Glossary
All terms used in sudoku, described briefly and clearly.
Basics
Box
One of the 9 three-by-three squares that make up the board. Each digit must appear once in each box.
Candidate
A digit that can legally appear in an empty cell, meaning it doesn't appear in any of its peers yet.
Cell
A single board square. A 9×9 board has 81 cells. Each holds exactly one digit 1-9 or is empty with a list of candidates.
Column
A vertical line of 9 cells from top to bottom. The board has 9 columns.
Difficulty
Determined by number of given clues and required techniques. Easy has 35-45 givens, expert 24-27.
Elimination
Crossing out a candidate from a cell's notes because we know it doesn't fit. Most advanced techniques are elimination systems.
Given
A digit placed on the board at the start of the game that cannot be changed. Your starting point.
Notes / pencil marks
Small digits placed in a cell as potential candidates. Help you track possibilities without committing.
Peer
Every other cell in the same row, column or 3×3 box as the selected cell. Each cell has exactly 20 peers.
Row
A horizontal line of 9 cells from left to right. The board has 9 rows.
Scanning
The simplest technique: scan all 9 units for a chosen digit and check where it must go. The baseline method for easy puzzles.
Unique solution
Every well-formed puzzle has exactly one solution. You can rely on logic, never need to guess.
Unit
Common term for a row, column or box, i.e. a set of 9 cells where the "each digit once" rule applies.
Cell states
Bilocation digit
A digit that can only go to 2 cells within a given unit. Symmetric counterpart to bivalue - about the digit within a unit, not the cell.
Bivalue cell
An empty cell with exactly 2 candidates. Starting point for many techniques (XY-Wing, ALS, alternating chains).
Locked candidates
When a candidate in a box is "locked" to one row/column, it eliminates that digit from the rest of the row/column (e.g. Pointing Pair).
Naked
A pattern where all candidates are visible directly. Naked single = cell has 1 candidate. Naked pair = 2 cells share the same 2 notes.
Subset
A group of N cells in a unit that together contain exactly N candidates. Lets you eliminate those digits from other cells (Naked Subset) or other positions (Hidden Subset).
Basic techniques
Claiming (Box-Line)
Reverse of pointing: all candidates of a digit in a row/column lie in one box. Other cells of that box lose the digit.
Naked Pair
Two cells in a unit containing exactly the same 2 candidates (e.g. {3,7} and {3,7}). Those digits can be eliminated from all other cells in that unit.
Naked Single
A cell with only one candidate left - place it without hesitation. The simplest technique, drives most progress on easy puzzles.
Naked Triple
Three cells in a unit containing exactly 3 candidates between them (each may not have all). Eliminates those digits from other cells of the unit.
Pointing Pair / Triple
All candidates of a digit in a box lie in a single row or column. The digit must come from that box, so the rest of the row/column loses it.
Advanced techniques
Jellyfish
Size-4 version: four rows where the digit occupies the same 4 columns. Rare in practice but cleanly logical.
Swordfish
Extension of X-Wing to 3 rows and 3 columns. The digit in each of those rows lies in the same 3 columns - elimination from the rest of those columns.
Unique Rectangle
Four cells in 2 rows, 2 columns and 2 boxes - if 3 contain the same candidate pair, the puzzle would have two solutions. Uniqueness lets you remove that pair from the fourth cell.
X-Wing
A digit has exactly 2 spots in 2 different rows, both in the same 2 columns (or vice versa). Forms a rectangle - the digit is eliminated from the rest of those columns.
XY-Wing
Three bivalue cells forming a „wing": pivot {X,Y} links to two wings {X,Z} and {Y,Z}. Digit Z is eliminated from common peers of both wings.
XYZ-Wing
XY-Wing variant with 3 candidates in pivot: {X,Y,Z}, {X,Z}, {Y,Z}. Digit Z is eliminated from peers common to all three cells.
Chains and others
AIC (Alternating Inference Chain)
A chain alternating strong links (digit HERE or THERE) and weak links (digit HERE eliminates digit THERE). The chain ends produce eliminations.
Coloring
Marking cells with two colors based on "if A then not B" relationships. Color conflicts within a unit reveal that one color is false.
Forcing Chain
A logical chain: assume digit X is here, follow the cascade of forced moves. When both hypotheses lead to the same conclusion - certain elimination.
Trial & Error
A non-canonical method: place a digit on speculation and check for contradiction. Elegant sudoku avoids it - there should always be a purely logical solution.