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Sudoku glossary

The words sudoku solvers use, and that sudokUI's hints use, each defined once and precisely.

The board

cell also square: One of the 81 squares of the grid. It holds a given, a digit you have placed, or pencil marks while it is unsolved. See given, cell name, peer.
row: A horizontal line of nine cells. Each digit from 1 to 9 appears exactly once in every row. See column, line, unit.
column: A vertical line of nine cells. Each digit from 1 to 9 appears exactly once in every column. See row, line, unit.
box also block, region, nonet: One of the nine squares of three by three cells marked by thick lines. Each digit from 1 to 9 appears exactly once in every box. Boxes are numbered 1 to 9 from the top left, row by row. See unit, band, stack.
unit also house: A row, a column or a box: any group of nine cells that must contain each digit from 1 to 9 exactly once. The grid has 27 units. See row, column, box, peer.
line: A row or a column. The word is used when a rule works the same way in both directions. See row, column, unit.
band also floor: Three boxes side by side, covering three neighbouring rows. The grid has three bands: top, middle and bottom. Not to be confused with a difficulty band. See stack, chute, difficulty band.
stack also tower: Three boxes on top of each other, covering three neighbouring columns. The grid has three stacks: left, middle and right. See band, chute.
chute: A band or a stack: three boxes in a line, together with the three rows or columns that run through them. See band, stack, box.
intersection also mini-line, minirow, minicolumn, box-line intersection: The three cells that a box shares with a row or column crossing it. Locked candidates work on intersections, and a grouped node lies inside one. See locked candidates, pointing, claiming, grouped node.
peer also buddy: A cell that shares a row, column or box with another cell. Every cell has 20 peers, and no peer can hold the same digit as the cell itself. See sees, unit.
sees: Two cells see each other when they share a row, column or box, so they cannot hold the same digit. Two candidates for the same digit see each other when their cells do. See peer, unit, weak link.
digit also number, value: One of the nine symbols 1 to 9. Digits are labels, not quantities, so no arithmetic is involved. See cell, candidate.
given also clue: A digit printed in the puzzle from the start. Givens are always correct and cannot be changed. See cell, unique solution.
solution: A completely filled grid that keeps every given and obeys the rule in all 27 units. See unique solution, proper puzzle.
proper puzzle also valid puzzle: A puzzle with exactly one solution. Uniqueness techniques are valid only for proper puzzles. See unique solution, uniqueness.

Notation

pencil mark also note, pencilmark: A small digit written in a cell as a note, usually to record a candidate. sudokUI has two positions for pencil marks, corner and centre. See candidate, corner mark, centre mark, Snyder notation, pencil mark grid.
pencil mark grid also PM: The grid with every candidate of every unsolved cell written in. Most techniques beyond singles are read from it. See pencil mark, auto candidates.
corner mark also corner pencil mark: A pencil mark drawn at its digit's fixed spot in a three by three layout; when centre marks share the cell, the corner marks go round its edge in digit order. Corner is a position, not a meaning, though Snyder notation usually goes there. See pencil mark, centre mark, Snyder notation.
centre mark also centre pencil mark, center mark: A pencil mark written in the middle of the cell, the usual place for a full list of candidates. Check reads centre marks as the cell's remaining candidates; hints and Scan read corner and centre marks alike, once you have said your marks are your remaining candidates. See pencil mark, corner mark, candidate, auto candidates.
Snyder notation also Snyder marks: A marking method named after Thomas Snyder: in each box, a digit is marked only if it has exactly two possible places there, though some solvers also mark three. The marks are partial, so a missing mark does not mean the digit is eliminated. See pencil mark, corner mark, box.
cell name also r1c1 notation: The address of a cell, written as its row and column numbers counted from the top left: r3c5 is the cell in row 3, column 5. Some solvers combine cells, so r57c2 means r5c2 and r7c2; sudokUI hints name each cell separately. See cell, row, column.
auto candidates also Auto: A sudokUI tool, switched on with the Auto candidates button, that works out the candidates of every unsolved cell and keeps them up to date. New games start with it off; a practice puzzle that jumps straight to its technique starts with it on. See candidate, pencil mark, centre mark.
Check: A sudokUI button that compares your placed digits with the solution and checks that each marked cell still lists its true digit: the auto candidates when they are on, otherwise your centre marks, and your corner marks too once you have said your marks are your remaining candidates. Mistakes are tinted red. See centre mark, solution.
Steps: The sudokUI list of the whole solve path from the start of the puzzle, with the crux marked. Clicking a step sets the board to the position just before it. See solve path, crux.

