# Terminology

From

Jump to navigationJump to search**Sudopedia**, the Free Sudoku Reference GuideThe 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

- 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.

- 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.

- Claiming
- An alias used for Locked Candidates type 2.

- Clue
- An alias used for given.

- 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.

- 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

- Jigsaw Sudoku
- A Sudoku Variant that has irregularly shaped regions.

## K

- 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.

## O

- Opposite | Opposite Parity
- Different parities in a single cluster. Only one of them can be true.
*See also:*Conjugate pair

- 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.

- Pinned Digit
- An alias used for Hidden Single.

- 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

- 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.

- 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.

- Sector
- An alias used for house.

- Segment
- An alias used for intersection.

- Set
- An alias used for house.

- 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.

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

- 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.

- 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.

- 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.

## X

- X-Cycle
- A loop containing candidates for a single digit.
*See also:*Fishy Cycle

- XY-Chain
- A chain of cells with 2 candidates each.

- 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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