The puzzle is most frequently a 9×9 grid made up of 3×3 subgrids (called "regions"). Some cells already contain numbers, known as "givens". The goal is to fill in the empty cells, one number in each, so that each column, row, and region contains the numbers 1 through 9 exactly once. Each number in the solution therefore occurs only once in each of three "directions", hence the "single numbers" implied by the puzzle's title.
The attraction of the puzzle is that the completion rules are simple, yet the line of reasoning required to reach the completion may be difficult. Published puzzles often are ranked in terms of difficulty. This also may be expressed by giving an estimated solution time. While, generally speaking, the greater the number of givens, the easier the solution, the opposite is not necessarily true. The true difficulty of the puzzle depends upon how easy it is to logically determine subsequent numbers.
The puzzle was first published in New York in the late 1970s by the specialist puzzle publisher Dell Magazines in its magazine Math Puzzles and Logic Problems, under the title Number Place. The person who designed the puzzle and composed the first of its kind is not recorded, but it was probably Walter Mackey, one of Dell's puzzle constructors. The puzzle was introduced in Japan by Nikoli in the paper Monthly Nikolist in April 1984 as "Süji wa dokushin ni kagiru ", which can be translated as "the numbers must be single" or "the numbers must occur only once" . The puzzle was named by Kaji Maki, the president of Nikoli. At a later date, the name was abbreviated to Sudoku (pronounced sue-do-koo; sü = number, doku = single); it is a common practice in Japanese to take only the first kanji of compound words to form a shorter version. In 1986, Nikoli introduced two innovations which guaranteed the popularity of the puzzle: the number of givens was restricted to no more than 30 and puzzles became "symmetrical" (meaning the givens were distributed in rotationally symmetric cells). It is now published in mainstream Japanese periodicals, such as the Asahi Shimbun. Nikoli still holds the trademark for the name Sudoku; other publications (at least in Japan) use other names.
In 1989 Loadstar/Softdisk Publishing published DigitHunt on the Commodore 64, which was apparently the first home computer version of Sudoku. At least one publisher still uses that title. Bringing the process full-circle, Kappa reprints Nikoli Sudoku in GAMES Magazine under the name Squared Away; the New York Post and USA Today now also publish the puzzle. It is also often included in puzzle anthologies, such as The Giant 1001 Puzzle Book (under the title Nine Numbers).
To understand how to play and solve a sudoku puzzle, let's first introduce the terms we use on this web site.
Grid, Cells and Values
The whole puzzle area is called a grid. Typically it is composed of 9x9=81 cells (or squares). Some of the cells are already assigned with values, while others are left blank for players to solve.
Rows and Columns
A row refers to all cells in a horizontal line. And a column refers to all cells in a vertical line. There are, obviously, totally 9 rows and 9 columns in the puzzle above, and each contains 9 cells. To save confusion, rows and columns are refered by Capitalised letters and numbers respectively. For example, cell [G6] means the cell in Row G and Column 6, where there is a value 7 located.
The term block is used for a set of nine adjacent cells. Alternate colors are used to mark the blocks in a puzzle grid, as shown in the figure above. For example, Block at cell [A1] refers to the top-left block, which starts at Row A and Column 1.
Any one column, row or block is called a unit (or a group). Each unit of nine cells must have a unique occurence of numbers 1 to 9.
Sudoku Puzzle Difficulty
People may think the difficulty of a puzzle is based on the quantity of initial given numbers. This is, however, not always the case. Sometimes, a puzzle with more given numbers may probably be more difficult than another one with less given numbers.
Practically, one of the measures to establish the level of difficulty is to find out which and how many sudoku strategies are involved in solving a sudoku puzzle. The easiest puzzle may require only the very basic techniques to solve. A harder puzzle, in the other hand, tends to require very advanced strategies.
People are always not satisfied with what they already have. Even though the 9x9 grid with 3x3 blocks is by far the most common, more and more sudoku variations appear and become part of the sudoku family.
Another variant is to enforce additional restrictions on the placement of numbers beyond the usual row, column and block requirements. For example, Sudoku X requires the numbers in the main diagonals of the grid also be unique. Killer Sudoku, however, requires the values in a cage (a group of cells surrounded by dashed lines) must be unique and sum up to the total specified in the upper right of the cage.