Sudopedia - User contributions [en]

Box Canonicalization of a Grid

2021-10-29T12:29:55Z

127.0.0.1:

The steps below are used for canonicalization of solution grids. For canonicalization of puzzle grids, put number 0 in all the empty cells, and compare the numeric value per row or column.

== 1. Select the [[chute]] with the lowest canonical value ==

Use [[Box Canonicalization of a Floor]] on the 3 [[floor]]s and the 3 [[tower]]s.

The best way to do this is to use rotations and floor-swapping to put the chute to test in the position of the top floor.
When executing box canonicalization, relabel all digits in the grid and swap whole columns and towers when needed. This keeps the 2 lower floors in sync with the floor being tested.

== 2. Order the rows of the lower 2 floors for the best result from the previous step ==

Order rows 4-6 on by the value in column 1.

Order rows 7-9 on by the value in column 1.

Order floors 2 and 3 by the value in '''r4c1''' and '''r7c1'''

{{stub}}

Box Canonicalization of a Grid

2021-10-29T12:27:29Z

127.0.0.1: Created page with "== 1. Select the chute with the lowest canonical value == Use Box Canonicalization of a Floor on the 3 floors and the 3 towers. The best way to do this is to..."

== 1. Select the [[chute]] with the lowest canonical value ==

Use [[Box Canonicalization of a Floor]] on the 3 [[floor]]s and the 3 [[tower]]s.

The best way to do this is to use rotations and floor-swapping to put the chute to test in the position of the top floor.
When executing box canonicalization, relabel all digits in the grid and swap whole columns and towers when needed. This keeps the 2 lower floors in sync with the floor being tested.

== 2. Order the rows of the lower 2 floors for the best result from the previous step ==

Order rows 4-6 on by the value in column 1.

Order rows 7-9 on by the value in column 1.

Order floors 2 and 3 by the value in '''r4c1''' and '''r7c1'''

{{stub}}

Box Canonicalization of a Floor

2021-10-29T12:10:08Z

127.0.0.1: /* Steps to normalize a starting permutation */

A [[floor|band]] of 3 rows from a Sudoku solution [[grid]] can be modified to its minimum lexicographic equivalent.

For a Sudoku grid with only [[given]]s a different algorithm is used, to account for missing [[digit]]s.
== Steps to find all 108 starting permutations ==

* Try each of the 3 [[box]]es as box 1. (3 permutations)
* Permute the 3 [[row]]s. (6 permutations)
* Permute the 3 [[column]]s in box 1. (6 permutations)

== Steps to normalize a starting permutation==

* Relabel the numbers so that box 1 reads:
123
456
789
* Sort box 2 and 3 so that box 2 contains 4 in the top row.
* Sort the [[column]]s in box 2 so that r1c4=4, r1c5 < r1c6
* Sort the columns in box 3 so that r1c7 < r1c8 < r1c9.

=== Notes ===

There are a total of 36288 different configurations for a normalized floor, 416 of which are unique.

== Compare results ==
* The numbers to compare can be found in cells a-q below:
1 2 3 | 4 a b | c d e
4 5 6 | f g h | i j k
7 8 9 | l m n | o p q
* Of the 108 starting permutations, choose the one with the lowest numerical value
* For all possible configurations of the 27 numbers in a band, there are only 416 essentially different ones.

Terminology

2021-10-29T11:54:15Z

127.0.0.1: /* U */

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.
__NOTOC__

== 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 [[backtrack]]ing.

; [[Asymmetrical|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 link]]s.

; [[Backdoor]]
: Placement of a digit from the solution into a cell which reduces the difficulty level of the remaining puzzle.

; [[Backtrack]]ing
: 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 [[pencilmark]]s.

; [[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]] + [[Guardian]]s
: 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 [[pencilmark]]s.

; [[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 [[scramble]]d 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]]
: 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|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 [[row]]s, [[column]]s and [[box]]es and extra houses for [[Sudoku Variations|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 [[cage]]s, but lies inside the tested [[house]](s).

; [[Innie-outie difference]]
: In [[Killer]] Sudoku, the difference between the [[innie]]s and [[outie]]s 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]]
: A Sudoku variant that has irregularly shaped regions.

== K ==
; [[K9]]
: A way to reference [[Sudoku]] [[cell]]s, 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]].

; [[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|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.
: ''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 [[cage]]s, 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 ==

; 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 [[house]]s for [[Sudoku Variations]].

; Remaining Possibilities
: An alias for [[candidate]]s.

; [[Remote Pairs|Remote Pair]]
: A solving technique that combines several [[Naked Pair]]s.

; [[Restricted common]]
: A digit which cannot be present in 2 [[Almost Locked Set]]s at the same time.

; [[rncn]]
: A way to reference [[Sudoku]] [[cell]]s, 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 [[cell]]s ''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 [[box]]es.

; [[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 [[digit]]s 1 to 9.

; [[Sumo]]
: A [[Gattai]]-13 [[Sudoku]] variant with 16 overlapping [[box]]es.

; [[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 Single]]s. These can also be found with [[pencilmark]]s.

; 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 Rectangle]]s.

; [[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 [[digit]]s 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

* [http://www.sudocue.net/glossary.php Glossary at www.suocue.net] by ''Ruud van der Werf''

* [http://en.wikipedia.org/wiki/List_of_Sudoku_terms_and_jargon Glossary of Sudoku] by Wikipedia®

* [http://www.playr.co.uk/sudoku/dictionary.php?letter=a Lexicon of Sudoku] at Sudoku Players Forum (http://www.playr.co.uk/sudoku)

{{incomplete}}

UR

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#REDIRECT:[[Unique Rectangle]]

Terminology

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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.
__NOTOC__

== 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 [[backtrack]]ing.

; [[Asymmetrical|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 link]]s.

; [[Backdoor]]
: Placement of a digit from the solution into a cell which reduces the difficulty level of the remaining puzzle.

; [[Backtrack]]ing
: 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 [[pencilmark]]s.

; [[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]] + [[Guardian]]s
: 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 [[pencilmark]]s.

; [[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 [[scramble]]d 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]]
: 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|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 [[row]]s, [[column]]s and [[box]]es and extra houses for [[Sudoku Variations|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 [[cage]]s, but lies inside the tested [[house]](s).

; [[Innie-outie difference]]
: In [[Killer]] Sudoku, the difference between the [[innie]]s and [[outie]]s 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]]
: A Sudoku variant that has irregularly shaped regions.

== K ==
; [[K9]]
: A way to reference [[Sudoku]] [[cell]]s, 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]].

; [[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|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.
: ''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 [[cage]]s, 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 ==

; 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 [[house]]s for [[Sudoku Variations]].

; Remaining Possibilities
: An alias for [[candidate]]s.

; [[Remote Pairs|Remote Pair]]
: A solving technique that combines several [[Naked Pair]]s.

; [[Restricted common]]
: A digit which cannot be present in 2 [[Almost Locked Set]]s at the same time.

; [[rncn]]
: A way to reference [[Sudoku]] [[cell]]s, 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 [[cell]]s ''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 [[box]]es.

; [[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 [[digit]]s 1 to 9.

; [[Sumo]]
: A [[Gattai]]-13 [[Sudoku]] variant with 16 overlapping [[box]]es.

; [[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 Single]]s. These can also be found with [[pencilmark]]s.

; 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 Rectangle]]s.

; [[Unit]]
: An alias used for [[house]].

