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 
BlockBlock 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 lefttop to rightbottom. 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. Multicoloring also examines the interactions between clusters. Both of these techniques only take a
single digit into consideration. Ultracoloring 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:
Contradictions play an important role in the proof of solving techniques. In advanced techniques, conflicts are often a part of the
technique itself.

CrossHatching 
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 SudokuX 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 DoubleImplication 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 
DoubleImplication 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 2dimensional 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 CrossHatching

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 SudokuX 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 RowColumn 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.

LineBox 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 
Minicol 
Alias used for Boxcol

Minirow 
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 XYWing. Each XYWing 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 XYWing. Each XYWing 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/ColumnBlock Interactions 
Alias used for Locked Candidates type 1.

RowColumn 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 XWing, size 3 is a Swordfish and size 4 is a Jellyfish.

Scope 
Alias used for house 
Seafood 
Alias used for RowColumn 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 crosshatching. Where standard crosshatching
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 CrossHatching, 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 rowcolumn subset of size 5. In standard sudoku, a squirmbag always has a smaller
complementary rowcolumn 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, ZStrands ascend and NStrands 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:
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.

SubBlock 
Alias used for intersection 
Subgrid 
Alias used for box 
Swordfish 
A RowColumn 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:
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.

XWing 
A RowColumn Subset of size 2, a medium solving technique.

XYWing 
A semiadvanced 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.

YWing 
An alias used for XYWing
