# SudoCue - Sudoku Glossary

Last update: August 17, 2006. This page is protected by copyright

This glossary can be used together with the Sudoku Solving Guide. It contains an alphabetical list of Sudoku terms and solving techniques. The latter have a link to the section in the solving guide that explains the technique. When you see a dotted line below a word, the term is defined in this glossary. Advanced browsers will show a brief explanation when you hover your mouse above the word. Click the link to navigate to the glossary entry.

 45 The sum of all digits in a house. This sum is used in solving Killer Sudoku puzzles, by comparing it to the the sum of all cages that partially overlap a house. When several houses are involved, the technique uses multiples of 45. Aligned Pair Two cells in the same intersection. This term is only used for the Aligned Pair Exclusion solving technique. Aligned Pair Exclusion An advanced solving technique that examines all possible combinations for an aligned pair. Each combination is tested for validity and excluded when it would cause a conflict. When a candidate has no combinations left, it can be eliminated. Almost Locked Set A set of N unsolved cells with candidates for N+1 digits. The acronym ALS is more commonly used. N can be between 1 and 8. In solving strategies, the Almost Locked Set can be used as a strong inference between participating candidates. When all candidates of a single digit within the set are connected with a weak input link, the remaining candidates are locked in the set. The candidates for any of the remaining digits can therefore be used in a subsequent weak output link. ALS The acronym for Almost Locked Set Alternating Inference A requirement for propagating inferences through a chain or loop. Two adjacent inferences in a chain or loop cannot both be strong or weak, but they must alternate APE The acronym for Aligned Pair Exclusion Ariadne’s Thread A popular metaphore for Backtracking Backdoor A candidate which, when placed, leads to the solution without the need for any advanced solving techniques. Every sudoku, no matter how difficult, has a few backdoors. They are the targets for guessing. The best backdoors are those that allow the puzzle to be completed with singles only. Backtracking A brute force method to solve a sudoku puzzle, capable of finding all solutions in case there are more than one. This technique is not used by humans, but by computer programs, such as SudoCue. A backtracking algorithm is designed to be fast, not helpful. They are built into sudoku programs so that they can verify that the puzzles entered into the program have a unique solution. Band Alias used for floor, also used as an alias for chute. Bar For a brief period, this term was used for the intersection between a row and a box. It is no longer used for this purpose. B/B Plot A graphical representation of all bivalue cells and bilocation units. This diagram helps advanced players to locate possible chains or loops in the grid. Bifurcation A solving strategy that is frowned upon by many people. When the usual solving techniques can no longer advance the puzzle, a bivalue cell or a bilocation unit is selected, and both candidates are tested. In a proper sudoku, one of the alternatives will eventually lead to a conflict, allowing the player to eliminate this candidate. The other candidate can then be placed. Big Number A collective term used for the given and solved values in cells, as opposed to small numbers for candidates. Bilocation (unit) A unit constraint with only two candidates left. This causes a strong link between these two candidates, making them very useful in various solving techniques. Bivalue (cell) A cell with only two candidates left. This causes a strong link between these two candidates, making them very useful in various solving techniques. Block Alias used for box Block-Block Interactions Alias used for Locked Candidates type 2. Box Group of 9 cells in a 3x3 square formation. There are 9 boxes in a standard sudoku, usually numbered 1 through 9 from left-top to right-bottom. A thicker or darker border is often used to show where the boxes are in a sudoku grid. Each box must contain all 9 different digits in the solution, thus acting as a constraint for the puzzle. Boxcol Group of 3 cells lined up in the intersection of a box and a column. Boxrow Group of 3 cells lined up in the intersection of a box and a row. Braid In braiding analysis, a situation in which 2 of the 3 digits in a segment travel in the same direction and the 3rd digit follows an opposite strand. See also: Rope. Braiding (analysis) An advanced technique based on the observation that at least 2 of 3 digits in a segment must share 2 other segments in the same chute. The traveling paths are called strands. Buddy Alias used for peer Cage A group of cells for which the sum of all solutions is given. In Killer Sudoku, cages replace the given values. There are 2 methods to draw cages in a grid. The most common method is a dotted border around the cage. The second method uses separate colors for adjacent cages. Candidate A possible solution for an unsolved cell. Each candidate represents a digit. Solving a sudoku puzzle is mainly done by elimination of candidates. When a cell contains a value, the remaining values are no longer considered candidates for that cell. In addition, all peers of that cell lose their candidates for that digit, because each house can only contain one instance of each digit. Cell Smallest element in a sudoku grid, capable of containing a single digit. A cell can have 3 distinct state:. It can be a given, a solved cell or an