== 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 [[digit]]s 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

* [http://www.sudocue.net/glossary.php Glossary at www.suocue.net] by ''Ruud van der Werf''

* [http://en.wikipedia.org/wiki/List_of_Sudoku_terms_and_jargon Glossary of Sudoku] by Wikipedia®

* [http://www.playr.co.uk/sudoku/dictionary.php?letter=a Lexicon of Sudoku] at Sudoku Players Forum (http://www.playr.co.uk/sudoku)

{{incomplete}}

Terminology

2021-10-29T11:51:09Z

127.0.0.1: /* S */

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.
__NOTOC__

== 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 [[backtrack]]ing.

; [[Asymmetrical|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 link]]s.

; [[Backdoor]]
: Placement of a digit from the solution into a cell which reduces the difficulty level of the remaining puzzle.

; [[Backtrack]]ing
: 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 [[pencilmark]]s.

; [[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]] + [[Guardian]]s
: 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 [[pencilmark]]s.

; [[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 [[scramble]]d 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]]
: 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|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 [[row]]s, [[column]]s and [[box]]es and extra houses for [[Sudoku Variations|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 [[cage]]s, but lies inside the tested [[house]](s).

; [[Innie-outie difference]]
: In [[Killer]] Sudoku, the difference between the [[innie]]s and [[outie]]s 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]]
: A Sudoku variant that has irregularly shaped regions.

== K ==
; [[K9]]
: A way to reference [[Sudoku]] [[cell]]s, 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]].

; [[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|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.
: ''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 [[cage]]s, 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 ==

; 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 [[house]]s for [[Sudoku Variations]].

; Remaining Possibilities
: An alias for [[candidate]]s.

; [[Remote Pairs|Remote Pair]]
: A solving technique that combines several [[Naked Pair]]s.

; [[Restricted common]]
: A digit which cannot be present in 2 [[Almost Locked Set]]s at the same time.

; [[rncn]]
: A way to reference [[Sudoku]] [[cell]]s, 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 [[cell]]s ''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 [[box]]es.

; [[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 [[digit]]s 1 to 9.

; [[Sumo]]
: A [[Gattai]]-13 [[Sudoku]] variant with 16 overlapping [[box]]es.

; [[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 Single]]s. These can also be found with [[pencilmark]]s.

; 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 Rectangle]]s.

; [[Unit]]
: An alias used for [[house]].

== 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 [[digit]]s 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

* [http://www.sudocue.net/glossary.php Glossary at www.suocue.net] by ''Ruud van der Werf''

* [http://en.wikipedia.org/wiki/List_of_Sudoku_terms_and_jargon Glossary of Sudoku] by Wikipedia®

* [http://www.playr.co.uk/sudoku/dictionary.php?letter=a Lexicon of Sudoku] at Sudoku Players Forum (http://www.playr.co.uk/sudoku)

{{incomplete}}

SC

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#REDIRECT:[[Simple Colors]]

Terminology

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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.
__NOTOC__

== 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 [[backtrack]]ing.

; [[Asymmetrical|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 link]]s.

; [[Backdoor]]
: Placement of a digit from the solution into a cell which reduces the difficulty level of the remaining puzzle.

; [[Backtrack]]ing
: 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 [[pencilmark]]s.

; [[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]] + [[Guardian]]s
: 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 [[pencilmark]]s.

; [[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 [[scramble]]d 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]]
: 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|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 [[row]]s, [[column]]s and [[box]]es and extra houses for [[Sudoku Variations|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 [[cage]]s, but lies inside the tested [[house]](s).

; [[Innie-outie difference]]
: In [[Killer]] Sudoku, the difference between the [[innie]]s and [[outie]]s 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]]
: A Sudoku variant that has irregularly shaped regions.

== K ==
; [[K9]]
: A way to reference [[Sudoku]] [[cell]]s, 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]].

; [[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|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.
: ''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 [[cage]]s, 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 ==

; 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 [[house]]s for [[Sudoku Variations]].

; Remaining Possibilities
: An alias for [[candidate]]s.

; [[Remote Pairs|Remote Pair]]
: A solving technique that combines several [[Naked Pair]]s.

; [[Restricted common]]
: A digit which cannot be present in 2 [[Almost Locked Set]]s at the same time.

; [[rncn]]
: A way to reference [[Sudoku]] [[cell]]s, 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 [[cell]]s ''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 [[box]]es.

; [[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 [[digit]]s 1 to 9.

; [[Sumo]]
: A [[Gattai]]-13 [[Sudoku]] variant with 16 overlapping [[box]]es.

; [[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 Single]]s. These can also be found with [[pencilmark]]s.

; 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 Rectangle]]s.

; [[Unit]]
: An alias used for [[house]].

== 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 [[digit]]s 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

* [http://www.sudocue.net/glossary.php Glossary at www.suocue.net] by ''Ruud van der Werf''

* [http://en.wikipedia.org/wiki/List_of_Sudoku_terms_and_jargon Glossary of Sudoku] by Wikipedia®

* [http://www.playr.co.uk/sudoku/dictionary.php?letter=a Lexicon of Sudoku] at Sudoku Players Forum (http://www.playr.co.uk/sudoku)

{{incomplete}}

POM

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#REDIRECT:[[Pattern Overlay Method]]

PM

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#REDIRECT:[[pencilmark]]

Terminology

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127.0.0.1: /* M */

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.
__NOTOC__

== 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 [[backtrack]]ing.

; [[Asymmetrical|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 link]]s.

; [[Backdoor]]
: Placement of a digit from the solution into a cell which reduces the difficulty level of the remaining puzzle.

; [[Backtrack]]ing
: 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 [[pencilmark]]s.

; [[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]] + [[Guardian]]s
: 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 [[pencilmark]]s.

; [[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 [[scramble]]d 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]]
: 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|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 [[row]]s, [[column]]s and [[box]]es and extra houses for [[Sudoku Variations|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 [[cage]]s, but lies inside the tested [[house]](s).

; [[Innie-outie difference]]
: In [[Killer]] Sudoku, the difference between the [[innie]]s and [[outie]]s 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]]
: A Sudoku variant that has irregularly shaped regions.

== K ==
; [[K9]]
: A way to reference [[Sudoku]] [[cell]]s, 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]].

; [[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|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.
: ''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 [[cage]]s, 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 ==

; 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 [[house]]s for [[Sudoku Variations]].

; Remaining Possibilities
: An alias for [[candidate]]s.

; [[Remote Pairs|Remote Pair]]
: A solving technique that combines several [[Naked Pair]]s.

; [[Restricted common]]
: A digit which cannot be present in 2 [[Almost Locked Set]]s at the same time.

; [[rncn]]
: A way to reference [[Sudoku]] [[cell]]s, 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 [[cell]]s ''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 [[box]]es.

; [[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 [[digit]]s 1 to 9.

; [[Sumo]]
: A [[Gattai]]-13 [[Sudoku]] variant with 16 overlapping [[box]]es.

; [[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 Single]]s. These can also be found with [[pencilmark]]s.

; 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 Rectangle]]s.

; [[Unit]]
: An alias used for [[house]].

== 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 [[digit]]s 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

* [http://www.sudocue.net/glossary.php Glossary at www.suocue.net] by ''Ruud van der Werf''

* [http://en.wikipedia.org/wiki/List_of_Sudoku_terms_and_jargon Glossary of Sudoku] by Wikipedia®

* [http://www.playr.co.uk/sudoku/dictionary.php?letter=a Lexicon of Sudoku] at Sudoku Players Forum (http://www.playr.co.uk/sudoku)

{{incomplete}}

MC

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#REDIRECT:[[Multi-Colors]]

Terminology

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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.
__NOTOC__

== 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 [[backtrack]]ing.

; [[Asymmetrical|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 link]]s.

; [[Backdoor]]
: Placement of a digit from the solution into a cell which reduces the difficulty level of the remaining puzzle.

; [[Backtrack]]ing
: 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 [[pencilmark]]s.

