List of Sudoku terms and jargon - AbsoluteAstronomy.com

This is a glossary of Sudoku
Sudoku
is a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid contains all of the digits from 1 to 9...

terms and jargon.

List organization and conventions

This list provides a brief glossary of Sudoku terminology.
Items are listed thematically, and usually only once, with a brief description and possibly a link to a detailed description. Links to example usage are provided as in-line numbered references (like [1]). Here the default usage of Sudoku refers to the prominent 9×9 format, as illustrated.

Grid layout and puzzle terms

A Sudoku grid has 9 rows, columns and boxes each having 9 cells. The full grid has 81 cells. Cells are commonly called squares, but in technical descriptions the term square is avoided since the boxes and grid are also squares.
Boxes are also known as blocks or zones. Three vertically stacked blocks make a stack. Three horizontally connected blocks make a band. A chute is either a band or a stack. A grid has 3 bands, 3 stacks and 6 chutes.

The use of the boxes to partition the grid can be generalized to other equal sized partition shapes, in which case the sub-areas are known as regions, zones, subgrids, or nonets. See Variants below. In some cases the regions are only equal sized, not equal shaped.

Rows, columns and regions are collectively referred to as units or scopes, of which the grid has 27. The One Rule can then be compactly stated as: 'Each digit appears once in each unit'.

Size refers to the size of a puzzle or grid. Often a composite row × column designation is used, e.g. size 9×9. In technical discussions size may mean the number of cells, e.g. 81. Since the number of cells in a region must be the side dimension of the square grid, e.g. 9 cells per block for a 9×9 grid, it is convenient to just use the region size, e.g. 9.

Puzzle terms

A puzzle is a partially completed grid. The initially defined values are known as givens or clues. A proper puzzle has a single (unique) solution. A proper puzzle that can be solved without trial and error (guessing) is known as a satisfactory puzzle. An irreducible puzzle (a.k.a. minimum puzzle) is a proper puzzle from which no givens can be removed leaving it a proper puzzle (with a single solution). It is possible to construct minimum puzzles with different number of givens. The minimum number of givens refers to the minimum over all proper puzzles and identifies a subset of minimum puzzles. See Mathematics of Sudoku-Minimum number of givens for values and details.

Sudoku variants

The classic 9×9 Sudoku format can be generalized to an

N×N row-column grid partitioned into N regions, where each of the N rows, columns and regions have N cells and each of the N digits occur once in each row, column or region.

This accommodates variants by region size and shape, e.g. 6 cell rectangular regions (The N×N Sudoku grid is always square). For prime N, polyomino

Polyomino

A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling with a connected interior....

s shaped regions can be used. The requirement to use equal sized regions, or have the regions cover the grid entirely can also be relaxed.

Other variation types include additional value placement constraints, alternate cell symbols (e.g. letters), alternate mechanism for expressing the clues, and composition with overlapping grids. This page provides a simple list of variants. See Sudoku - Variants for details and additional variants.

For rectangular regions the row-column dimensions of the region may be used to describe the grid as whole, e.g. 3×2, since each of the grid side dimensions must be the product of row *column, e.g. for a 3×2 rectangular region, the grid must be 6×6. For rectangles of size N×1 or 1×N, the region is a row or column, and Sudoku becomes a Latin square

Latin square

In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column...

Sudoku types and classes

Sub Doku : Grids smaller than 9×9. Sometimes referred to as Children's Sudoku (especially the 4×4 variant) as the reduced number of possibilities makes them easier to solve.
Super Doku : Grids larger than 9×9.
Prime Doku : N×N grid where N is prime. Generally constructed with polyomino

Polyomino

regions, e.g. Go Doku and pentominos.
Maximum Su Doku : The class of puzzles which have the maximum number of independent clues needed to allow a complete and unique solution.
Minimum Su Doku : The class of puzzles which have the minimum number of clues needed to allow a complete and unique solution.

Proper puzzle : A puzzle that has a unique solution.
Satisfactory puzzle : A puzzle that does not require trial and error. Note: the level of trial and error is usually not explicitly defined, see trial and error below.
Purely numeric puzzle: Puzzles which use purely numbers.
Purely literal puzzle: A sudoku puzzle which uses letters instead of numbers.
Numeroliteral puzzle: Puzzles using a combination of letters and numbers, usually seen in 12x12 sudoku puzzles.
Jigsaw Sudoku: regular 9x9 Sudoku that row and column rules apply, but instead of a 3x3 grid they are nine Jigsaw shapes.