unsolved cell. The latter is also known as an empty cell. Each cell is identified by its row and column coordinates. The exact notation system can vary. A cell is always a member of a single row, a single column and a single box. There are 81 cells in a standard sudoku grid. Cell Set Alias used by Gaby Vanhegan for house Chain A series of candidates which are linked together. Each candidate is a node in the chain. When all candidates in the chain represent the same digit, the digit is often omitted from the chain, causing the cells themselves to be seen as the nodes. The purpose of the chain is to provide evidence for a relationship between the first and last node in the chain. This relationship is then used in further deductions. Chute A part of the grid that is either a floor or a tower. Some solving techniques operate within a single chute. This term is listed in Wayne Gould’s basic terms. In specific cases, people prefer to use a descriptive term like “the top 3 rows”, or “the middle 3 columns”. Clue Alias used for given Cluster In coloring, a group of candidates which are all connected with strong links. A cluster has 2 possible solutions. Coloring An advanced solving technique which uses alternating colors to highlight parity of candidates in a cluster. Simple coloring only examines the effects of separate clusters. Multi-coloring also examines the interactions between clusters. Both of these techniques only take a single digit into consideration. Ultra-coloring extends the technique by examining the interactions between clusters for different digits. Column A group of 9 cells in a single vertical line. In some solving techniques, rows and columns are commonly referred to as “lines”. Each column must contain all 9 different digits in the solution, thus acting as a constraint for the puzzle. Conflict Alias used for contradiction Conjugate Pair The pair of remaining candidates in a bilocation unit. These two candidates have a strong link within that unit. One of these candidates must be true and the other one must be false. Conjugate pairs can be used to build chains and loops. Connected Pair Any pair of candidates for the same digit, for which we have proof that at least one of them will be true. Finding connected pairs is the purpose of coloring and chaining techniques, for it enables us to eliminate all candidates that can see both ends of the connected pair. A conjugate pair is always a connected pair, but not all connected pairs are conjugate pairs. There are connected pairs that can both be true at the same time. Constraint A group of candidates of which only one can be true. It is sometimes used as an alias for house, but that is an incorrect use of this term. A house encapsulates 9 unit constraints, one for each digit. Each cell also enforces a constraint, because it can only contain a single digit. In total, there are (27 x 9) + 81 = 324 constraints in a standard sudoku. Contradiction A situation that violates the rule, which can be any of the following: A cell or unit constraint has no candidates left Two candidates in a single cell or unit constraint are claimed to be true Contradictions play an important role in the proof of solving techniques. In advanced techniques, conflicts are often a part of the technique itself. Cross-Hatching Basic solving technique that helps locate hidden singles. The solver imagines lines coming from placed instances of a digit, helping to remember which candidates have been eliminated by these placements. Cycle An alias used for loop Dancing Links Dancing Links is a Backtracking algorithm published by Donald E. Knuth. Given the right parameters, it can solve any complex problem, including sudoku puzzles. In sudoku programs, the algorithm is often optimized by directly running on the sudoku constraint definitions. It can easily be adapted to solve sudoku variants. Diagonal Each sudoku has two diagonals, running from r1c1 to r9c9 and from r9c1 to r1c9. In the Sudoku-X variant, both diagonals must also contain digits 1 through 9, thus adding a total of 18 unit constraints. The diagonals are also used for symmetry. DIC The acronym for Double-Implication Chain Digit A numerical value between 1 and 9, which must be placed in the cells in order to complete the puzzle. For each digit, there must be 9 instances in the solution to satisfy all constraints. Some sudoku variants use other symbols than digits, like letters or pictures. Other variants, like killer sudoku, depend on the numerical value of the digits. In standard sudoku, you do not need to perform any calculations with the digits. Disjoint Subset In the solving guide, I use this term for any group of N digits and N cells that are isolated from the remaining digits and cells in a house. In other texts, this term is sometimes used as an alias for naked and hidden subsets. I see these two types only as unresolved disjoint subsets. Therefore, it is not a solving technique in its own right, but a status that can be achieved by applying these two solving techniques. DLX The acronym for Dancing Links Domain Alias used for house Double-Implication Chain A chain that has implications in both directions, causing a strong or weak relationship between the two end nodes. Edge Alias used for link. This term is borrowed from graph theory, and is rarely used in the sudoku community. Elimination The act of removing a candidate from the grid, by means of logical deduction. Most advanced solving techniques result in one or more eliminations. Error Alias used for contradiction, also part of the term Trial & Error. Excluded Candidates Alias used by Paul Stephens for Hidden Subset False Possible state