; [[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]] + [[Guardian]]s
: 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 [[pencilmark]]s.

; [[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 [[scramble]]d 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]]
: 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|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 [[row]]s, [[column]]s and [[box]]es and extra houses for [[Sudoku Variations|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 [[cage]]s, but lies inside the tested [[house]](s).

; [[Innie-outie difference]]
: In [[Killer]] Sudoku, the difference between the [[innie]]s and [[outie]]s 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]]
: A Sudoku variant that has irregularly shaped regions.

== K ==
; [[K9]]
: A way to reference [[Sudoku]] [[cell]]s, 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]].

; [[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|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.
: ''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 [[cage]]s, 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 ==

; 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 [[house]]s for [[Sudoku Variations]].

; Remaining Possibilities
: An alias for [[candidate]]s.

; [[Remote Pairs|Remote Pair]]
: A solving technique that combines several [[Naked Pair]]s.

; [[Restricted common]]
: A digit which cannot be present in 2 [[Almost Locked Set]]s at the same time.

; [[rncn]]
: A way to reference [[Sudoku]] [[cell]]s, 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 [[cell]]s ''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 [[box]]es.

; [[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 [[digit]]s 1 to 9.

; [[Sumo]]
: A [[Gattai]]-13 [[Sudoku]] variant with 16 overlapping [[box]]es.

; [[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 Single]]s. These can also be found with [[pencilmark]]s.

; 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 Rectangle]]s.

; [[Unit]]
: An alias used for [[house]].

== 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 [[digit]]s 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

* [http://www.sudocue.net/glossary.php Glossary at www.suocue.net] by ''Ruud van der Werf''

* [http://en.wikipedia.org/wiki/List_of_Sudoku_terms_and_jargon Glossary of Sudoku] by Wikipedia®

* [http://www.playr.co.uk/sudoku/dictionary.php?letter=a Lexicon of Sudoku] at Sudoku Players Forum (http://www.playr.co.uk/sudoku)

{{incomplete}}

LoL

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#REDIRECT:[[Law of Leftovers]]

Terminology

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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.
__NOTOC__

== 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 [[backtrack]]ing.

; [[Asymmetrical|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 link]]s.

; [[Backdoor]]
: Placement of a digit from the solution into a cell which reduces the difficulty level of the remaining puzzle.

; [[Backtrack]]ing
: 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 [[pencilmark]]s.

; [[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]] + [[Guardian]]s
: 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 [[pencilmark]]s.

; [[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 [[scramble]]d 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]]
: 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|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 [[row]]s, [[column]]s and [[box]]es and extra houses for [[Sudoku Variations|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 [[cage]]s, but lies inside the tested [[house]](s).

; [[Innie-outie difference]]
: In [[Killer]] Sudoku, the difference between the [[innie]]s and [[outie]]s 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]]
: A Sudoku variant that has irregularly shaped regions.

== K ==
; [[K9]]
: A way to reference [[Sudoku]] [[cell]]s, 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]].

; [[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|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.
: ''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 [[cage]]s, 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 ==

; 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 [[house]]s for [[Sudoku Variations]].

; Remaining Possibilities
: An alias for [[candidate]]s.

; [[Remote Pairs|Remote Pair]]
: A solving technique that combines several [[Naked Pair]]s.

; [[Restricted common]]
: A digit which cannot be present in 2 [[Almost Locked Set]]s at the same time.

; [[rncn]]
: A way to reference [[Sudoku]] [[cell]]s, 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 [[cell]]s ''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 [[box]]es.

; [[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 [[digit]]s 1 to 9.

; [[Sumo]]
: A [[Gattai]]-13 [[Sudoku]] variant with 16 overlapping [[box]]es.

; [[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 Single]]s. These can also be found with [[pencilmark]]s.

; 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 Rectangle]]s.

; [[Unit]]
: An alias used for [[house]].

== 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 [[digit]]s 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

* [http://www.sudocue.net/glossary.php Glossary at www.suocue.net] by ''Ruud van der Werf''

* [http://en.wikipedia.org/wiki/List_of_Sudoku_terms_and_jargon Glossary of Sudoku] by Wikipedia®

* [http://www.playr.co.uk/sudoku/dictionary.php?letter=a Lexicon of Sudoku] at Sudoku Players Forum (http://www.playr.co.uk/sudoku)

{{incomplete}}

DIC

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#REDIRECT:[[Double Implication Chain]]

Category:Acronyms

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Grouped Turbot Fish

2021-10-29T11:39:35Z

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The '''Grouped Turbot Fish''' [[solving technique]] extends the definition of a regular [[Turbot Fish]], by allowing [[node]]s in the [[loop]] which are '''groups''' of [[candidate]]s instead of single candidates.

In fact, the Grouped Turbot Fish only covers a small area of [[Grouped Coloring]], since it is limited to [[discontinuous]] loops with 5 nodes. The [[Empty Rectangle]] is a pattern which often appears in a Grouped Turbot Fish.

== How it works ==

When all members of a group of candidates can [[see]] all members of another group, these groups are [[link]]ed. The only way this can happen is when all candidates in both groups belong to a single [[house]]. The groups have a [[strong link]] if no other candidates exist in that house, otherwise they have a [[weak link]]. To be useful in a Turbot Fish, each group must be linked at both ends. This limits the number of places where groups can be found. They must be located in an [[intersection]] to be able to interact with 2 houses.

The following diagram shows a '''Grouped Turbot Fish''':

[[Image:Grouped turbot.png]]

The Turbot Fish has two weakly linked groups ('''r46c5''' and '''r5c46'''). The cell '''r5c5''' cannot hold candidate X otherwise there is no weak link between r46c5 and r5c46. Any of the cells in r46c5 or r5c46 may miss the candidate X. It can be described with the following [[loop]]:
(X): r2c2-r2c5=r46c5-r5c46=r5c2-r2c2 => r2c2<>X

A more common variant is better known as [[Empty Rectangle]]. Here is a diagram:

[[Image:Empty rectangle.png]]

This Turbot Fish has two strongly linked groups ('''r46c5''' and '''r5c46'''). The cell '''r5c5''' may also hold candidate X, since this still establish a strong link between r456c5 and r5c456. Any of the cells in r46c5 or r5c46 may miss the candidate X. Here is the loop notation:
(X): r5c2-r2c2=r2c5-r46c5=r5c46-r5c2 => r5c2<>X

== Grouped Turbot Chain ==

Larger Turbot Fish are also known as [[Fishy Cycle]]s. This implies that there must also be a Grouped Turbot Chain. These do exist, but they are more difficult to recognize as a pattern.

Here is an example:

[[Image:grouped turbot cycle1.png]]

5 groups and 2 standalone candidates are included in this pattern. Here is the written chain:
(X): r13c46-r2c456=r2c8-r8c8=r8c46-r79c5=r123c5-r13c46 => r13c46<>X
Notice that groups may overlap when it does not disrupt the loop. r2c456 and r123c5 can safely overlap, but the groups in box 8 cannot.

[[Category:Solving Techniques]]

Almost Unique Rectangles

2021-10-29T11:30:57Z

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An '''Almost Unique Rectangle''' or '''AUR''' is a set of four cells populated in such a way that if one or two of them does not have a specific candidate 'x', then those four cells allow a [[Uniqueness Test]].

=== Example 1 ===

[[Image:aur-1.png]]

As one can see, the 4 cells in r13c25 would form a [[deadly pattern]] for digits 1 and 2 if it were not for the extra candidates for [[digit]] 8 and 9.

If the candidates for digit 8 were not present, it would form a '''Uniqueness Test 2''', allowing us to eliminate all other candidates for digit 8 in row 1.