Basic logic

candidate also possibility: A digit that is still possible in an unsolved cell: no peer of the cell holds it, and no logic has ruled it out. Solving removes candidates until every cell has one left. See pencil mark, elimination, peer, auto candidates.
placement: Writing a digit into a cell as its final value. A hint that ends in a placement has proved that the digit must go there. See elimination, single.
elimination also exclusion: Removing a candidate from a cell because logic proves the digit cannot go there. Most advanced techniques end in eliminations, not placements. See candidate, placement, technique.
contradiction also conflict: A state that breaks the rules: a cell with no candidates, a digit with no place in a unit, or the same digit twice in a unit. An assumption that leads to one is false. See forcing chain, Nishio, brute force.
single: A placement forced because only one possibility is left: a cell with one candidate (naked single) or a digit with one possible cell in a unit (hidden single). See naked, hidden, full house, placement.
full house also last digit: A unit with only one empty cell left, which must take the one digit the unit is missing. It is the simplest kind of single; strictly, last digit means the last empty cell of the whole grid. See single, unit.
naked: Describes a pattern found in the cells: N cells of one unit hold only N candidates between them. A naked single is a cell with one candidate; a naked pair removes its two digits from the unit's other cells. See hidden, single, subset, locked set.
hidden: Describes a pattern found in the digits: N digits of one unit have only N cells to go in. A hidden single is a digit with one possible cell; a hidden pair removes all other candidates from its two cells. See naked, single, subset.
subset also pair, triple, quadruple, quad: N cells of one unit that must hold N digits between them, found as a naked or a hidden pattern. Sizes two, three and four are called pair, triple and quadruple. See naked, hidden, locked set.
locked set also naked subset: N unsolved cells in one unit that hold exactly N candidates between them. Those digits must fill those cells, so they are removed from every other cell of the unit. HoDoKu's Locked Pair and Locked Triple are the special case that also lies in one intersection. See subset, naked, almost locked set.
locked candidates also intersection removal: A digit whose possible cells in one unit all lie inside its intersection with a second unit. The digit must go in the intersection, so it is removed from the rest of the second unit. See intersection, pointing, claiming.
pointing also locked candidates type 1, pointing pair, pointing triple: Locked candidates starting from a box: every place for a digit in the box lies in one row or column, so the digit is removed from the rest of that row or column. See locked candidates, claiming, intersection.
claiming also locked candidates type 2, box-line reduction: Locked candidates starting from a line: every place for a digit in a row or column lies in one box, so the digit is removed from the rest of that box. See locked candidates, pointing, intersection.
bivalue cell also bi-value cell: An unsolved cell with exactly two candidates. Exactly one of them is true, so the two are joined by a strong link and a weak link at once. See strong link, weak link, conjugate pair, BUG.
conjugate pair: The only two candidates for a digit in a unit. Exactly one is true: if one is false the other is true (strong link), and if one is true the other is false (weak link). See bilocation, strong link, weak link, colouring.
bilocation: A digit that has exactly two possible cells left in a unit. Those two candidates form a conjugate pair. See conjugate pair, bivalue cell, strong link.