for a candidate. Used in logical reasoning. A candidate can be either true or false. When it is false, it is not part of the solution and subject to elimination. Fixed Digit Alias used for given Floor A part of the grid that contains 3 rows and 3 boxes. There are 27 cells in a floor. Some solving techniques operate within a single floor or tower. Forced Digit Alias used for Naked Single Full House Final placement that completes a house. Basic solving technique. Given A cell containing a digit in the initial puzzle. They cannot be changed by the player. The placements of the givens define the sudoku puzzle. They are the primary source of information to find its solution. Currently, a minimum of 17 givens are required for a sudoku with a unique solution. Also used in the combinations: given digit, given number, given value. Grid A 2-dimensional graphical representation of a sudoku puzzle. It shows the 81 constituent cells, lined up in 9 rows and 9 columns, with a distinct border around the boxes. Some claim the grid is the actual puzzle, but a more popular view is that the grid merely represents the puzzle. When all cells in the grid contain a digit, we speak of the solution grid. Group Alias used for house Guess A solving strategy that is frowned upon by many people. When the usual solving techniques can no longer advance the puzzle, a random candidate is placed in a cell. When it leads to the solution, the puzzle is solved, otherwise it will probably lead to a conflict, in which case the guess is retracted and another one is made. Guessing is often employed by humans solvers, and occasionaly by computer programs. SudoCue does not have guessing implemented as a solving strategy. The opportunity to solve a puzzle with a simple guess must appeal to a lot of people and may have had an impact on the popularity of the game. Serious players want to avoid guessing at all costs and develop more advanced solving strategies that can be used as an alternative. The larger public has long since lost connection with this elite group. The advanced solving techniques are just too difficult to learn. On the other hand, a guess requires no prior education. Hatching Alias used for Cross-Hatching Hidden Pair A Hidden Subset of size 2, a medium solving technique. Hidden Quad A Hidden Subset of size 4, a medium solving technique. Hidden Single Single candidate left in a unit constraint. The placement of hidden singles is a basic solving technique. The term “hidden” has grown into the sudoku community, but these singles are not really hard to spot. Without pencilmarks, the term “hidden” is meaningless. Hidden Subset N digits with candidates in N cells in a house. Medium solving technique. The size N can be 2 for a pair, 3 for a triple and 4 for a quad. The name hidden subset is well chosen. It is not easy to find these subsets in a pencilmarked grid. The remaining candidates in the cells belonging to the set can be eliminated. Hidden Triple A Hidden Subset of size 3, a medium solving technique. House A group of 9 cells, which must each contain a different digit in the solution. In standard sudoku, a house can be a row, a column or a box. There are 27 houses in a standard sudoku grid. Additional houses may occur in sudoku variants, such as the diagonals in Sudoku-X or the window panes in Windoku. Improper Sudoku A sudoku which has multiple solutions. Inference Deductions that can be made between two linked candidates. A distinction is made between strong and weak inference. Initial Value Alias used for given. There are other combinations with “initial”: digit, clue, number. Intersection In general, an intersection defines the cells that any two houses have in common. Because there is only one cell in the intersection of a row and a column, these are usually ignored. Remains the intersection between a row and a box, or a column and a box. There are 3 cells in each of these 54 intersections. Intersection Removal Alias used for Locked Candidates Jellyfish A Row-Column Subset of size 4, an advanced solving technique. Killer (Sudoku) A variant of Sudoku, where the given values have been replaced by cages. This variant has lead to the development of specialized solving techniques. Last Digit In SudoCue and the collateral documentation, this term is used for the last instance of a digit that needs to be placed in the grid. With 8 instances already placed, there is only one candidate left for this digit. This term is also used as an alias for Full House. Earlier versions of this glossary may have contributed to that confusion. Line Common name in some solving techniques where either a row or a column can be used. There are 18 lines in a standard sudoku grid. Half of them are rows and the other half are columns. Line-Box Interactions Alias used for Locked Candidates Link A connection between two or more candidates. These candidates must share a constraint, so they must either belong to the same cell, or use the same digit in a single house. A distinction is made between strong and weak links. Locked This term applies to candidates that are confined to a limited group of cells within a house, often narrowed down to an intersection. This implies that these candidates can not be used in that same house outside this limited group of cells, causing the elimination of these remaining candidates. Locked Candidates Candidates locked in an intersection. Basic solving technique. A distinction is made between 2 types. Type 1 causes eliminations in the row or column, and type 2 causes eliminations in the box. Some aliases refer to only one of these 2 types. Logic “Every puzzle can be solved by logic alone” is a