If the candidates for digit 9 were not present, it would form a '''Uniqueness Test 2''', allowing us to eliminate all other candidates for digit 9 in row 3.

In its present form, we can make no direct eliminations, but can use this pattern in a nice loop, using the strong link between digit 8 in r1c25 and digit 9 in r3c25.

The result is this [[Nice Loop]] fragment:
[r1c2|r1c5]=8|9=[r3c2|r3c5]

=== Example 2 ===

To show that this also works with 1 extra candidate at both sides:

[[Image:aur-2.png]]

If the candidate for digit 8 were not present, it would form a '''Uniqueness Test 1''', allowing us to eliminate all candidates for digit 9 for all [[peer]]s of '''r3c2'''.

If the candidate for digit 9 were not present, it would form a '''Uniqueness Test 1''', allowing us to eliminate all candidates for digit 8 for all peers of '''r1c5'''.

In its present form, we can make no direct eliminations, but can use this pattern in a nice loop, using the strong link between digit 8 in r1c5 and digit 9 in r3c2.

The result is this [[Nice Loop]] fragment:
[r1c5]=8|9=[r3c2]

== External Links ==

* [http://forum.enjoysudoku.com/almost-unique-rectangles-description-and-use-in-nice-loops-t2751.html almost-unique-rectangles-description-and-use-in-nice-loops] on the new Sudoku Player's forum.

[[Category:Uniqueness]]

Almost Unique Rectangles

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File:Aur-2.png

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Grouped Coloring

2021-10-29T08:48:39Z

127.0.0.1: Created page with "'''Grouped Coloring''' is a single digit solving technique which allows multiple candidates to the same digit to be included in a coloring pattern. {{grid|2=A..."

'''Grouped Coloring''' is a single [[digit]] [[solving technique]] which allows multiple [[candidate]]s to the same digit to be included in a [[coloring]] pattern.

{{grid|2=A|3=A|4=/|5=/|6=/|7=B|8=B|10=B|11=/|12=/|16=/|17=/|18=A|19=B|20=/|21=/|25=/|26=/|27=A|28=/|37=/|46=/|55=A|56=/|57=/|64=A|65=/|66=/|74=B|75=B|81=X}}

;Specific patterns for grouped coloring
* [[Empty Rectangle]]
* [[Grouped Turbot Fish]]

[[Category:Solving Techniques]]
{{stub}}

Killer Triple

2021-10-29T08:07:58Z

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A '''Killer Triple''' is a [[Killer Subset]] of size 3.

== How it works ==
Here is a simple example:

[[Image:KNTriplet1.png]]

The cage 8/2 in R9C56 = {17|26|35} must include one of {123}. It forms a naked triple on {123} with the cells in R9C12 = {123}. Therefore {123} of R9 is locked in R9C1256 and can be eliminated from the rest of R9, which means R9C9 = 4.

Here is another example of a killer triple:

[[Image:KNTriplet2.png]]

The cage 9/3 in R1C123 = {126|135|234} must include either {12} or {13} or {23}. It must include at least two digits out of {123}. It forms a naked triple on {123} with R1C4 = {123}. Therefore {123} of R1 is locked in R1C1234 and can be eliminated from the rest of R1.

== See Also: ==
* [[Killer| Killer Sudoku]]
* [[Killer Subset]]
* [[Killer Pair]]

[[Category:Solving Techniques]]
[[Category:Killer Sudoku]]

Killer Pair

2021-10-29T08:07:39Z

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A '''Killer Pair''' is a [[Killer Subset]] of size 2.

=== Naked Killer Pair ===

[[Image:Killer_pair_demo.gif]]

The cells R78C6 = 6 = {15} or {24}, i.e. they must contain either 1 or 2. They therefore form a naked pair in conjunction with the {12} in R3C6. This allows us to eliminate {12} for the rest of column 6, which means that R4C6 = 3.

=== Hidden Killer Pair ===

[[Image:KHPair.png]]

The candidates {12} of R5 are locked either in the cage 5/2 in R5C12 or in the cage 9/2 in R5C89. Neither the cage 5/2 nor the cage 9/2 may include both 1 and 2. Therefore each of these cages must include one of 1 or 2, which means the cage 9/2 in R5C89 = [81] or {27} and cannot have {36} nor {45}.

== See Also: ==
* [[Killer| Killer Sudoku]]
* [[Killer Subset]]
* [[Killer Triple]]

[[Category:Solving Techniques]]
[[Category:Killer Sudoku]]

Killer Subset

2021-10-29T08:07:13Z

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A '''Killer Subset''' is a variation of [[Naked Subset]]s and [[Hidden Subset]]s that can sometimes be found in [[Killer]] puzzles. The simplest Killer Subsets are found in many puzzles, and identifying them is a basic technique; the most complex Killer Subsets (containing 4 or 5 numbers) are comparatively rare, and are more typically found in the most difficult puzzles.

Killer Subsets are formed when a set of '''X''' [[digit]]s can be shown to have exactly '''X''' [[candidate]]s in a range of '''Y''' [[cell]]s in a [[house]] (where '''Y''' is greater than '''X'''). In such a case, the candidates in the set may be eliminated from all cells outside of '''Y'''.

Typically – but not always – the subset of candidates will be a contiguous range (for instance, {789} or {56}).

In ordinary Sudoku, subsets may be "[[Naked Subset|naked]]" or "[[Hidden Subset|hidden]]"; and in fact every Naked Subset has its complementary Hidden Subset and vice versa. An identical logic applies to Killer Subsets, too, in that complementary logic can be used to make the same eliminations; however, the "naked/hidden" distinction is less accurate as a description, since often both versions of the logic are hard to spot ("hidden" among the candidates).

== Names for each size ==
'''[[Killer Pair]]'''
: Size 2
'''[[Killer Triple]]'''
: Size 3
'''Killer Quad'''
: Size 4
'''Killer Quint'''
: Size 5
== How it works ==
Here is a simple example:

[[Image:Killer_pair_demo.gif]]

The cells R78C6 = 6 = {15} or {24}, i.e. they must contain either 1 or 2. They therefore form a naked pair in conjunction with the {12} in R3C6. This allows us to eliminate {12} for the rest of column 6, which means that R4C6 = 3.

Here is an example of a killer triple:

[[Image:KNTriplet1.png]]

The cage 8/2 in R9C56 = {17|26|35} must include one of {123}. It forms a naked triple on {123} with the cells in R9C12 = {123}. Therefore {123} of R9 is locked in R9C1256 and can be eliminated from the rest of R9, which means R9C9 = 4.

Here is another example of a killer triple:

[[Image:KNTriplet2.png]]

The cage 9/3 in R1C123 = {126|135|234} must include either {12} or {13} or {23}. It must include at least two digits out of {123}. It forms a naked triple on {123} with R1C4 = {123}. Therefore {123} of R1 is locked in R1C1234 and can be eliminated from the rest of R1.

Here is an example of a killer hidden pair:

[[Image:KHPair.png]]

The candidates {12} of R5 are locked either in the cage 5/2 in R5C12 or in the cage 9/2 in R5C89. Neither the cage 5/2 nor the cage 9/2 may include both 1 and 2. Therefore each of these cages must include one of 1 or 2, which means the cage 9/2 in R5C89 = [81] or {27} and cannot have {36} nor {45}.

Here is a much more complex example:

[[Image:Ruud34.gif]]

''(Weekly Assassin 34 by Ruud)''

In column 7, we can find a Killer Subset on {56789}. R1C7 contains {5689} and R45C7 contain {5789} – three cells out of the five we need. The other two cells are provided by the 18(3) cage at R678C7, because it must contain two cells from the subset {56789}. (This can be proved by contradiction: if it contained only one cell from {56789}, the maximum cage-sum would be 3+4+9 = 16.) Therefore we can eliminate {56789} from R239C7.

