Sudoku Glossary

The vocabulary of Sudoku, defined in plain language — over 50 terms from candidate to colouring, each linked to the technique it powers. Jump to a letter below.

4

45 Rule
A Killer Sudoku tactic: since every row, column and box sums to 45, adding the cages in a region reveals a single leftover cell (an innie) or protruding cell (an outie).

A

Almost Locked Set (ALS)
A group of N cells in one unit sharing N+1 candidates — one digit short of being locked. ALS logic powers several advanced elimination techniques.

B

Backtracking
The trial-and-error method behind brute force: guess a digit, advance, and rewind to the last guess whenever a contradiction appears.
Band
A horizontal group of three boxes — three stacked rows of boxes across the grid. A classic grid has three bands.
Bi-value Cell
A cell with exactly two candidates. Bi-value cells are the building blocks of wings and chains. Learn more
Bilocation
A unit in which a digit has exactly two candidate cells. The two locations form a strong link — the basis of fish, colouring and many chains. Learn more
Box
A 3×3 region of a classic grid (2×3 in 6×6, 2×2 in 4×4) that must contain each digit once.
Brute Force
Solving by trying values and backtracking on contradictions rather than by logic. Computers use it; human solvers avoid it in favour of deductions.

C

Cage
In Killer Sudoku, a dotted group of cells with a target sum. Its digits must add to the total and never repeat — the source of all killer-specific deductions.
Candidate
A digit that could legally go in a cell given the current row, column and box constraints. Also called a pencil mark.
Cell
One of the 81 squares of a classic grid (16 in a 4×4, 36 in a 6×6). Each cell holds exactly one digit in the finished puzzle.
Chain
A sequence of cells linked by alternating strong and weak inferences. Following the chain forces a digit on or off at its ends, the basis of forcing chains and remote pairs. Learn more
Chute
A band or a stack — any line of three boxes. A classic grid has six chutes: three bands and three stacks.
Claiming (Box/Line Reduction)
When a digit in a row or column appears only inside one box, the line "claims" it, so the digit can be removed from the rest of that box. Learn more
Colouring
Tracing a single digit through its strong links with two alternating colours; a cell seeing both colours, or a colour seeing itself twice, reveals an elimination. Learn more
Column
A vertical line of cells running down the grid. Like a row, each column must contain every digit exactly once.
Conjugate Pair
A unit in which a digit has exactly two candidate cells, so one of them must be that digit. Conjugate pairs are the strong links that colouring, skyscrapers and W-Wings are built from. Learn more
Cross-hatching
Scanning the rows and columns that already contain a digit to see which cell of a box is left for it — the fastest way to find hidden singles. Learn more

D

Deadly Pattern
A candidate arrangement that would allow two different solutions. Because a real puzzle is unique, such a pattern can never complete — uniqueness techniques eliminate the candidate that would create it. Learn more
Diagonal
In Sudoku X, each of the two main diagonals is an extra unit that must contain 1–9 once. The centre cell lies on both.

E

Elimination
Removing a candidate from a cell because the logic rules it out. Most techniques beyond singles work by elimination, narrowing cells until a single remains. Learn more

F

Fin
An extra candidate that spoils an otherwise clean fish. A finned fish still allows eliminations in the cells that can see the fin. Learn more
Fish
A family of single-digit patterns (X-Wing, Swordfish, Jellyfish) defined over N rows and N columns. Learn more

G

Given (Clue)
A digit printed in the puzzle at the start. Givens cannot be changed and define the unique solution.
Grid
The whole playing board: 9×9 cells split into nine boxes for classic Sudoku, 6×6 for mini, or 4×4 for kids.

H

Hidden Pair
Two digits that can go in only the same two cells of a unit. Every other candidate can be cleared from those two cells, even though they hold other notes. Learn more
Hidden Single
A digit that can be placed in only one cell of a unit, even if that cell shows other candidates. Learn more
Hidden Subset
N digits restricted to the same N cells of a unit (pair, triple or quad), so every other candidate can be erased from those cells. Learn more

J

Jellyfish
A four-line fish: the same single-digit fish logic over four rows and four columns. Learn more

L

Locked Candidate
A digit confined to the intersection of a box and a line, enabling pointing-pair or box/line-reduction eliminations. Learn more

M

Minimal Puzzle
A proper puzzle from which no given can be removed without creating a second solution. A classic Sudoku needs at least 17 givens to stay proper.