claim made by many puzzle makers. To substantiate such a claim, we need to define what logic actually means within the context of Sudoku. There are many subcategories of logic, and not all of them are equally useful for solving puzzles. I have recently started a discussion to clarify this issue. When the results come in, I will update this glossary and the relevant sections of the solving guide. Lone Number Alias used for Hidden Single Loop A series of candidates which are linked together to form a closed loop. Each candidate is a node in the loop. When all candidates in the loop represent the same digit, the digit is often omitted from the loop, causing the cells themselves to be seen as the nodes. The purpose of the loop depends on whether it’s continuous or discontinuous. Markup Alias used for Pencilmark Minigrid Alias used for box Mini-col Alias used for Boxcol Mini-row Alias used for Boxrow Naked Pair A Naked Subset of size 2, a basic solving technique. Naked Quad A Naked Subset of size 4, a medium solving technique. Naked Single Single candidate left in a cell. The placement of naked singles is a basic solving technique. Naked Subset N cells with candidates for N digits in a house. Basic to medium solving technique. The size N can be 2 for a pair, 3 for a triple and 4 for a quad. A naked pair is considered by many to be a basic technique, while triples and quads are medium techniques. Naked Triple A Naked Subset of size 3, a medium solving technique. Nice Loop A loop which follows a strict set of rules and notation system. Node A candidate which is part of a chain or loop. Nonet Alias used for box, mainly by the Killer Sudoku community. Number Alias used for digit Number Chain Alias used by Gaby Vanhegan for Naked Subset Number Claiming Alias used by Paul Stephens for Locked Candidates Number Pair Alias used by Gaby Vanhegan for Naked Pair Number Place The name originally used by Dell Magazines for what we now call Sudoku. Pair Alias used by Paul Stephens for Naked Pair. In a wider context, the term “pair” refers to any two cells that interact in some way. Pairs are used in several medium and advanced solving techniques. Parity One of 2 states for a candidate within a chain, loop or cluster. Parity can be shown by colors, upper or lower case letters or selected symbols, like the plus and minus sign. All candidates with the same parity are either true or false together. Peer cell in the same house as another cell. Each cell has 20 peers. When a cell contains a certain digit, none of its peers can contain that digit. In advanced solving techniques, this effect is known as weak inference. Peers have a weak or strong link. Pencilmark Visual representation of a candidate. Also known as the small numbers in the grid. Pincer A cell that is part of an XY-Wing. Each XY-Wing has 2 pincer cells, which also form a connected pair. Pinned Digit Alias used for Hidden Single Pivot A cell that is part of an XY-Wing. Each XY-Wing has a single pivot cell, with strong links to both pincers. Placement The act of setting the value of a cell to one of the digits, by means of logical deduction. Most basic solving techniques result in a single placement, and only a few advanced solving techniques can cause placements. PM The acronym for Pencilmark Pointing Pair Alias used for Locked Candidates type 1. Proper Sudoku A sudoku which has a unique solution. Quadrant Alias mistakingly used for box Reduction Alias used for elimination Region Alias used for box. Because this alias is sometimes also used for a house in general, it is avoided in the documentation on this site. Rinse The removal of pencilmarks after a placement is made. Rope In braiding analysis, a situation in which all 3 digits in a segment travel in the same direction. See also: Braid. Row A group of 9 cells in a single horizontal line. In some solving techniques, rows and columns are commonly referred to as “lines”. Each row must contain all 9 different digits in the solution, thus acting as a constraint for the puzzle. Row/Column-Block Interactions Alias used for Locked Candidates type 1. Row-Column Subset A medium solving technique where all candidates for N rows are locked in N columns or vice versa. This name is a little artificial, as these techniques have a different name, depending on the size N. Size 2 is an X-Wing, size 3 is a Swordfish and size 4 is a Jellyfish. Scope Alias used for house Seafood Alias used for Row-Column Subset techniques. Sector Alias used for house See In sudoku texts, two cells that can “see” each other are peers. Segment Alias used for intersection or house. Also used for fragments of a chain or loop. Segment is nominated to be removed from this site’s documentation, because it is used in too many different contexts. The term Triad is the suggested replacement. Use the comment form to respond to this suggestion. Set Alias used for house Single Collective name for naked or hidden single. Single Candidate Alias used for Naked Single Slicing & Dicing A basic solving technique, which is a form of cross-hatching. Where standard cross-hatching only looks at placed digits, this extended form also takes locked candidates into account. This technique is implemented in SudoCue as Unlocked Single. Small Number Visual representation of a candidate. Also known as a pencilmark. Solution This term is used in two ways, depending on the context. The most common use is the solution for the entire sudoku puzzle, where every cell contains a digit without violating the rules of the game. A proper sudoku has only one solution, so it is fair to speak of “the solution”. Within the context of a single cell, “solution” refers