Links and chains

link: A logical relation between two candidates, or between nodes, that a chain can use. Links are strong or weak, and a strong link can also be used as a weak one. See strong link, weak link, inference, chain.
strong link also strong inference: A link between candidates A and B meaning that if A is false then B is true, so at least one of them is true. Conjugate pairs and bivalue cells give strong links. See weak link, conjugate pair, bivalue cell, inference.
weak link also weak inference: A link between candidates A and B meaning that if A is true then B is false, so at most one of them is true. Two candidates in one cell, or for one digit in one unit, are weakly linked. See strong link, sees, inference.
inference: One step of reasoning from one candidate to the next. A strong inference says that if this is false, that is true; a weak inference says that if this is true, that is false. See strong link, weak link, chain, link.
chain: A sequence of nodes joined by links, each inference feeding the next, so that one state of the first node forces a state of the last. See node, inference, alternating inference chain, nice loop.
node: One element of a chain. It is usually a single candidate, meaning one digit in one cell, but it can also be a grouped node or an almost locked set. See chain, grouped node, almost locked set.
alternating inference chain also AIC: A chain whose links alternate strong and weak, beginning and ending with a strong link. At least one of its two end nodes is true, so any candidate that is weakly linked to both ends is eliminated. See chain, strong link, weak link, nice loop, grouped node.
grouped node also group node: A node made of the two or three candidates for one digit inside one intersection. It counts as true when any one of its cells holds the digit. See node, intersection, alternating inference chain.
nice loop also loop: A chain of alternating strong and weak links that closes into a loop by returning to where it started. It is continuous if the alternation holds all the way round, and discontinuous if it breaks at one node. See continuous loop, discontinuous loop, X-cycle, alternating inference chain.
continuous loop also continuous nice loop, AIC loop: A nice loop whose links alternate without a break. Every link in it, strong or weak, then has exactly one true end, so any other candidate that is weakly linked to both ends of any of its links is eliminated. See nice loop, discontinuous loop, weak link.
discontinuous loop also discontinuous nice loop: A nice loop whose alternation breaks at one node. Two strong links meeting there prove that candidate true, and two weak links meeting there prove it false. When a strong link on one digit and a weak link on another meet in one cell, the digit of the weak link is false there. See nice loop, continuous loop, strong link, weak link.
X-cycle also fishy cycle: A nice loop on a single digit: a closed chain of strong and weak links between the possible cells of one digit. See nice loop, X-chain, conjugate pair.
X-chain: An AIC on a single digit. At least one end is true, so the digit is removed from every cell that sees both ends. See alternating inference chain, X-cycle, turbot fish.
XY-chain: An AIC made only of bivalue cells, with weak links between cells on a shared digit. If both ends hold digit Z, Z is removed from every cell that sees both ends. See alternating inference chain, bivalue cell, remote pair, XY-wing.
remote pair: An XY-chain of an even number of cells that all hold the same two digits. Both digits are removed from every cell that sees both ends. See XY-chain, bivalue cell.
colouring also Simple Colors, simple colours, coloring: Giving a cluster's candidates two colours so that the ends of every conjugate pair differ. Exactly one colour is true everywhere: two candidates of one colour that see each other make that colour false (colour wrap), and an outside candidate that sees both colours is eliminated (colour trap). See cluster, conjugate pair, sees, multi-colouring.
multi-colouring also Multi Colors: Colouring two separate clusters of one digit. If a colour of one cluster sees both colours of the other, it is false; if one colour of each cluster see each other, a candidate seeing the other two colours is eliminated. See colouring, cluster.
cluster: A set of candidates connected to each other by conjugate pairs (and, in 3D Medusa, by bivalue cells). Settling one of them settles them all, which is why a cluster can be coloured in two colours. See colouring, conjugate pair, 3D Medusa.
3D Medusa: Colouring across several digits, joining candidates through both conjugate pairs and bivalue cells. Its rules extend colour wrap and colour trap to candidates in the same cell. See colouring, cluster, bivalue cell.
forcing chain: A technique that follows each case of a premise, such as every candidate of one cell, to its consequences. What holds in every case is true, and a single case that ends in a contradiction is false. See chain, forcing net, Nishio, contradiction.
forcing net: A forcing chain whose reasoning may branch and rejoin, so that one conclusion can depend on several earlier ones together. It is the last logical technique sudokUI tries before brute force. See forcing chain, Nishio, brute force.
Nishio also Nishio forcing chain: A test of one candidate: assume it is true and follow the consequences. If they lead to a contradiction, the candidate is false and is eliminated. In the strict sense only that one digit is followed; sudokUI follows the singles of every digit. See forcing chain, forcing net, elimination.

