Sudoku, also known as Number
Place or Nanpure, is a logic-based placement puzzle. The aim
of the puzzle is to enter a numerical digit from 1 through 9
in each cell of a 9×9 grid made up of 3×3 subgrids
(called "regions"), starting with various digits given in some
cells (the "givens"); each row, column, and region must contain
only one instance of each numeral. Completing the puzzle requires
patience and logical ability. An early variant of the puzzle
was published in a French newspaper in 1895 and may have been
influenced by the great Swiss mathematician Leonhard Euler,
who repopularized Latin squares.
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Euler is frequently cited as the source of the puzzle, but examples of Latin Squares were engraved in ancient architecture as numerological talismans. Euler made no changes to their rules. Arabic numerologists had already compiled an exhaustive list of order 3 through order 9 Greco-Latin Squares in the Jabirean Corpus by 990 AD.
The modern puzzle Sudoku was invented in Indianapolis in 1979. Interest in Sudoku stems from a revival in Japan in 1986, when the venerable puzzle publisher Nikoli discovered the game as invented by Howard Garns and initially distributed for children under the name "Number Place" in an older Dell Magazines publication, and republished the format leading to widespread international popularity in 2005.
What's with the Name
The name "Sudoku" is the Japanese abbreviation of a longer phrase, "Suuji wa dokushin ni kagiru", meaning "the digits must remain single". It is a trademark of puzzle publisher Nikoli Co. Ltd. in Japan. In Japanese, the word is pronounced [sɯːdokɯ]; in English, it is usually spoken with an Anglicised pronunciation, [səˈdəʊkuː] (BrE) [səˈdoʊkuː] (AmE) or [ˈsuːdəʊku] (BrE) [ˈsuːdoʊku] (AmE). Other Japanese publishers refer to the puzzle as Number Place, the original U.S. title, or as "Nampure" for short. Some non-Japanese publishers spell the title as "Su Doku".
The numerals in Sudoku puzzles are used for convenience; arithmetic relationships between numerals are irrelevant. Any set of distinct symbols will do; letters, shapes, or colours may be used without altering the rules. In fact, ESPN published Sudoku puzzles substituting the positions on a baseball field for the numbers 1-9. Dell Magazines, the puzzle's originator, has been using numerals for Number Place in its magazines since they first published it in 1979.
The attraction of the puzzle is that the rules are simple, yet the line of reasoning required to solve the puzzle may be complex. The level of difficulty can be selected to suit the audience. The puzzles are often available free from published sources and may be custom-made using software.
Construction of Sudoku
Building a Sudoku puzzle can be performed by pre-determining the locations of the givens and assigning them values only as needed to make deductive progress. This technique gives the constructor greater control over the flow of puzzle solving, leading the solver along the same path the compiler used in building the puzzle. Great caution is required, however, as failing to recognize where a number can be logically deduced at any point in construction—regardless of how tortuous that logic may be—can result in an unsolvable puzzle when defining a future given contradicts what has already been built. Building a Sudoku with symmetrical givens is a simple matter of placing the undefined givens in a symmetrical pattern to begin with.
Nikoli Sudoku are hand-constructed, with the author being credited; the givens are always found in a symmetrical pattern. Dell Number Place Challenger puzzles also list authors. The Sudoku puzzles printed in most UK newspapers are apparently computer-generated but employ symmetrical givens; The Guardian famously claimed that because they were hand-constructed, their puzzles would contain "imperceptible witticisms" that would be very unlikely in computer-generated Sudoku.
Even though the 9×9 grid with 3×3 regions is by far the most common, variations abound: sample puzzles can be 4×4 grids with 2×2 regions; 5×5 grids with pentomino regions have been published under the name Logi-5; the World Puzzle Championship has previously featured a 6×6 grid with 2×3 regions and a 7×7 grid with six heptomino regions and a disjoint region. Larger grids are also possible, with Daily SuDoku's 16×16-grid Monster SuDoku, the Times likewise offers a 12×12-grid Dodeka sudoku with 12 regions each being 4×3, Dell regularly publishing 16×16 Number Place Challenger puzzles (the 16×16 variant often uses 1 through G rather than the 0 through F used in hexadecimal), and Nikoli proffering 25×25 Sudoku the Giant behemoths.
Another common variant is for additional restrictions to be enforced on the placement of numbers beyond the usual row, column, and region requirements. Often the restriction takes the form of an extra "dimension"; the most common is for the numbers in the main diagonals of the grid to also be required to be unique. The aforementioned Number Place Challenger puzzles are all of this variant, as are the Sudoku X puzzles in the Daily Mail, which use 6×6 grids.
Puzzles constructed from multiple Sudoku grids are common. Five 9×9 grids which overlap at the corner regions in the shape of a quincunx is known in Japan as Gattai 5 (five merged) Sudoku. In The Times and The Sydney Morning Herald this form of puzzle is known as Samurai SuDoku. Puzzles with twenty or more overlapping grids are not uncommon in some Japanese publications. Often, no givens are to be found in overlapping regions. Sequential grids, as opposed to overlapping, are also published, with values in specific locations in grids needing to be transferred to others.
Alphabetical variations have also emerged; there is no functional difference in the puzzle unless the letters spell something. Some variants, such as in the TV Guide, include a word reading along a main diagonal, row, or column once solved; determining the word in advance can be viewed as a solving aid. The Code Doku devised by Steve Schaefer has an entire sentence embedded into the puzzle; the Super Wordoku from Top Notch embeds two 9-letter words, one on each diagonal. It is debatable whether these are true Sudoku puzzles: although they purportedly have a single linguistically valid solution, they cannot necessarily be solved entirely by logic, requiring the solver to determine the embedded words. Top Notch claim this as a feature designed to defeat solving programs.
Here are some of the more notable single-instance variations:
- A three-dimensional Sudoku puzzle was invented by Dion Church and published in the Daily Telegraph in May 2005.
- The 2005 U.S. Puzzle Championship includes a variant called Digital Number Place: rather than givens, most cells contain a partial given—a segment of a number, with the numbers drawn as if part of a seven-segment display.
- The online journal Speculative Grammarian has published a number of linguistics-themed Sudoku-like puzzles called LingDoku, which require the solver to solve for two variables at once, including a simple 3x3 puzzle, and a slightly more complicated 4x4 puzzle.
A new variant without any given numbers for start comes up this summer (2006) from India byYoogi Games, named Greater-Than or Comparison Sudoku. All rules of a standard Sudoku are the same, but you have to find out by comparisons the sequence of the digits (or letters if you want, but the symbols used must be in ascending order) from one through nine for each region. Therefore, each cell's border line inside every region is notched in the meaning of < (less than) – or vice versa.