Variants by size

Polyomino

: A shape composed of equal sized, side-adjacent squares. Often used for Sudoku region variants. Polyomino

Polyomino

s are named by size: (5)pentomino

Pentomino

A pentomino is a polyomino composed of five congruent squares, connected along their edges ....

, (6)hexomino

Hexomino

A hexomino is a polyomino of order 6, that is, a polygon in the plane made of 6 equal-sized squares connected edge-to-edge. The name of this type of figure is formed with the prefix hex-. When rotations and reflections are not considered to be distinct shapes, there are 35 different free hexominoes...

, (7)heptomino

Heptomino

A heptomino is a polyomino of order 7, that is, a polygon in the plane made of 7 equal-sized squares connected edge-to-edge. The name of this type of figure is formed with the prefix hept-. When rotations and reflections are not considered to be distinct shapes, there are 108 different free...

, (8)octomino

Octomino

An octomino is a polyomino of order 8, that is, a polygon in the plane made of 8 equal-sized squares connected edge-to-edge. The name of this type of figure is formed with the prefix oct-. When rotations and reflections are not considered to be distinct shapes, there are 369 different free...

, and (9)nonomino

Nonomino

A nonomino is a polyomino of order 9, that is, a polygon in the plane made of 9 equal-sized squares connected edge-to-edge. The name of this type of figure is formed with the prefix non-. When rotations and reflections are not considered to be distinct shapes, there are 1,285 different free...

.

Du-sum-oh : 5×5, 6×6, 7×7, 8×8 or 9×9 grid with irregular, polyomino

Polyomino

, shaped regions and minimal number of clues.

Du-Sum-Oh puzzles are also known as Latin Squares Puzzles (invented by Mark Thompson), Squiggly Sudoku, Jigsaw Sudoku, Irregular Sudoku, or Geometric Sudoku. These puzzles typically have anywhere from 5 to 9 rows. The number of rows is always equal to the number of columns. The regions are polyominos made of the same number of squares that are in any one row of the puzzle. The irregularity of the regions compensates for the relatively small number of givens.

5×5

Go Doku : 5×5 grid with pentomino

Pentomino

A pentomino is a polyomino composed of five congruent squares, connected along their edges ....

regions. Go is Japanese for 5.
Logi-5 : 5×5 grid with pentomino

Pentomino

A pentomino is a polyomino composed of five congruent squares, connected along their edges ....

regions

6×6

These use 6 2×3 rectangular regions:
Roku Doku
(unnamed) : featured at the World Puzzle Championship

World Puzzle Championship

The World Puzzle Championship is an annual international puzzle competition run by the World Puzzle Federation. The first one was held in New York in 1992...

Sudoku X - with unique main diagonals

7×7

(unnamed) : 7×7 grid with six heptomino

Heptomino

regions and a disjoint region, featured at the World Puzzle Championship

World Puzzle Championship

The World Puzzle Championship is an annual international puzzle competition run by the World Puzzle Federation. The first one was held in New York in 1992...

9×9

Sudoku : Classic 9×9 grid with nine 3×3 regions.
Jigsaw Sudoku : 9×9 grid with nonomino

Nonomino

regions.
Du-sum-oh : 5×5, 6×6, 7×7, 8×8 or 9×9 grid with irregular, polyomino

Polyomino

, shaped regions and minimal number of clues.

Only 'One Rule' variant puzzles with simple givens are listed in this section. For variants with other clue mechanisms, see Constraint and clue variants.

16×16

Number Place Challenger

Sudoku

is a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid contains all of the digits from 1 to 9...

: Sixteen 4×4 regions.

Constraint and clue variants

Puzzles with additional constraints on the placement of values including various forms of expressing the constraints (e.g. < > relations, sums, linked cells, etc).

Main diagonals unique : the cell values along both main diagonals must be unique, see Sudoku X.
Relative digit location : digits use the same relative location within selected regions. The matching cells or regions are often color coded.

Mathematics of Sudoku

Mathematics of Sudoku

The class of Sudoku puzzles consists of a partially completed row-column grid of cells partitioned into N regions each of size N cells, to be filled in using a prescribed set of N distinct symbols , so that each row, column and region contains exactly one of each element of the set...

has identified numerous additional constraints as analytic possibilities.

Samunamupure (clue sums) : Regions of various shapes and sizes. The usual constraints of no repeated value in any row, column or region apply. The clues are given as sums of values within regions (e.g. a 4-cell region with sum 10 must consist of values 1,2,3,4 in some order).