Fish

fish also squirmbag, whale, leviathan: A pattern on one digit: N base sets whose candidates for the digit all lie inside N cover sets. Every candidate of the digit in the cover sets that is not in a base set is eliminated. Sizes 2 to 7 are X-wing, swordfish, jellyfish, squirmbag, whale and leviathan. See base set, cover set, X-wing, fin, franken fish, mutant fish.
X-wing: The smallest fish: in two rows (or columns) a digit has places only in the same two columns (or rows), so it is removed from the rest of those. Despite the name it is a fish, not a wing. See fish, swordfish, base set, cover set.
swordfish: A fish of size three: in three lines a digit has places only in the same three crossing lines, so it is removed from the rest of those. See fish, X-wing, jellyfish.
jellyfish: A fish of size four: in four lines a digit has places only in the same four crossing lines, so it is removed from the rest of those. See fish, swordfish.
base set also base unit, base sector: One of the N units that define a fish. No candidate of the digit may lie in two base sets, though the units themselves may overlap; a candidate that does is treated as an endo fin. Each base set must hold the digit exactly once, which makes N true cells in all. See fish, cover set, fin, endo fin.
cover set also cover unit, cover sector: One of the N units that together contain every candidate of a fish's base sets. The base sets need N true cells and each cover set takes only one, so cover candidates outside the base sets lose the digit. See fish, base set, fin, cannibalism.
fin also exo fin: A base candidate of a fish that lies outside every cover set. Either one of the fins is true or the plain fish holds, so a finned fish eliminates only those cover candidates outside the base sets that also see every fin. See fish, finned fish, endo fin, sashimi.
finned fish also finned X-wing, finned swordfish: A fish with one or more fins. Its eliminations are the plain fish's eliminations that also see every fin. See fin, fish, sashimi.
endo fin: A base candidate that lies in two base sets, possible only in franken and mutant fish. It is treated as a fin, because if it were true the base sets would hold fewer than N true cells. See fin, base set, franken fish.
cannibalism also cannibalistic fish: A base candidate that lies in two cover sets is eliminated by its own fish, because if it were true one cover set would hold the digit twice. In a finned fish it must also see every fin. See cover set, fish.
sashimi also sashimi fish: A finned fish that would not be a proper fish of its size without its fins, for example because a base set would be left with only one candidate. Eliminations follow the same rule as for any finned fish. See fin, fish, base set.
franken fish: A fish in which boxes are allowed among the base sets or the cover sets. Apart from boxes, one side uses only rows and the other only columns. See fish, base set, cover set, mutant fish.
mutant fish: A fish whose base sets or cover sets mix rows, columns and boxes in any way. See fish, franken fish.
kraken fish: A finned fish combined with chains: a candidate is eliminated if it is false both when the plain fish holds and when any one fin is true. See finned fish, forcing chain.

