Sudoku Glossary

The board

Grid

The 9×9 playing area of a Sudoku puzzle, made up of 81 cells. A completed grid holds the digits 1 to 9 exactly once in every row, every column and every 3×3 box.

Cell

One of the 81 squares of the grid. A cell holds either a single solved digit or, while you are solving, a set of candidates that might still go there.

Row

One of the nine horizontal lines of nine cells. Each row must contain the digits 1 to 9 exactly once.

Column

One of the nine vertical lines of nine cells. Each column must contain the digits 1 to 9 exactly once.

Box

One of the nine 3×3 blocks marked by the heavy grid lines, also called a block or nonet. Each box must contain the digits 1 to 9 exactly once.

Unit

Any group of nine cells that must contain the digits 1 to 9 exactly once — that is, any row, any column, or any box. Also called a house. Most solving techniques are stated in terms of units rather than naming rows, columns and boxes separately.See also: House

House

Another name for a unit: any row, column or box. The two terms are used interchangeably in Sudoku literature.See also: Unit

Peer

A cell that shares a unit with another cell. Every cell has 20 peers — the other eight cells in its row, the other eight in its column, and the four remaining cells of its box. A digit placed in a cell can be eliminated from all of its peers.

Band

A horizontal group of three boxes spanning three rows. A grid has three bands.

Stack

A vertical group of three boxes spanning three columns. A grid has three stacks.

Chute

A collective name for a band or a stack — any group of three boxes lying in a line. Killer Sudoku techniques based on the Rule of 45 often work across a chute rather than a single unit.See also: Band, Stack, Rule of 45

Solving basics

Given

A digit printed in the puzzle at the start, also called a clue. Givens cannot be changed and are the fixed constraints every deduction works from. Killer Sudoku puzzles frequently begin with no givens at all.See also: Clue

Clue

Another name for a given: a digit supplied by the puzzle before you begin solving.See also: Given

Candidate

A digit that could still legally go in a particular cell, given everything placed so far. Solving a Sudoku is the process of eliminating candidates until only one remains in a cell, or only one cell remains for a digit in a unit.

Pencil mark

A candidate written into a cell as a small note rather than as a solved digit. Pencil marks are a record of what remains possible; keeping them accurate is what makes the advanced techniques usable at all.See also: Candidate

Elimination

The removal of a candidate from a cell because it has been proved impossible there. Most techniques produce eliminations rather than immediate placements, and the eliminations then cascade into placements.

Placement

Writing a solved digit into a cell. A placement follows either from a Naked Single (one candidate left in the cell) or a Hidden Single (one cell left for that digit in a unit).

Scanning

Reading across rows, columns and boxes to find where a digit can and cannot go, without writing candidates. It is the fastest opening method and solves most Easy puzzles on its own.

Bifurcation

Choosing one of two possibilities, following the consequences, and backtracking if a contradiction appears. It is guessing with bookkeeping. Every puzzle up to Extreme on this site is solvable by pure logic without it; Diabolical puzzles are defined as those that require it.

Subsets

Naked subset

A group of N cells in one unit whose candidates, taken together, come to exactly N digits. Those digits are then locked into those cells and can be eliminated from every other cell of the unit. Naked means the cells contain nothing else.See also: Hidden subset

Hidden subset

A group of N digits in one unit that can only be placed in the same N cells. Those cells must take those digits, so every other candidate can be eliminated from them. Hidden means the cells may also carry other candidates — that is exactly what conceals the pattern.See also: Naked subset

Single

A forced placement. A Naked Single is a cell with only one candidate left; a Hidden Single is a digit with only one available cell in a unit. Singles are the two techniques every other technique ultimately feeds.

Pair

A subset of size two — two cells holding the same two candidates (naked), or two digits confined to the same two cells (hidden).

Triple

A subset of size three. The three cells need not each carry all three digits; it is enough that between them they use only those three.

Quad

A subset of size four. Quads are rare and are usually easier to spot as the hidden complement of a naked subset elsewhere in the same unit.

Locked set

A set of N cells within a unit that between them hold exactly N candidates. Because the digits cannot go anywhere else, the set is locked and its digits are unavailable to the rest of the unit.

Almost Locked Set

A set of N cells holding N+1 candidates — one digit short of being locked. Removing any single candidate would lock it. Pairing two Almost Locked Sets that share a digit is the basis of the ALS-XZ technique.See also: ALS-XZ

Links, chains and colouring

Strong link

A relationship between two cells in a unit where a digit has exactly two possible positions. If it is not in one, it must be in the other. Strong links are the backbone of fish patterns, colouring and every chain technique.See also: Weak link

Weak link

A relationship where two cells share a unit and a candidate, so at most one of them can hold that digit — but possibly neither. Chains alternate strong and weak links.See also: Strong link

Bi-value cell

A cell with exactly two candidates. Because one of the two must be true, bi-value cells act as switches and are the building blocks of XY-Wings, XY-Chains and Remote Pairs.