== Examples of puzzles containing killer subsets of size 4 or 5 ==

* [http://www.sudocue.net/weeklykiller.php?id=34 Weekly Assassin 34 (Ruud)]
* [http://www.ndorward.com/blog/?p=157 Killer 10 (ND)]
* [http://jcbonsai.free.fr/sudoku/?p=170 JC Godart Corresponding Killer] - the first puzzle in the set contains a {1235} quad in C4.

Killer Pair

2021-10-29T07:59:28Z

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A '''Killer Pair''' is a [[Killer Subset]] of size 2.

=== Naked Killer Pair ===

[[Image:Killer_pair_demo.gif]]

The cells R78C6 = 6 = {15} or {24}, i.e. they must contain either 1 or 2. They therefore form a naked pair in conjunction with the {12} in R3C6. This allows us to eliminate {12} for the rest of column 6, which means that R4C6 = 3.

=== Hidden Killer Pair ===

[[Image:KHPair.png]]

The candidates {12} of R5 are locked either in the cage 5/2 in R5C12 or in the cage 9/2 in R5C89. Neither the cage 5/2 nor the cage 9/2 may include both 1 and 2. Therefore each of these cages must include one of 1 or 2, which means the cage 9/2 in R5C89 = [81] or {27} and cannot have {36} nor {45}.

== See Also: ==
* [[Killer| Killer Sudoku]]
* [[Killer Subset]]
* [[Killer Triple]]
* [[Killer Quad]]

[[Category:Solving Techniques]]
[[Category:Killer Sudoku]]

Killer Triple

2021-10-29T07:56:53Z

127.0.0.1: Created page with "A '''Killer Triple''' is a Killer Subset of size 3. == How it works == Here is a simple example: Image:KNTriplet1.png The cage 8/2 in R9C56 = {17|26|35} must includ..."

A '''Killer Triple''' is a [[Killer Subset]] of size 3.

== How it works ==
Here is a simple example:

[[Image:KNTriplet1.png]]

The cage 8/2 in R9C56 = {17|26|35} must include one of {123}. It forms a naked triple on {123} with the cells in R9C12 = {123}. Therefore {123} of R9 is locked in R9C1256 and can be eliminated from the rest of R9, which means R9C9 = 4.

Here is another example of a killer triple:

[[Image:KNTriplet2.png]]

The cage 9/3 in R1C123 = {126|135|234} must include either {12} or {13} or {23}. It must include at least two digits out of {123}. It forms a naked triple on {123} with R1C4 = {123}. Therefore {123} of R1 is locked in R1C1234 and can be eliminated from the rest of R1.

== See Also: ==
* [[Killer| Killer Sudoku]]
* [[Killer Subset]]
* [[Killer Pair]]
* [[Killer Quad]]

[[Category:Solving Techniques]]
[[Category:Killer Sudoku]]

Killer Pair

2021-10-29T07:51:29Z

127.0.0.1: Created page with "A '''Killer Pair''' is a Killer Subset of size 2. == How it works == Here is a simple example: Image:Killer_pair_demo.gif The cells R78C6 = 6 = {15} or {24}, i.e. t..."

A '''Killer Pair''' is a [[Killer Subset]] of size 2.

== How it works ==
Here is a simple example:

[[Image:Killer_pair_demo.gif]]

The cells R78C6 = 6 = {15} or {24}, i.e. they must contain either 1 or 2. They therefore form a naked pair in conjunction with the {12} in R3C6. This allows us to eliminate {12} for the rest of column 6, which means that R4C6 = 3.

== See Also: ==
* [[Killer| Killer Sudoku]]
* [[Killer Subset]]
* [[Killer Triple]]
* [[Killer Quad]]

[[Category:Solving Techniques]]
[[Category:Killer Sudoku]]

XY-Cycle

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An '''XY-Cycle''' or '''XY-Ring''' is a ''Continuous [[Nice Loop]]'' limited to [[cell]]s with only 2 [[candidate]]s each. These do not need to be candidates for the same 2 [[digit]]s as in [[Remote Pairs]], but 2 adjacent cells in the loop must share one of the candidates for the loop to be correct.

The cycles are similar to [[XY-Chain]]s.

rncx(a,b) - rncy(b,c) - rmcy(c,d) - rmcx(d,a) - rncx

In [[Nice Loop]] notation, this would be:

-[rncx]-b-[rncy]-c-[rmcy]-d-[rmcx]-a
This XY-Cycle [[eliminate]]s the following candidates:
# All other candidates for digit b in row n
# All other candidates for digit c in column y
# All other candidates for digit d in row m
# All other candidates for digit a in column x

The XY-Cycle does not need to have an even number of cells, as long as the last cell can see the first and shares a candidate with it.

Loop

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A '''loop''' is a cyclic pattern of [[link]]ed [[cell]]s or [[candidate]]s.

Loops are usually represented by [[chain]]s, where the first and the last cell are the same. Like a chain, [[implication]]s in a loop can either travel in a single direction or in both directions. A bidirectional loop is better known as a [[Nice Loop]].

Examples of loops are:
* [[Turbot Fish]]
* [[Fishy Cycle]]
* [[XY-Cycle]]
* [[Nice Loop]]

Notation systems are similar to chain notation, with '''Nice Loop''' notation especially designed for loops.
[[Category:Solving Techniques]]
[[Category:Chains and Loops]]

Weak Link Square

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'''Weak link squares''' are a property of several [[Sudoku Variations|sudoku variants]]. A weak link square is a set of four cells that are not all in one group (line, diagonal ...) and of that each pair of cells is weak linked. So its impossible that any two cells of this square have the same value.

The following diagrams shows 3 types of weak link squares in [[Sudoku-X]]:

[[Image:Weak Link Square1.gif]] [[Image:Weak Link Square2.gif]] [[Image:Weak Link Square4.gif]]

In weak link squares there work techniques like [[Naked Pair]]s and [[Naked Triple]]s.

If we have additional that in such a square there are only 4 different candidates at all then also many other techniques like [[Hidden Single]]/[[Hidden Pair]]/[[Hidden Triple]], weak link square-line interaction, weak link square-diagonal interaction, [[Pointing Pair]] and [[Pointing Triple]] work.

Adding as 5th cell R5C5 to weak link squares of the first type we get ''weak link pentagons'' with similar properties. There exist in many sudoku variants also ''weak link triangles''.

There are also [[Skewed Fish]] where the [[defining set]]s are [[diagonal]]s and the [[secondary set]]s are weak link squares.



[[Category:Solving Techniques]]
[[Category:Sudoku-X]]

Skewed XY-Wing

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A '''Skewed XY-Wing''' is an [[XY-Wing]] where at least the [[pivot]] and one [[pincer]] are on the same [[diagonal]].

=== Example 1 ===

In the this example, the pivot and one pincer are on the same diagonal.

[[Image:Skewed_xy_wing1.png]]

=== Example 2 ===

In this example, the pivot and one pincer are on the same diagonal and the pattern [[eliminate]]s 2 [[candidate]]s.

[[Image:Skewed_xy_wing2.png]]

=== Example 3 ===

In this example, one of the pincers is present in both diagonals, one connected to the pivot, one to the target.

[[Image:Skewed_xy_wing3.png]]

=== Counter Example 1 ===

In this example the picture looks almost perfect, with both pincers on a diagonal, but the pivot is not on a diagonal. This is a regular [[XY-Wing]] with one of the diagonals assisting in the elimination.

