childrens printable sudoku puzzles

This is a glossary of Sudoku 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 ). 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

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 , polyominos 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.

Sudoku types and classes

Variants by size

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.

4×4

5×5

6×6

These use 6 2×3 rectangular regions:

7×7

8×8

Super Sudoku X - 4 4×2 + 4 2×4 rectangular blocks.

9×9

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

12×12

16×16

25×25

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).

Mathematics of Sudoku has identified numerous additional constraints as analytic possibilities.

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.

• 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.. - these patterns are only useful for Sudoku larger than 9×9.

Cell reference schemes

• 1...81 or 0...80
• Row & column
• Box & cell

Math related terms

• Latin square - 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.

See also

• Mathematics of Sudoku, particularly for enumeration results for number of solutions, clues or puzzles.

References

1. ^ The Toronto Metro 's daily Sudoku
2. ^ ^{a b c d e f g h i j} Mathematics of Sudoku, Names section
3. ^ ^{a b} Dusumoh
4. ^ ^{a b c d e f g} Sudoku hints

Notes

• ^   Teach yourself Sudoku , James Pitts ISBN 0-340-91376-2 pg. 5
• ^   Sudoku for Dummies Volume 2 . Andrew Heron, Edmund James ISBN 0-470-02651-0 pg. 18
• ^   Sudoku for Dummies Volume 2 . Andrew Heron, Edmund James ISBN 0-470-02651-0 pg. 25
• MAA Math Games - Sudoku Variations - from 9/5/05
• 'Shendoku , DR Shenton &