Bi-location

A digit with exactly two possible cells in a unit. Bi-location is the unit-level counterpart of a bi-value cell and is what creates a strong link.See also: Strong link

Chain

A sequence of linked cells in which the truth of one end forces the truth or falsity of the other. Following the alternation from end to end lets you eliminate candidates that would contradict both possible states.

Colouring

Assigning two alternating colours along a network of strong links on a single digit. The two colours represent the two possible states of the whole network; any cell that sees both colours cannot hold that digit.See also: Parity

Parity

Which of two alternating states a cell occupies in a colouring or chain. Cells of the same parity are all true together or all false together, which is what makes the eliminations valid.See also: Colouring

Fish patterns

Fish

A family of single-digit techniques in which a digit is confined to N rows across the same N columns, or the reverse. X-Wing is the size-2 fish, Swordfish size 3, and Jellyfish size 4.See also: Base set, Cover set

Base set

The units in which the fish pattern is found — for example the two rows of an X-Wing. The digit must be placed somewhere in each base set.See also: Cover set

Cover set

The perpendicular units the pattern lands in — the two columns of an X-Wing found in rows. Eliminations happen in the cover sets, not the base sets. Getting this direction backwards is the single most common error with fish techniques.See also: Base set

Fin

An extra cell holding the digit that spoils an otherwise clean fish. The pattern still yields eliminations, but only in cells that also see the fin, since the fin is the one way the fish could fail.

X-Wing

The smallest fish. A digit appears in exactly two cells in each of two rows, and those cells share the same two columns — so the digit can be eliminated from every other cell of those two columns. The pattern works identically with rows and columns swapped.

Swordfish

The size-3 fish: a digit confined to three cells or fewer across three rows, all within the same three columns, allowing elimination from the rest of those columns. Individual rows need not hold the digit in all three columns.

Jellyfish

The size-4 fish, and the largest standard one. Any pattern larger than a Jellyfish is equivalent to a smaller fish on the complementary set of units, so the family stops here.

Uniqueness

Uniqueness

The assumption that a well-formed Sudoku has exactly one solution. Techniques built on it are valid only because a puzzle with two solutions would be defective — they prove a pattern impossible by showing it would create a second solution.

Deadly pattern

A configuration that, if completed, could be filled in two different ways, producing two valid solutions. Since a proper puzzle has only one, whatever prevents the deadly pattern must be true.See also: Uniqueness

Unique Rectangle

Four cells at the corners of a rectangle, spanning exactly two rows, two columns and two boxes, sharing the same two candidates. That arrangement would allow two solutions, so it cannot complete — which forces eliminations on the corner that carries extra candidates.

BUG+1

Bivalue Universal Grave plus one. If every unsolved cell but one has exactly two candidates, the grid is one step from a position with multiple solutions. The odd cell out must take the candidate that appears three times in its units.

Killer Sudoku

Cage

A dashed group of cells in Killer Sudoku carrying a target sum. The digits in a cage must add to that sum and may not repeat within it, on top of all the normal Sudoku rules.

Cage sum

The small number printed in the corner of a cage, giving the total its cells must add to. Because digits cannot repeat inside a cage, the sum plus the cage size together limit which digit sets are possible.

Combination

One of the digit sets that can fill a cage of a given size and sum. A three-cell cage summing to 7 has only one combination, {1,2,4}; listing the combinations and discarding the impossible ones is the core Killer skill.

Unique combination cage

A cage whose size and sum admit exactly one digit set, pinning those cells before any digit is placed. For any cage size only the two lowest and two highest reachable totals are forced this way.

Rule of 45

Every unit contains the digits 1 to 9 exactly once and therefore sums to 45. Comparing 45 against the cages covering a unit reveals the total of whatever cells stick out or fall short.See also: Innie, Outie

Innie

A cell inside a unit that is not covered by any cage lying wholly within that unit. Its value is 45 minus the sum of the fully contained cages.See also: Rule of 45, Outie

Outie

A cell of a cage that extends beyond the unit being analysed. Its value is the cage total minus the part of the cage inside the unit, once the Rule of 45 has fixed that part.See also: Rule of 45, Innie

Keep Going

Each of these terms is used in context in the Learning Hub, which covers 28 Classic techniques and 6 Killer techniques with worked examples. If you are starting from scratch, How to Play covers the rules first.