

What is Sudoku?Written by BuySudokuPuzzles.com
Introduction to Sudoku (pronounced SUEdoughcoo) How to play The goal of the puzzle is to fill in every empty cell in the 3x3 regions with the numbers 1 through 9, and make sure all rows and columns of the 9x9 puzzle have the number 19 only once.Sounds simple right? Let's take a look at a typical Sudoku grid: Each puzzle starts with some numbers already filled in (called givens) to make the puzzle unique and to give you clues on how to start. In order to be considered a true "Sudoku", every puzzle must only have one unique solution. The solving strategies for a Sudoku puzzle can go from easy to advanced, so we have made another section to cover solving strategies. If you are interested in solving strategies, please visit our section on Sudoku solving strategies. For more information on the mathematics and the origin and history of Sudoku please continue reading. Mathematics of Sudoku Solving Sudoku puzzles (as well as any other NPhard problem) can be expressed as a graph colouring problem. The aim of the puzzle in its standard form is to construct a proper 9colouring of a particular graph, given a partial 9colouring. The graph in question has 81 vertices, one vertex for each cell of the grid. The vertices can be labeled with the ordered pairs (x,y), where x and y are integers between 1 and 9. In this case, two distinct vertices labeled by (x,y) and (x',y') are joined by an edge if and only if: x = x', or, y = y', or, ceil(x/3) = ceil(x'/3) and ceil(y/3) = ceil(y'/3) The puzzle is then completed by assigning an integer between 1 and 9 to each vertex, in such a way that vertices that are joined by an edge do not have the same integer assigned to them. A valid Sudoku solution grid is also a Latin square. There are significantly fewer valid Sudoku solution grids than Latin squares because Sudoku imposes the additional regional constraint. Nonetheless, the number of valid Sudoku solution grids for the standard 9x9 grid has been calculated to be 6,670,903,752,021,072,936,960. This number is equal to 9! x 722 x 27 x 27,704,267,971, the last factor of which is prime. The result was derived through logic and brute force computation. When symmetries were taken into account, there are 5,472,730,538 essentially different Sudoku grids. History of Sudoku The puzzle was introduced in Japan by Nikoli in the paper Monthly Nikolist in April 1984 as "Suuji 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 (su = 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 32 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. Within Japan, Nikoli still holds the trademark for the name Sudoku; other publications in Japan use alternative 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. Yoshimitsu Kanai published his computerized puzzle generator under the name Single Number for the Apple Macintosh in 1995 in Japanese and English, for the Palm (PDA) in 1996, and for the Mac OSX in 2005. Bringing the process fullcircle, Dell Magazines, which publishes the original Number Place puzzle, now also publishes two Sudoku magazines: Original Sudoku and Extreme Sudoku. Additionally, Kappa reprints Nikoli Sudoku in GAMES Magazine under the name Squared Away; the New York Post, USA Today, The Boston Globe, Washington Post, and San Francisco Chronicle 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). Within the context of puzzle history, parallels are often cited to Rubik's Cube, another logic puzzle popular in the 1980s. Sudoku has been called the "Rubik's cube of the 21st century". 

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