Terms related to solving

The meanings of most of these terms can be extended to region shapes other than blocks. To simplify reading, definitions are given only in terms of blocks or boxes.

scanning : the process of working through a puzzle to look for or eliminate values
cross hatching : process of elimination that checks rows and columns intersecting a block for a given value to limit the possible locations in the block
counting : process of stepping through the values for a row, column or block to see where they can or cannot be used
Box line reduction strategy : A form of intersection removal in which candidates which must belong to a line can be ruled out as candidates in a block (or box) that intersects the line in question.
Candidate : Potential value for a cell.
Contingency : A condition limiting the location of a value.
Chain : A sequence of contingencies connected by alternative values.
Higher circuits : Related locations outside the immediate row, column and grid. The locations are related by value contingencies.
Independent clues : A set of clues that cannot be deduced from each other. Often depends on the order of choosing the clues for a given grid.
Intersection removal : When any one number occurs twice or three times in just one unit (or scope) then we can remove that number from the intersection of another unit. For example, if a certain number must occur on a certain line, then occurrences of that number found in a block that intersects this line can be ruled out as candidates. Sometimes called Pointing (or matched) Pairs (or twins)/Triples (triplets) as they point out a candidate that can be removed.
Trial and error : the process of guessing successive candidate values in conjunction with deductive elimination. A.k.a.: what-if, bifurcation, garden of forking paths, depth first search, exhaustive search, back-tracking search, Ariadne's thread. Note: there is no clear boundary between trial-and-error and the use of pattern recognition strategies to eliminate values (higher circuits), the latter being a condensed form of analysis based on elimination by contradiction, i.e. the same as what-if. ¡
nishio : what-if method of elimination, where the use of a candidate that would make its other (necessary) placements impossible is eliminated.
The One Rule : fill in all (blank) cells so that each row, column and box contains the values 1-9. Same as: fill in the grid so that each row, column and box contains the values 1-9 exactly once, without changing the clues.
Single or singleton or lone number : the only candidate in a cell
Hidden single : a candidate that appears with others, but only once in a given row, column or box.
Locked candidate : a candidate limited to a row or column within a block.
Naked pair : Two cells in a row, column or block, which together contain only the same two candidates. These candidates can be excluded from other cells in the same row, column or block.
Hidden pair : Two candidates that appear only in two cells in a row, column or block. Other candidates in those two cells can be eliminated.
Trio : Three cells in a unit sharing three numbers exclusively. See "Triples and quads".
Triples and quads : the concepts applied to pairs can also be applied to triples and quads.
X-wing : See N-fish (with N=2).
Swordfish : See N-fish (with N=3).
N-fish http://www.setbb.com/phpbb/viewtopic.php?t=240&mforum=sudoku : Analogues of hidden pairs/triples/quads for multiple rows and columns. A pattern formed by all candidate cells for some digit in N rows (or columns), that spans only N columns (rows). All other candidates for that digit in those columns (rows) can then be excluded. Names for various N-fish:

2-fish : X-wing
3-fish : Swordfish
4-fish : Jellyfish
5-fish : Squirmbag - For 9×9 Sudoku, there's no in point naming higher-order (>4) fish, since every N-fish comes paired with a 9-N fish whose effect is the same (thus any 5-fish is paired with a jellyfish; any 6-fish with a swordfish; any 7-fish with an x-wing; any 8-fish with a hidden or naked single). Nevertheless, a 5-fish is occasionally called a squirmbag.
6+ fish : 6-gronk, 7-gronk.. http://vanhegan.net/sudoku/dictionary.php?letter=g#Gronk - these patterns are only useful for Sudoku larger than 9×9.

Remote Pairs http://www.brainbashers.com/sudokuremotepairs.htm: When a long string of naked pairs that leads around the grid exists, any cells that are in the intersection of the cells at the beginning and the end of the string may not be either of the numbers in the naked pairs, for example, 4 and 7.

Math related terms

Latin square
Latin square
In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column...

- Related puzzle with only row and column constraints.
Constraints - Rules or conditions. In Sudoku, the rule(s) requiring each digit appear once in each row, column and region.
Triplet - The set of 3 values in a row or column within a block.

List organization and conventions

Grid layout and puzzle terms

Puzzle terms

Sudoku variants

Sudoku types and classes

Variants by size

5×5

6×6

7×7

9×9

16×16

Constraint and clue variants

Terms related to solving

Math related terms

See also