[[Image:almost_skewed_xy_wing.png]]

=== Counter Example 2 ===

In this example, one of the diagonals is used to target a [[candidate]] to [[eliminate]], but this is no skewed XY-Wing, not even a regular [[XY-Wing]]. Only one of the pincers is involved in the elimination.

[[Image:no_skewed_xy_wing.png]]

[[Category:Solving Techniques]]
[[Category:Sudoku-X]]

File:Skewed xy wing3.png

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Weak Link Square

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'''Weak link squares''' are a property of several [[Sudoku Variations|sudoku variants]]. A weak link square is a set of four cells that are not all in one group (line, diagonal ...) and of that each pair of cells is weak linked. So its impossible that any two cells of this square have the same value.

The following diagrams shows 3 types of weak link squares in [[Sudoku-X]]:

[[Image:Weak Link Square1.gif]] [[Image:Weak Link Square2.gif]] [[Image:Weak Link Square4.gif]]

In weak link squares there work techniques like [[Naked Pair]]s and [[Naked Triple]]s.

If we have additional that in such a square there are only 4 different candidates at all then also many other techniques like [[Hidden Single]]/[[Hidden Pair]]/[[Hidden Triple]], weak link square-line interaction, weak link square-diagonal interaction, [[Pointing Pair]], [[Pointing Triple]] and [[Pointing Quad]] work.

Adding as 5th cell R5C5 to weak link squares of the first type we get ''weak link pentagons'' with similar properties. There exist in many sudoku variants also ''weak link triangles''.

There are also [[Skewed Fish]] where the [[defining set]]s are [[diagonal]]s and the [[secondary set]]s are weak link squares.



[[Category:Solving Techniques]]
[[Category:Sudoku-X]]

File:Medusa 5.png

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File:Medusa 4.png

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Solving technique

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These are the methods used to solve a Sudoku. There are many different solving techniques discovered in the last few years, mainly because there is a large community of puzzlers who share their knowledge on the various [[Sudoku Forums]].

Because there are so many, a rough subclassification has been made:

== [[Single]]s ==
; [[Full House]]
: A [[house]] with a single empty [[cell]].

; [[Last Digit]]
: The last instance of a [[digit]].

; [[Hidden Single]] | Pinned Digit
: A single candidate remaining for a digit in a house.

; [[Naked Single]] | Forced Digit | Sole Candidate
: A single candidate remaining in a cell.

== [[Intersection]]s ==
; [[Locked Candidates]] | Intersection Removal | Line-Box Interaction | Pointing (Pair, Triple) | Claiming
: [[Candidate]]s are locked in the [[intersection]] of a [[line]] and a [[box]].

; [[Locked Pair]]
: A [[Naked Pair]] located in a single intersection.

; [[Locked Triple]]
: A [[Naked Triple]] located in a single intersection.

; [[Almost Locked Candidates]]
: A box-line intersection where the line or the box contains an [[Almost Locked Set]], and the remaining cells in the line or box outside the intersection does not contain digits from the Almost Locked Set.

== [[Subset]]s ==
; [[Naked Subset]]
: '''N''' cells with candidates for '''N''' digits.

:; [[Naked Pair]]
:: '''2''' cells with candidates for '''2''' digits.

:; [[Naked Triple]]
:: '''3''' cells with candidates for '''3''' digits.

:; [[Naked Quad]]
:: '''4''' cells with candidates for '''4''' digits.

; [[Hidden Subset]]
: '''N''' digits with candidates in '''N''' cells.

:; [[Hidden Pair]]
: '''2''' digits with candidates in '''2''' cells.

:; [[Hidden Triple]]
: '''3''' digits with candidates in '''3''' cells.

:; [[Hidden Quad]]
: '''4''' digits with candidates in '''4''' cells.

== [[Fish]] ==
; Basic Fish
: Rows and columns only.

:; [[X-Wing]]
:: 2 rows vs. 2 columns

:; [[Swordfish]]
:: 3 rows vs. 3 columns

:; [[Jellyfish]]
:: 4 rows vs. 4 columns

:; [[Squirmbag]]
:: 5 rows vs. 5 columns

; [[Fish and Subsets]]
: general relationship between Fish and Subsets.

; [[Finned Fish]]
: Fish patterns with additional candidates in a single box.

; [[Sashimi Fish]]
: Incomplete basic fish patterns with a [[fin]].

; [[Franken Fish]]
: Fish patterns that include box constraints.

; [[Mutant Fish]]
: Fish patterns with mixed sets of constraints.

; [[Kraken Fish]]
: A fish pattern with indirect connections to a candidate which can be eliminated.

== Single Digit Patterns ==
; [[Skyscraper]]
: Two parallel strong links, weakly connected at the base.

; [[2-String Kite]]
: Two crossing strong links, weakly connected in a box.

; [[Empty Rectangle]]
: A single-digit technique that makes use of a [[box]] whose [[candidate]]s for that [[digit]] are contained within the union of a [[boxrow]] and a [[boxcol]].

== [[Coloring]] ==
; [[Simple Colors]]
: Uses only 2 colors to form a single color [[cluster]].

; [[Multi-Colors]] | [[Supercoloring]]
: Uses multiple colors (4, 6 or a higher multiple of 2) to form multiple color clusters.

; [[Weak Colors]]
: Extends Simple-Colors by the use of [[hinge]] linkages.

; [[X-Colors]]
: Uses only 2 colors, but also takes the [[implication]]s for each color into account.

; [[Color Trap]]
: A technique that uses a single cluster to eliminate candidates outside the cluster.

; [[Color Wrap]]
: A technique that uses a single cluster to detect a [[contradiction]] in one of the colors.

; [[Color Wing]]
: A technique that uses multiple clusters to eliminate candidates outside these clusters. Same as Multi-Colors.

; [[3D Medusa]] Coloring | Advanced Coloring | Ultracoloring
: A set of techniques that uses colors on multiple digits.

== Uniqueness ==
; [[Uniqueness Test]]
: A set of techniques that avoids the [[Unique Rectangle]] [[deadly pattern]].

; [[Avoidable Rectangle]]
: A set of techniques that avoids the [[Unique Rectangle]] [[deadly pattern]]. Perhaps unique in solving techniques in that it employs solved [[cell]]s as well as those unsolved.

; [[Bivalue Universal Grave]]
: A set of techniques that avoids the [[Bivalue Universal Grave]] [[deadly pattern]].

; [[BUG Lite]]
: A set of techniques that avoids the [[BUG Lite]] [[deadly pattern]].

; [[Reverse BUG]]
: While [[Bivalue Universal Grave|BUG]] looks at [[candidate]]s of unsolved cells, [[Reverse BUG]] looks at solved cells instead.

; [[Reverse BUG Lite]]
: While [[BUG Lite]] looks at [[candidate]]s of unsolved cells, [[Reverse BUG Lite]] looks at solved cells instead.

; [[Uniqueness Clue Cover]]
: Eliminates candidates by making the uniqueness assumption, using the [[given]]s.

; [[Uniqueness Controversy]]
: These solving techniques assume that the [[Sudoku]] puzzle has a unique solution. It is not universally accepted that this assumption is a valid one.

== [[Chain]]s and [[Loop]]s ==
; [[Forcing Chain]]
: Generic term for any type of chain.

; [[X-Chain]]
: Single digit chain of cells.

; [[XY-Chain]]
: Chain of [[bivalue]] cells.

; [[Remote Pairs]]
: Simplified form of XY-Chain, involving only two digits.

; [[Fishy Cycle]] | X-Cycle
: Single digit [[continuous]] loop.

; [[Generalized Fishy Cycles]]
: Strong generalization of Fishy Cycles and several other techniques. More difficult to apply.

; [[Broken Wing]]
: Eliminations caused by loops of odd length.