to the digit that particular cell contains in the solution to the puzzle. Square Alias often used for a cell, but sometimes also for a box. To avoid this confusion, this term is not used in the sudoku documentation on this site. Squeezing A basic solving technique, which is a form of Cross-Hatching, limited to a single chute. When the chute has 2 placements of a digit, there are only 3 cells left where the remaining digit can go. When 2 of those 3 cells already contain another digit, the third digit can be placed in the only empty cell. In easier puzzles, squeezing is a very fast solving method, because it has a very limited scope. Squirmbag A row-column subset of size 5. In standard sudoku, a squirmbag always has a smaller complementary row-column subset. Stack Alias used for tower. For a brief period, the term was also used for an intersection of a column and a box. It is no longer used in this context. Strand One of six diagonals of segments within a chute used in braiding analysis. Going left to right, Z-Strands ascend and N-Strands descend. Strong Inference Deductions that can be made from two linked candidates. For candidates A and B, strong inference implies that A and B cannot both be false at the same time. This leads to the following deductions: When A is false, B is true When B is false, A is true In chain notation, strong inference is represented by an equal sign: ‘=’ Strong Link A link between 2 candidates in a bivalue cell or bilocation unit. These are very important in advanced solving techniques. Because these candidates are the only two left for a constraint, one of them must be true and the other must be false. A strong link can be used for both strong and weak inference in a chain. Sub-Block Alias used for intersection Subgrid Alias used for box Swordfish A Row-Column Subset of size 3, a medium solving technique. Symbol Alias used for digit T&E The acronym for Trial & Error. Tier Alias used for floor Tower A part of the grid that contains 3 columns and 3 boxes. There are 27 cells in a tower. Some solving techniques operate within a single floor or tower. Traveling Pairs Original name for the observation which is the foundation for braiding analysis. Triad Suggested term for the 3 cells in an intersection. According to the Free Dictionary, the definition of this word is “A group of three”, which perfectly suits our needs. Trial & Error A solving method that is placed between bifurcation and guessing. It has a bad reputation amongst sudoku players, because it is so closely related to guessing. Nevertheless, it is a sound scientific method. Many chain and loop techniques show all the signs of Trial & Error, but are seriously in denial. Triplet Alias that has been used for intersection, also an alias for naked triple. True Possible state for a candidate. Used in logical reasoning. A candidate can be either true or false. When it is true, it is path of the solution and placed in the associated cell. Unit Alias used for house. In some cases, the unit refers to a single constraint in a house. This makes it possible to identify all candidates for a single digit within a single house. Because this use of the term is not very common, I have decided to clarify this use by calling it a Unit Constraint. Unit Constraint A constraint for a single digit within a house. When named, the unit constraint must show both the house and the digit to which it applies, e.g. R1D7. Value This term is strongly related to digit, but it is not an alias. Where “digit” refers to the numbers in general, the term “value” refers to the digit as a property of a specific cell. Thus, the value of a cell can be one of the available digits, or nothing, when the cell is unsolved. The phrase “Digit 6 is placed in R1C8” is equivalent to “The value of R1C8 is 6” Vertex Alias used for node. This term is borrowed from graph theory, and is rarely used in the sudoku community. Victim A candidate that can be eliminated by the application of a solving technique. I have introduced this term in the solving guide to make it easier to read. A solving technique may have multiple victims. It is common practice to write it like this: R1C1<>4. Weak Inference Deductions that can be made from two linked candidates. For candidates A and B, weak inference implies that A and B cannot both be true at the same time. This results in the following deductions: When A is true, B is false When B is true, A is false In chain notation, weak inference is represented by a dash: ‘-’ Weak Link A link between 2 candidates in a cell or unit constraint, which has more than 2 candidates left. Because there are other candidates in the constraint that could be true, this type of link is not as powerful as a strong link. It can only be used for weak inference in a chain. X-Wing A Row-Column Subset of size 2, a medium solving technique. XY-Wing A semi-advanced solving technique, using a chain of only 3 cells. Because it uses such a short chain, it is also classified as a pattern recognition technique. The cell in the middle is called the pivot, and both end cells are known as pincers. Y-Wing An alias used for XY-Wing
Please report your comments, corrections and additions to this glossary on the contact form or through the user forum. It is my intention to make this glossary the most complete lexicon for sudoku terminology available on the Net. In order to achieve this ambition, your input is invaluable. I would like to express my thanks to Gaby Vanhegan, who has done a tremendous job in collecting a lot of terms used in sudoku forums. Many of them have been added to this glossary.
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