in the pencilmark grid to represent different grades of parity.
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.
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.
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 unique. 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
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 | Killer Sudoku
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 puzzles.
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.
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 a game on a NxN grid, then the maximum number of clues is N^2-3.
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
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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.
Number
An alias used for digit.

## O

Opposite | Opposite Parity
Different parities in a single cluster. Only one of them can be true.
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
Any incomplete Sudoku grid which follows the One rule. There may be one or more solutions.

## R

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 Proper puzzle
Region
An alias used for box.
Remaining Possibilities
An alias for candidate
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 row minlex is 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).
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
A link caused by a bivalue cell or bilocal unit.
Subgrid
An alias used for box.
Subset
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.
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.
Sumo
A Gattai-13 Sudoku variant with 16 overlapping boxes.
Swordfish
A fish of size 3.
Symbol
An alias used for digit.
Symmetric 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.
Target Number
A number selected for analysis using techniques that seek to find the location of the number within a group.
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.
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.

## V

Valid
A Sudoku is valid if and only if it has a unique solution.
Value
An alias used for digit.
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
A link between 2 peers or 2 candidates in a single cell.
Windoku | NRC-Sudoku
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.
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.