; [[Nice Loop]]s
: Several types of loops formed by cells following strict rules and a notation system.

; [[Double Implication Chain]] | DIC
: There are 2 interpretations circulating. The first originates from a reliable source [http://www.sudoku.com/forums/viewtopic.php?t=2143].
* A Forcing Chain that has implications in both directions.
* 2 Forcing Chains starting from a bivalue cell or a [[bilocal]] unit showing a [[verity]].

; [[Alternating Inference Chain]] | AIC
: A chain that connects nodes of one or more candidates using alternating weak and strong [[inference]]s.

; [[Oriented Chains]]
: Oriented chains are generalisations of the basic xy-chains. The central idea is that the information collected from previous candidates in a chain (and/or from the target) can be used to select the next candidates. Oriented chains are either 2D or 3D:
:- oriented 2D chains: xyt-chains, xyz-chains and xyzt-chains, together with their "hidden" counterparts: hxyt-chains, hxyz-chains and hxyzt-chains;
:- [[oriented 3D chains]]: nrct-chains, nrcz-chains, nrczt-chains.
:(The original reference to all these chains is the book "The Hidden Logic of Sudoku". Further web references forthcoming)

== Wings ==
; [[XY-Wing]]
: Three [[cell]]s with [[pivot]] cell '''XY''' and two [[pincer]] cells '''XZ''' and '''YZ'''.

; [[XYZ-Wing]]
: Three [[cell]]s with [[pivot]] cell '''XYZ''' and two [[pincer]] cells '''XZ''' and '''YZ'''.

; [[WXYZ-Wing]]
: Four [[cell]]s with [[pivot]] cell '''WXYZ''' and three [[pincer]] cells '''WZ''', '''XZ''' and '''YZ'''.

; [[W-Wing]]
: Four [[cell]]s in a [[chain]]: a cell '''WX''', a cell with '''X''' as a [[candidate]], another cell with '''X''' as a [[candidate]], another cell '''WX''', such that the two cells containing '''X''' as a [[candidate]] have a [[strong link]].

== [[Almost Locked Set]]s ==
; [[ALS-XZ]] rule
: 2 Almost Locked Sets with [[restricted common]] digit '''X''' perform eliminations for common digit '''Z'''.

; [[ALS-XY-Wing]] rule
: 3 Almost Locked Sets with 2 restricted common digits '''Y''' and '''Z''' perform eliminations for common digit '''X'''.

; [[ALS-XY-Chain]]
: Very similar to [[XY-Chain]], except that the [[node]]s in the [[chain]] are Almost Locked Sets.

; [[Death Blossom]]
: A stem cell of N candidates pointing to N petals, each an Almost Locked Set.

; [[Almost ALS]]
: An almost locked set with 1 extra digit.

== Enumeration on Selected Cells ==
; [[Aligned Pair Exclusion]]
: Checks combinations of [[digit]]s in a pair of [[cell]]s located in an [[intersection]].

; [[Aligned Triple Exclusion]]
: Checks combinations of [[digit]]s in a triple of [[cell]]s located in an [[intersection]].

; [[Subset Exclusion]]
: Extension of [[Aligned Pair Exclusion]] to arbitrary sets that need not be aligned.

== Miscellaneous ==
; [[Sue de Coq]]
: Uses two intersecting sets '''A''' and '''B''', where '''A''' is a set of N cells with N candidates in a line, '''B''' is a set of N cells with N candidates in a box, and the sets '''A - B''' and '''B - A''' have no common candidates.

; [[Subset Counting]] | Extended Subset Principle
: Considers the number of times a digit can be placed in a selected subset of cells.

; [[Braid Analysis]] | Braiding | Traveling Pairs
: Analyzes the distribution of digits in a [[chute]], especially how pairs repeat in a chute.

; [[Constraint Subsets]]
: Generalized view of [[subset]] and [[fish]] techniques.

; [[Equivalence Marks]]
: Similar to [[coloring]], but uses marks instead of colors to represent parity.

; [[Gurth's Symmetrical Placement]]
: Technique for puzzles with rotational symmetry.

== Techniques of Last Resort ==
Most of these techniques are controversial. They are either too complex to be used by human solvers, or they require a lot of extra work, or they are not based on logic.

; [[Forcing Net]]
: A general term for techniques that investigate branching chains.

; [[Tabling]] | Trebor's Tables
: All implications for each move are collected in tables.

; [[Graded Equivalence Marks]] | GEM
: A system of marking candidates starting from 2 complementary starting positions.

; [[Bowman Bingo]]
: A systematic approach to investigate implications.

; [[Trial & Error]] | [[Ariadne's Thread]] | [[Bifurcation]]
: The implications for a single move are investigated.

; [[Nishio]]
: Trial & Error limited to single digit.

; [[Templating]] | [[Pattern Overlay Method]] | POM
: All possible ways to place a digit in the remaining candidate space are investigated.

; [[Guess]]ing
: Random moves are made, without any logic behind them.

== Brute Force ==
These are primarily designed for computer solver programs.
* [[Backtracking Algorithms]]

== External Links ==
* [http://Forum.EnjoySuDoku.com/viewtopic.php?t=3315 Collection of solving techniques]

[[Category:Solving Techniques]]

Hidden Single

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The '''Hidden Single''' is a lot less sinister than its name suggests.

In fact, most of the [[Sudoku]]s published in newspapers and magazines can be solved by hidden singles only. Together with the [[Naked Single]] it belongs to the [[single]]s, the most elementary [[solving technique]]s.

A '''Hidden Single''' is a single [[candidate]] remaining for a specific [[digit]] in a [[row]], [[column]] or [[box]]. In Sudoku variants, additional [[constraint]]s can also produce Hidden Singles.

An alternative term is '''Pinned Digit'''.

It may sound like a daunting task, checking 27 [[house]]s for each of the 9 digits, thus performing 243 checks, but most players do not check each of these combinations individually. Instead, they use techniques like [[Scanning]] and [[Cross-Hatching]] to locate the hidden singles.

== Example ==

The following example has a Hidden Single for [[digit]] 4 at the [[cell]] '''r6c5''' (row 6, column 5). This is the only cell with 4 as a [[candidate]] in the middle [[box]].

[[Image:HiddenSingle.png]]

Some [[Sudoku Programs|Sudoku Helpers]], such as [[SudoCue]] and [[Simple Sudoku]], have the ability to highlight the cells for a chosen digit. Such highlighting makes Hidden Singles particularly obvious. The following is the same example [[grid]] with all cells having 4 as a candidate highlighted.

[[Image:HiddenSingle-Highlight.png]]

The six puzzles below can all be solved only using the placement of hidden singles.

1..2..3...2..1..4...3..5..67..6..5...5..8..7...8..4..18..7..4...3..6..2...9..2..7
..1...2.....3.4...5...6...1.5.1.2.7...8...4...2.9.7.8.9...7...8...5.9.....3...7..
1...2...3.4.....1...5.4.6.....2.1...7.8...1.5...4.8.....7.6.8...8.....2.4...3...7
1...2...3.4.....5....6.7.....5...8..7...8...2..6...9.....8.2....1.....6.2...7...1
1..2..3......4..5...6..7..82.....7...5..1..4...7.....98..1..2...6..2......4..6..7
...........12.34...235.617..35...74.....3.....76...82..143.825...87.23...........