Wings and other patterns

turbot fish: A single-digit chain of two conjugate pairs joined by a weak link. The digit is removed from every cell that sees both free ends. Skyscraper and two-string kite are special cases. See X-chain, skyscraper, two-string kite, empty rectangle.
skyscraper: Two parallel conjugate pairs of one digit, in two rows or two columns, with one end of each in the same crossing line. The digit is removed from cells that see both other ends. See turbot fish, conjugate pair.
two-string kite also 2-String Kite: A conjugate pair in a row and one in a column for the same digit, with one end of each in the same box. The digit is removed from the cell that sees both other ends. See turbot fish, conjugate pair, box.
empty rectangle also ER: A box whose candidates for a digit all lie in one row and one column of the box, combined with a conjugate pair outside it. Together they act as a chain that removes the digit from one cell. See turbot fish, box, conjugate pair.
wing: A small pattern, such as the XY-wing, XYZ-wing, WXYZ-wing or W-wing, proving that a digit Z must go in one of a few cells. Z is removed from every cell that sees all of them. The X-wing is a fish, not a wing. See pivot, pincer, XY-wing, W-wing.
pivot also hinge: The middle cell of an XY-wing or XYZ-wing, which sees both pincers. In an XY-wing it holds XY; in an XYZ-wing it holds XYZ, so eliminations must also see it. See wing, pincer, XY-wing, XYZ-wing.
pincer also pincer cell: One of the two outer cells of an XY-wing or XYZ-wing, each of which sees the pivot. The pincers hold XZ and YZ. See wing, pivot.
XY-wing also Y-wing: A bivalue pivot XY that sees two bivalue pincers XZ and YZ. Whatever the pivot is, one pincer is Z, so Z is removed from every cell that sees both pincers. See wing, pivot, pincer, XY-chain.
XYZ-wing: An XY-wing whose pivot also holds Z. One of the three cells is Z, so Z is removed only from cells that see the pivot and both pincers. See XY-wing, pivot, pincer.
WXYZ-wing also bent quad: Four cells holding four digits between them, in which every digit except Z is restricted, meaning all its places see each other. One of the four must then be Z, so Z is removed from every cell that sees all the Zs among them. sudokUI finds it as a bivalue cell plus a three-cell set. See wing, almost locked set, ALS-XZ, bivalue cell.
W-wing: Two bivalue cells with the same digits XZ, joined by a strong link on X whose ends each see one of them. One of the two cells is Z, so Z is removed from every cell that sees both. See wing, bivalue cell, strong link.
almost locked set also ALS: N unsolved cells in one unit that hold exactly N+1 candidates between them. If any one of those digits is removed from all the cells, they become a locked set of the N digits that remain. A bivalue cell is the smallest ALS. See locked set, restricted common candidate, ALS-XZ.
restricted common candidate also RCC, restricted common: A digit shared by two almost locked sets, where all its cells in one see all its cells in the other, and none of them lies in cells the two sets share. It can be true in at most one set, and a set that loses it becomes a locked set. See almost locked set, locked set, sees.
ALS-XZ: Two almost locked sets joined by an RCC X and sharing another digit Z. One set becomes locked, so Z is removed from every cell that sees all the Zs in both. With two RCCs (doubly linked) both sets become locked. See almost locked set, restricted common candidate.
ALS-XY-wing: Three almost locked sets A, B and C, where A and C each share a different RCC with B, and A and C share a digit Z. Z is removed from every cell that sees all the Zs in A and C. See ALS-XZ, almost locked set.
death blossom: A stem cell whose every candidate is an RCC with its own almost locked set, the petals. Whichever candidate the stem takes, one petal becomes locked, so a digit Z common to all petals is removed from cells that see all their Zs. See almost locked set, restricted common candidate.
Sue de Coq: Two or three cells of one intersection whose candidates split between a set in the rest of the box and a set in the rest of the line. Each part is locked, so its digits are removed from the rest of its unit. See intersection, almost locked set, locked set.
template also pattern overlay, POM: One complete way to place a digit in all nine rows, columns and boxes that agrees with the current grid. A candidate found in no template is eliminated, and a cell found in every template takes the digit. See elimination, placement, Exocet.
Exocet also Junior Exocet, JE: Two base cells in one intersection, with three or four candidates between them, and two target cells in the other two boxes of their chute that do not see them. When every base digit is confined to at most two lines in the rest of the chute, the targets must take the same two digits as the base, so the targets lose every candidate the base cells lack. See intersection, chute, template, elimination.