N

Naked Pair
Two cells in one unit that hold only the same two candidates. Those two digits are locked to those cells, so they can be erased from the rest of the unit. Learn more
Naked Single
A cell with only one remaining candidate, which must therefore be its value. Learn more
Naked Subset
A group of N cells in a unit whose combined candidates total exactly N digits (pair, triple or quad), locking those digits out of the rest of the unit. Learn more
Nishio
A what-if test: tentatively place a candidate, follow its forced consequences, and if they break the puzzle, eliminate that candidate. Learn more

P

Peer
A cell that shares a row, column or box with a given cell, so the two can never hold the same digit. Each cell in a classic grid has 20 peers.
Pencil Marks
Small candidate notes written into a cell to track which digits remain possible. See Snyder notation for an efficient scheme. Learn more
Pincer
One of the two outer cells of a wing. Whichever value the pivot takes, one pincer is forced to a shared digit, eliminating it from cells the pincers both see. Learn more
Pivot
The hinge cell of a wing: in an XY-Wing it is the bi-value cell that sees both pincers; in an XYZ-Wing it carries three candidates and is also part of the elimination. Learn more
Pointing Pair
When a digit in a box is confined to one row or column, it "points" along that line, so the digit can be removed from the rest of the line outside the box. Learn more
Proper Puzzle
A puzzle with exactly one solution. Every well-made Sudoku is proper, which is what lets uniqueness techniques work. Learn more

R

Region
The nine-cell group that replaces the 3×3 box in Jigsaw Sudoku. It can be any connected shape, but like a box it must still contain 1–9 once.
Row
A horizontal line of cells running across the grid. Each row must contain every digit exactly once — nine cells, 1–9, in classic Sudoku.

S

Sashimi
A finned fish whose core pattern would fall apart without the fin. The eliminations still hold for cells that see the fin. Learn more
Scanning
Searching a unit or the whole grid for forced placements — usually for hidden singles by digit — before resorting to pencil marks or advanced techniques. Learn more
Single
A cell or unit where a digit has only one possible home. Naked singles (one candidate in a cell) and hidden singles (one cell for a digit in a unit) are the bread and butter of solving. Learn more
Skyscraper
A single-digit chain pattern: two conjugate pairs that share one line but whose other ends are mis-aligned, so cells seeing both far ends lose the digit. Learn more
Snyder Notation
A sparse pencil-marking method: mark a digit in a box only when it has exactly two possible cells there, keeping the grid readable while exposing pairs. Learn more
Stack
A vertical group of three boxes running down the grid. A classic grid has three stacks; together with the bands they frame box-based deductions.
Swordfish
A three-line fish — the X-Wing pattern stretched across three rows and three columns for one digit. Learn more
Symmetry
A balanced arrangement of givens — often rotationally symmetric — used by puzzle makers for visual appeal. It is an aesthetic choice, not a solving rule.

U

Uniqueness
The property that a valid puzzle has exactly one solution. Unique-rectangle and BUG techniques exploit it. Learn more
Unit
Any group of cells that must contain each digit exactly once — a row, a column, or a box (and the diagonals in Sudoku X).

W

Wing
A small family of bi-value patterns — XY-Wing, XYZ-Wing and W-Wing — where a pivot forces a shared digit into a pincer, enabling an elimination. Learn more

X

X-Wing
A single-digit pattern over two rows and two columns: the digit is confined to the same two columns in two rows, forming a rectangle that clears those columns elsewhere. Learn more
XY-Wing
Three bi-value cells forming a hinge (pivot) and two pincers. Whichever value the pivot takes, a shared digit is forced into one pincer, eliminating it from cells both pincers see. Learn more

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