# Sudoku Rules

This wiki page is for explaining the basic rules of classic sudoku, a popular number-placement logic puzzle.

# History

The Korean mathematician Choi Seok-jeong (최석정, 崔錫鼎) was the first to publish an example of Latin squares of order nine, in order to construct a magic square in the early 18th century (link), predating Leonhard Euler by at least 67 years. Latin squares do not contain subsquares, but the concept laid the foundation for the development of sudoku.

The modern sudoku puzzle was first published in May 1979 in the United States anonymously. Most likely designed by Howard Garns, a retired architect and freelance puzzle constructor, it was originally called "Number Place" and appeared in *Dell Pencil Puzzles & Word Games* magazine (issue #16), page 6 (link).

Sudoku was introduced in Japan by Maki Kaji, president of the Nikoli puzzle company, in the Monthly Nikolist magazine in April 1984 as *Sūji wa dokushin ni kagiru* (数字は独身に限る), which translates roughly to "the digits must be single" or "the digits are limited to one occurrence". The name was later shortened to *Sūdoku* (数独) by taking the first kanji of the compound words. In Japan, *Sūdoku* is a registered trademark, and the puzzle is commonly referred to as "Number Place" (ナンバープレース, *Nanbāpurēsu*) or, more informally, *Nanpure* (ナンプレ).

It subsequently spread worldwide in the early 2000s, thanks in part to the efforts of New Zealander Wayne Gould, who developed a computer program ("Pappocom Sudoku" link) to mass produce unique sudoku puzzles for the global market. In November 2004 the *London Times* was convinced to publish the puzzles.

# Classic Sudoku

Classic sudoku is a grid-based puzzle consisting of a 9x9 grid, divided into nine 3x3 regions called boxes. The objective of sudoku is to fill the grid with digits from 1 to 9, in a way that meets the following rules:

- Each row of the grid must contain all digits from 1 to 9, with no repetitions.
- Each column of the grid must contain all digits from 1 to 9, with no repetitions.
- Each box (3x3 region) of the grid must contain all digits from 1 to 9, with no repetitions.

While most people agree that a well-formed sudoku puzzle *should* have a unique solution grid, there is some debate over whether this assumption can be made when solving a puzzle. This impacts the use of what are known as Uniqueness Techniques in the sudoku-solving process (see Uniqueness for further discussion of the issue).

## Terminology

Here are some common terms used when discussing sudoku puzzles:

- Grid: The 9x9 arrangement of cells in a sudoku puzzle.
- Cell: An individual square within the sudoku grid, which must be filled with a digit.
- Row: A horizontal line of 9 cells in the grid.
- Column: A vertical line of 9 cells in the grid.
- Box: A 3x3 region within the grid, containing 9 cells.
- Given: A cell in the grid that is pre-filled with a digit, providing a starting point for solving the puzzle.
- Solution Grid: A completely filled sudoku grid that adheres to all the rules and has no contradictions.

See Sudoku Glossary for definitions of other sudoku-related terms.

## Solving Techniques

There are various techniques to solve sudoku puzzles, ranging from basic strategies to more advanced methods. Some common techniques include:

- Singles: Filling in cells that have only one possible digit.
- Pairs, Triples, and Quads: Identifying sets of cells that can only contain specific digits, which helps eliminate possibilities in other cells.
- Candidate Elimination: Removing possibilities in cells based on the constraints of the row, column, and box.
- Swordfish, X-Wing, and Jellyfish: Advanced techniques that involve identifying patterns across multiple rows or columns to eliminate candidates.

See Solving Techniques for a list of modern known classic sudoku solving techniques.

## Other Grid Sizes

"Classic sudoku" is not limited to 9x9 grids; the term can also be used to describe sudoku puzzles with different grid sizes, as long as they do not include additional constraints. For NxN grids where N is a square number (N = k*k), the grid is divided into N boxes, each of size kxk. For example, a 4x4 sudoku consists of four 2x2 boxes, and a 16x16 sudoku has sixteen 4x4 boxes.

When N is not a square number, the regions (or boxes) are typically designed as rectangles. The width of each rectangle is the smallest factor of N greater than the square root of N, while the height is calculated as N divided by the width. For instance, a 6x6 grid generally features six 3x2 regions.

## Variations

There are many variations of sudoku, which introduce additional rules or constraints to the basic puzzle. Some popular sudoku variations include:

- Diagonal Sudoku (Sudoku X): Sudoku with the additional rule that both main diagonals must also contain each digit exactly once.
- Irregular Sudoku (Jigsaw Sudoku): Sudoku where the 3x3 boxes are replaced by irregularly shaped regions.
- Killer Sudoku: Sudoku that incorporates kakuro-style clues, with groups of cells having a sum constraint.
- Anti-Knight Sudoku: Sudoku where no two identical digits can be a knight's move apart (as in chess).

For more information on sudoku variations, see the Sudoku Variants wiki page.