Sudoku grew its vocabulary the way port cities grow dialects — Japanese publishing conventions, American magazine terms, and 2000s-era forum slang all deposited layers. The result is precise once you know it and baffling before that. This glossary defines the working vocabulary in dependency order: grid anatomy first, then candidate language, then the pattern and technique terms built from them. Terms in bold are defined within the entry where they first appear.
Grid anatomy
- Cell
- One of the 81 squares of the grid, addressed by row and column — “r4c7” is shorthand for row 4, column 7.
- Row, Column, Box
- The three kinds of nine-cell regions that must each contain 1–9 exactly once. Boxes (also called blocks or, in older American usage, regions) are the nine 3×3 squares, numbered 1–9 in reading order.
- Unit (or House)
- Any row, column, or box — the generic term for a nine-cell region bound by the one-of-each rule. There are 27 units, and every cell belongs to exactly three.
- Peer
- A cell that shares a unit with a given cell. Each cell has exactly 20 peers: 8 in its row, 8 in its column, and 4 more in its box not already counted. A digit placed in a cell excludes that digit from all 20 peers — the atomic fact behind every technique.
- Band and Stack
- A band is three horizontally adjacent boxes (three whole rows); a stack is three vertically adjacent boxes. Together they are called chutes. Useful for describing grid symmetries and scanning patterns.
- Given (or Clue)
- A digit printed in the starting grid. Givens are fixed; everything else is yours to deduce. The minimum for a valid puzzle is 17 givens — proved in 2012, and explained in The Mathematics of Sudoku.
Candidate language
- Candidate (or Pencil Mark)
- A digit still legally possible in an unsolved cell — no peer currently contains it. Written candidates are pencil marks; see Pencil Marks Done Right for notation systems, including Snyder notation (marking only digits confined to two cells of a box).
- Bivalue cell
- A cell with exactly two candidates remaining. The raw material of chains and of the Naked Pair.
- Bilocation (or Conjugate Pair)
- A digit restricted to exactly two cells within a unit. One of the two must hold the digit — a powerful either/or that seeds X-Wings, coloring, and chain techniques.
- Elimination
- Removing a candidate from a cell by proving the digit cannot go there. Most techniques beyond singles don't place digits at all — they eliminate, and placements follow.
Placement techniques
- Naked Single (or Sole Candidate)
- A cell with exactly one candidate left; place it. Full lesson.
- Hidden Single
- A digit with exactly one possible cell in some unit, even though that cell shows other candidates; place it. Full lesson. The standard search motion for these is cross-hatching — sweeping a digit's rows and columns across a box — covered in the scanning guide.
Subset (elimination) techniques
- Naked Pair / Triple / Quad
- Two, three, or four cells of one unit whose candidates collectively span only that many digits. Those digits belong to those cells, so they clear from the rest of the unit. Lessons: Pair, Triple, Quad.
- Hidden Pair / Triple / Quad
- Two, three, or four digits confined to that many cells of one unit; all other candidates clear from those cells. Lessons: Pair, Triple, Quad. Naked and hidden subsets are complementary faces of one pigeonhole argument — proved in Why Subsets Work.
- Omission (Locked Candidates / Pointing / Box-Line Reduction / Intersection Removal)
- A digit confined to one line within a box (pointing: eliminate along the rest of the line) or to one box within a line (box-line reduction: eliminate in the rest of the box). Five names, one technique. Full lesson.
Fish
- Fish
- The family of single-digit patterns where n rows confine a digit to n columns (or vice versa), eliminating it from those columns elsewhere. The n source units are the base sets; the n crossing units are the cover sets.
- X-Wing / Swordfish / Jellyfish / Squirmbag
- The size-2, 3, 4, and 5 fish respectively. Sizes above 4 are never necessary — a smaller complementary fish always exists. Lessons: X-Wing, Swordfish; family logic and name origins in The Fish Family Explained.
- Finned / Sashimi fish
- A fish spoiled by one or two extra candidates (the fin); eliminations survive only in cells that see the fin. Sashimi is the variant where the fin substitutes for a missing corner of the pattern. Beyond this site's ladder, but the same cover-set argument.
Puzzle-level terms
- Proper puzzle
- A puzzle with exactly one solution. The uniqueness convention — and the techniques and controversies attached to it — gets a full treatment in the uniqueness guide.
- Minimal puzzle
- A proper puzzle in which removing any single given would create multiple solutions. Minimality is about redundancy, not difficulty — minimal puzzles can be easy.
- Unavoidable set / Deadly pattern
- A set of solution cells that can be rearranged into a different valid grid (unavoidable set); at least one given must land inside each. The corresponding candidate configuration that a proper puzzle can never leave unresolved is a deadly pattern — the basis of the Unique Rectangle technique.
- Bifurcation (or Trial and Error)
- Guessing a candidate in a bivalue cell and backtracking on contradiction. Logically sound, universally effective, and generally considered a concession rather than a technique.
- Rating
- A publisher's estimate of difficulty, usually derived from which techniques a mechanical solver needed. Why ratings disagree across publishers is the subject of What Makes a Sudoku Hard?
Beyond the ladder
- Wings (XY-Wing, XYZ-Wing, W-Wing)
- Three-cell patterns linking bivalue/trivalue cells across units, eliminating candidates that see both ends. The gateway from pattern techniques to chain logic.
- Coloring / Chains
- Techniques that follow alternating strong and weak links between candidates across the grid, eliminating any candidate that contradicts both parities. The general framework (Alternating Inference Chains) subsumes nearly every named technique as a special case.
- Strong link / Weak link
- A strong link joins two candidates of which at least one is true (e.g. a bilocation pair); a weak link joins two of which at most one is true (e.g. two candidates in one cell). Chain techniques alternate them.
Vocabulary is scaffolding, not skill — the terms earn their keep when a walkthrough can say “the pointing pair in box 7 eliminates the 3s in row 9” and you see it at once. Put names to patterns on real boards: browse the worked walkthroughs, or generate a puzzle that requires the technique you just looked up.