== See also ==

* [[Naked Single]]

== External links ==

* [http://www.sudocue.net/guide.php#HiddenSingle Hidden Single] by ''Ruud van der Werf''
* [http://homepages.cwi.nl/~aeb/games/sudoku/solving3.html Forced Digit] by ''Andries E. Brouwer''
* [http://www.angusj.com/sudoku/hints.php Hidden Single] by ''Angus Johnson''
* [http://www.brainbashers.com/sudokupinnedsquares.asp Pinned Square] by ''Kevin Stone''
* [http://www.sadmansoftware.com/sudoku/technique2.htm Hidden Single] by ''Simon Armstrong''
* [http://www.paulspages.co.uk/sudoku/howtosolve/#Stage2 Single-Sqaure Candidate] by ''Paul Stephens''
* [http://www.playr.co.uk/sudoku/solving.hiddensingle.php Hidden Single Number] by ''Gaby Vanhegan''
* [http://sudoku.awardspace.biz/solving_sudoku_basic.php?strategy=single%20position Single Position] by ''Vincent Tandart''
* [http://freewebs.com/experiencesudoku ExperienceSudoku] by ''Christopher Rucinski''

[[Category:Solving Techniques]]

Chain

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A '''chain''' is a series of [[link]]ed [[cell]]s or [[candidate]]s.

Because [[implication]]s can only be transferred between candidates, it is not possible to omit the candidates without placing certain restrictions on the chain. For example, one can restrict the chain to cells which all have a candidate for a single [[digit]]. The so called [[X-Chain]] then shows implications between the candidates for the selected digit, without explicitly mentioning them. Another method by which candidates could be omitted can be seen in an [[XY-Chain]]. This type of chain is limited to cells which only have 2 candidates left. Although it is customary to name the digits involved, a reader, given the candidate grid, is able to verify the chain if only the initial candidate is given.

The implications in a chain can either travel in a single direction (from left to right) or in both directions. A chain that operates in both directions is considered more valuable than a unidirectional chain.

When the chain ends with the same cell it started with, the chain becomes a [[loop]], even when two different candidates are involved. A loop that operates in both directions is a [[Nice Loop]].

Besides single candidates, it is possible to include more complex structures, such as [[Almost Locked Set]]s into a chain. Several alternative structures have been discovered which can be included in chains. Most of these structures use the qualifier '''almost''' in their name.

Some people use terminology from [[wikipedia:Graph theory|Graph theory]] to name the components of chains. A cell or candidate is called a '''vertex''' or '''node''' and the link between them is an '''edge'''.

There are several notation systems for chains. These all look very similar. Once you've mastered one of the notation systems, it is not so difficult to read and interpret alternative notation systems.
Some examples of chain notation systems are:
* [[Forcing Chain]] notation
* [[Nice Loop]] notation
* [[Eureka]] notation

A chain by itself is not a[[ solving technique]]. It is merely the proof that accompanies a solving technique. However, several named chain types are recognized by the Sudoku community as valid solving techniques.
[[Category:Solving Techniques]]
[[Category:Chains and Loops]]

Sudoku Puzzle Symmetries

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==== Symmetry Operations ====

The following operations on a puzzle pattern are possible.

* Identity operation - do nothing at all.
* Rotate 180 degrees
* Rotate 90 degrees
* Reflect across c5
* Reflect across r5
* Reflect along diagonal from r1c1 to r9c9
* Reflect along diagonal from r1c9 to r9c1
* Swapping towers
* Swapping floors
* Swapping columns in a tower
* Swapping rows in a floor.

==== Sudoku Puzzle Symmetry Groups ====

Now the operations above are not independent. For example you can't have four-fold rotational symmetry without having two-fold rotational symmetry.

==== Impossible Patterns ====

{{stub}}

Sudoku Programs

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Many Sudoku players use a computer program to assist them in solving these puzzles. If you are looking for such a program, you can find several of them in this list. The most popular programs are described in detail on a separate page. This information is not yet complete. Feel free to complete it if you are an experienced user.

== Sudoku Programs ==
=== Programs for Ordinary Sudoku ===
These programs focus on ordinary Sudoku, and may also support [[Sudoku Variations|Sudoku Variants]].

; [[Simple Sudoku]]
: A popular program, easy to use. Generator, helper and solver. Only a limited set of [[solving technique]]s have been implemented. Windows only.

; [[Sudoku Susser]]
: Powerful helper and solver, available for Mac-OS, Windows and Linux.

; [[SudoCue]]
: Powerful user configurable solver, helper with several tools, generator. Supports [[Sudoku-X]], [[Windoku]] and [[Sudoku-DG|Disjoint Groups]] variants. Windows only.

; [[Sudoku Assistenten]]
: A powerful PC based solver, analyzer and generator.

; [[Sudoku Explainer]]
: A Java solver, analyzer and generator. The most advanced solving techniques that are implemented are heavy on [[Forcing Chain]]s and [[Forcing Net]]s.

; [[YasSS]]
: A fast, open source command line Sudoku solver for ordinary Sudokus.

; [[Cudoku]]
: Simple solver, helper and generator. Very easy to use, Windows version only.

; [[SudokuXS]]
: A solver, helper and generator for Palm OS.

; [[SadMan Sudoku]]
: A popular and easy to use solver, helper and generator for Windows.

; Starfish Sudoku
: A powerful, easy to use and fun Sudoku player for Windows ''(no longer available)''

; [[HoDoKu]]
: Powerful solver/generator/analyzer, supports more than 70 different techniques. Written in Java.

; [[Sudoku Snake]]
: A very powerful generating, design and solving program for the PC that supports a wide variety of solving techniques and user tools. Contains two modes, design and solve.

; [[SudokuSolver]]
: A Sudoku program which supports many [[Sudoku Variations]]

; Free Sudoku
: A free, popular sudoku game download. ''(no longer available)''

; [[Xsudo]]
: An advanced Sudoku generator and solver with strong emphases on analysing and solving very hard Sudokus. Windows only.

; iSudoku
: A sudoku generator, solver, analyzer, and tutor of techniques. ''(no longer available)''

; [[Philsfolly]]
: An interactive logic-based sudoku solver and tutor which can solve just about any 9x9 sudoku. Web based and written in javascript.

; [[Into Sudoku]]
: The best program I have found for learning specific solving techniques by using the "hint" function. Program graphically illustrates loops, chains, etc. the best. Is not the easiest interface for simpler functionalities. Works on XP SP3 but I have not tested it yet on Windows 7. (2011-04-04, DrDrTed)

=== Programs for Sudoku Variants ===
These programs focus on one or more of the [[Sudoku Variations|Sudoku Variants]], and may also support ordinary Sudoku.

; [[JSudoku]]
: A Java generator, helper and solver. The focus of this solver is [[Killer|Killer Sudokus]], although ordinary [[Sudoku]] is also supported. ''(no longer available)''

; [[SumoCue]]
: A helper and solver for the [[Killer]] and [[Jigsaw]] variants. Windows only.

; [[Perfect Sudoku]]
: A helper and solver for the [[Killer]] variant. Windows only. ''(no longer available)''

; [[Cross Plus A]]
: A powerful solver for many variants: [[Killer]], [[Samurai]], [[Flower Sudoku]], [[Sudoku-X]], [[Jigsaw]], [[Greater Than]], [[Consecutive Puzzle|Consecutive Sudoku]], [[Even-Odd]], [[Sukaku]]. A generator for [[Greater Than]] and [[Even-Odd]] Sudoku. Windows only.

; [[SudoGu]]
: A very powerful generator, helper and solver for many variants. German and English UI. Windows only.

; [[FadoGu]]
: A generator, helper and solver for [[Sudoku-DG]]. Same author ad similar user interface as [[SudoGu]]. German language. Windows only.

== Online Sudoku Solvers ==
The [[Sudoku Websites#Online Sudoku Solvers|Sudoku Websites]] page contains a list of online [[sudoku]] solvers.

== See Also ==
* [[Sudoku Websites]]
* [[Sudoku Clipboard and File Formats]]