Uniqueness

uniqueness also uniqueness technique: The fact that a proper puzzle has exactly one solution, used as a solving argument. Any candidate that would leave a deadly pattern, and so two solutions, is false. See unique solution, deadly pattern, unique rectangle, BUG.
unique solution: The one and only way to complete a proper sudoku from its givens. sudokUI checks that every puzzle it generates, and every puzzle you import or type in, has exactly one solution. See uniqueness, given, brute force.
deadly pattern: A set of cells, none of them givens, whose digits could be swapped among themselves without breaking any rule. That would mean two solutions, so the solution of a proper puzzle never contains such a pattern. See uniqueness, unique rectangle, BUG, given.
unique rectangle also UR, uniqueness test: Four cells, none of them givens, in two rows, two columns and two boxes, sharing the same two candidates. With only those two digits in all four it would be a deadly pattern, so at least one extra candidate in the rectangle is true. See deadly pattern, uniqueness, hidden rectangle.
hidden rectangle also HR: A unique rectangle found through conjugate pairs on its two digits rather than through bivalue cells. It removes one of the two digits from the corner opposite the conjugate pairs. See unique rectangle, conjugate pair.
avoidable rectangle also AR: A rectangle in which some cells are already solved by you, not given, and the rest could complete a deadly pattern. The candidate that would complete it is false. See unique rectangle, given.
BUG also bivalue universal grave: A state where every unsolved cell has exactly two candidates and every candidate occurs exactly twice in each of its units. Such a state has no solution or more than one, so a proper puzzle can never reach it. See bivalue cell, deadly pattern, uniqueness, BUG+1.
BUG+1: A BUG with one extra candidate in one cell. That candidate, the one that occurs three times in its units, must be true. See BUG, bivalue cell.

Solving and rating

technique also strategy: A named pattern of logic that justifies a placement or an elimination, such as a hidden single or an X-wing. Each technique has a score that counts towards the rating. See rating, solve path, technique score.
technique score also step score: The fixed number of points a technique adds each time it is used. sudokUI uses HoDoKu's default scores, from 4 for a naked single up to 10000 for brute force, and scores the techniques HoDoKu lacks next to their closest relatives. See technique, rating, HoDoKu.
solve path also solution path: The ordered list of steps that solves a puzzle. sudokUI builds it by trying techniques in a fixed order, roughly easiest first, and taking the first that works at every step, and shows it under Steps. See technique, crux, rating, Steps.
crux also hardest step: The most expensive step of the solve path: the one whose technique has the highest score, or the first of them if several tie. sudokUI marks it in the Steps list. See solve path, technique, rating.
rating also difficulty rating, puzzle score: A puzzle's difficulty as a number: the sum of the technique scores of every step along the solve path. Because scores and solving order follow HoDoKu, ratings can be compared with HoDoKu's for puzzles that need only techniques HoDoKu also has. See solve path, technique score, difficulty band, HoDoKu.
difficulty band also difficulty level, level: One of eight named levels of difficulty: Beginner, Easy, Medium, Tricky, Hard, Unfair, Extreme and Nightmare. A puzzle's band follows from its total score and from the hardest techniques it needs: one Hard-class step makes it at least Tricky, two make it at least Hard. HoDoKu itself has five levels. See rating, technique, HoDoKu, band.
brute force also backtracking, trial and error, guessing: Solving by trial and error: try a digit, carry on, and go back when a contradiction appears. In sudokUI it checks that a puzzle has a unique solution, and it is the solver's last resort, scored at 10000. See unique solution, forcing net, rating.
HoDoKu: A free, open source (GPLv3) sudoku program in Java by Bernhard Hobiger, known for its solver, technique guide and difficulty scores. sudokUI takes its technique scores and solving order from HoDoKu, so ratings of puzzles that need only HoDoKu's techniques can be compared. See rating, difficulty band, technique.

See the terms at work: every technique explained, or play sudokUI and ask for a hint.