Sudoku · Glossary

Sudoku glossary

Solvers have a small vocabulary of their own. These are the words you’ll meet in solving guides, here and elsewhere, with a short definition of each. Where a term has its own page with a worked example, the entry links to it.

The grid

A row, a column and a box. The marked cell belongs to the shaded row and column, and to the top-right box.

Grid: The whole puzzle: 81 cells in nine rows and nine columns. Also called the board.
Cell: One square of the grid. It holds a single digit when solved. Also called a square.
Row: A horizontal line of nine cells. Rows are numbered 1 to 9 from the top.
Column: A vertical line of nine cells. Columns are numbered 1 to 9 from the left.
Box: One of the nine outlined three-by-three squares. Also called a block or a region. Boxes are numbered 1 to 9, left to right and top to bottom.
Unit: Any row, column or box: a group of nine cells that must hold each digit once. Also called a house.
Band: Three boxes side by side, which is the same as three neighboring rows. The grid has three bands.
Stack: Three boxes one above another, which is the same as three neighboring columns. The grid has three stacks.
Peer: A cell that shares a row, column or box with another cell. Every cell has 20 peers, and none of them can hold the same digit as it does. Solvers also say that a cell “sees” its peers.

Clues and notes

Given: A digit printed in the grid at the start. Givens can’t be changed. Also called a clue.
Candidate: A digit that could still go in a cell, because none of the cell’s peers holds it yet.
Notes: Small digits written in a cell to record its candidates. Also called pencil marks.
Elimination: Removing a candidate from a cell because logic shows it can’t go there. Most techniques produce eliminations, and placements follow from them.
Snyder notation: A light way of taking notes, named after the champion solver Thomas Snyder: write a digit as a note only when it has exactly two possible cells in a box. It keeps the grid readable and makes pairs easy to see.
Conflict: The same digit twice in one row, column or box. A conflict means an earlier entry was wrong.

Singles and scanning

Single: A cell whose digit is settled by the basic rules alone. Singles come in two kinds, naked and hidden.
Naked single: A cell with only one candidate left, because its peers already hold the other eight digits. Also called a sole candidate. See a worked example: Naked single
Hidden single: A digit with only one possible cell left in a row, column or box. The cell may have other candidates, which is why the single is “hidden”. See a worked example: Hidden single
Full house: The last empty cell of a row, column or box. It takes whichever digit is missing. Also called a last digit.
Scanning: Looking along rows and columns to find where a digit can go in a box, without writing notes. Also called cross-hatching. See a worked example: Scanning

Pairs and triples

Naked pair: Two cells in one unit whose only candidates are the same two digits. Those digits must go in those cells, so they can be removed from the rest of the unit. See a worked example: Naked pair
Naked triple: Three cells in one unit that hold only three digits between them. Those digits can be removed from the rest of the unit. See a worked example: Naked triple
Hidden pair: Two digits that can go in only the same two cells of a unit. Those cells must hold those digits, so their other candidates can be removed. See a worked example: Hidden pair
Subset: The general name for pairs, triples and quads, naked or hidden: a group of cells in one unit tied to the same number of digits. Also called a locked set.

Intersections and fish

Locked candidates: A digit confined to the cells where a box and a line overlap. The name covers both pointing pairs and box-line reduction. Also called intersection removal. See a worked example: Locked candidates
Pointing pair: Within a box, a digit whose only possible cells lie in one row or column. The digit can be removed from the rest of that line. With three cells it is a pointing triple. See a worked example: Pointing pair
Box-line reduction: Within a row or column, a digit whose only possible cells lie in one box. The digit can be removed from the rest of that box. Also called claiming. See a worked example: Box-line reduction
X-Wing: A digit with exactly two possible cells in each of two rows, in the same two columns. The digit can be removed from the rest of those columns. It works with rows and columns swapped as well. See a worked example: X-Wing
Fish: The family of patterns the X-Wing belongs to. The versions with three and four lines are called the Swordfish and the Jellyfish.

Puzzles and solving

Unique solution: A properly made puzzle has exactly one solution, and it can be reached by logic. A grid with several solutions forces a guess.
Minimal puzzle: A puzzle in which every given is needed: remove any one and the solution is no longer unique. The fewest givens a nine-by-nine puzzle can have is 17. Read more: Minimal puzzle
Guessing: Trying a digit to see whether it leads to a conflict. Also called trial and error or bifurcation. It works, but a well-made puzzle never requires it.
Latin square: A grid in which each symbol appears once in every row and column. A solved Sudoku is a Latin square whose boxes also hold each digit once. Read more: Latin square
Number Place: The name under which the puzzle was first published in 1979, and still a common name for it in Japan. Read more: Number Place
Mini Sudoku: Sudoku on a smaller grid. The usual sizes are four-by-four and six-by-six, where the boxes are rectangles of three cells by two. Read more: Mini Sudoku