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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. The rapid rise of sudoku from relative obscurity in Britain to a front-page feature in national newspapers attracted commentary in the media (see References below) and parody (such as when The Guardian's G2 section advertised itself as the first newspaper supplement with a sudoku grid on every page [18]). sudoku became particularly prominent in newspapers soon after the 2005 general election leading some commentators to suggest that it was filling the gaps previously occupied by election coverage. A simpler explanation is that the puzzle attracts and retains readers—sudoku players report an increasing sense of satisfaction as a puzzle approaches completion. Recognizing the different psychological appeals of easy and difficult puzzles The Times introduced both side by side on 20 June 2005. From July 2005 Channel 4 included a daily sudoku game in their Teletext service (at page 391). On 2 August 2005 the BBC's programme guide Radio Times started to feature a weekly Super sudoku. The Dutch company Mobile Excellence International developed together with their Vietnamese partner the first mobile i-mode sudoku game. The game was launched throughout Europe in September 2005. [19] sudoku is recommended by some teachers as an exercise in logical reasoning. It is also fairly simple to build a backtracking search. Typically this involves assigning a value (say, 1, or the nearest available number to 1) to the first available cell (say, the top left hand corner) and then moves on to assign the next available value (say, 2) to the next available cell. This continues until a conflict occurs, in which case the next alternative value is used for the last cell changed. If a cell cannot be filled, the program backs up one level (from that cell) and tries the next value at the higher level (hence the name backtracking). Although far from computationally efficient, this "brute force" method will find a solution, given sufficient computation time (even a fairly naive implementation will typically not take a noticeable amount of time). A more efficient program could keep track of potential values for cells, eliminating impossible values until only one value remains for a cell, then filling that cell in and using that information for more eliminations, and so on until the puzzle is solved. Counting 1-9 in regions, rows, and columns to identify missing numerals. Counting based upon the last numeral discovered may speed up the search. It also can be the case (typically in tougher puzzles) that the easiest way to ascertain the value of an individual cell is by counting in reverse—that is, by scanning the cell's region, row, and column for values it cannot be, in order to see which is left. The maximum number of givens that can be provided while still not rendering the solution unique is four short of a full grid; if two instances of two numbers each are missing and the cells they are to occupy form the corners of an orthogonal rectangle, and exactly two of these cells are within one region, there are two ways the numbers can be assigned. Since this applies to Latin squares in general, most variants of sudoku have the same maximum. The inverse problem—the fewest givens that render a solution unique—is unsolved, although the lowest number yet found for the standard variation without a symmetry constraint is 17, a number of which have been found by Japanese puzzle enthusiasts [12] [13], and 18 with the givens in rotationally symmetric cells. An alternative technique, that some find easier, is to "mark up" those numerals that a cell cannot be. Thus a cell will start empty and as more constraints become known it will slowly fill. When only one mark is missing, that has to be the value of the cell. One advantage to this method of marking is that, assuming no mistakes are made and the marks can be overwritten with the value of a cell, there is no longer a need for any erasures. This is a row, 9 cells wide. A filled-in row must have one of each digit. That means that each digit appears only once in the row. There are 9 rows in the grid, and the same applies to each of them. 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" (?? literally means "single; celibate; unmarried"). The puzzle was named by Kaji Maki (?? ??), the president of Nikoli. At a later date, the name was abbreviated to sudoku (??, pronounced SUE-dough-coo; 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.

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. [6] 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. A three-dimensional sudoku puzzle was invented by Dion Church and published in the Daily Telegraph in May 2005. Even though most solving algorithms are able to solve puzzles in under a second, very fast solvers are preferred for trial-and-error puzzle-creation algorithms, which must be able to test large numbers of partial problems for validity in a short time. The two main approaches to analysis are "candidate elimination" and "what-if". Some cells already contain numerals, known as "givens" (or sometimes as "clues"). The goal is to fill in the empty cells, one numeral in each, so that each column, row, and region contains the numerals 1–9 exactly once. 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. The first principle is based on cells where only matched numerals appear. The second is based on numerals that appear only in matched cells. The validity of either principle is demonstrated by posing the question, 'Would entering the eliminated numeral prevent completion of the other necessary placements?' If the answer to the question is 'Yes,' then the candidate numeral in question can be eliminated. Advanced techniques carry these concepts further to include multiple rows, columns, and regions.

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One method of candidate elimination works by identifying "matched cells". Cells are said to be matched within a particular row, column, or region (scope) if two cells contain the same pair of candidate numerals (p,q) and no others, or if three cells contain the same triplet of candidate numerals (p,q,r) and no others. The placement of these numerals anywhere else within that same scope would make a solution for the matched cells impossible; thus, the candidate numerals (p,q,r) appearing in unmatched cells in that same row, column or region (scope) can be deleted. Although for standard sudoku problems highly optimized and sophisticated backtracking programs are fastest, another popular way of solving such constraint problems is Donald Knuth's Dancing Links Algorithm for solving the exact matrix cover problem, of which the sudoku problems are a special case. Knuth's algorithm can be applied by converting the sudoku puzzle to a matrix cover problem, solve this problem instead, and convert the solution obtained back to a completed sudoku grid. This method is now preferred by many sudoku programmers, by virtue of its execution speed, simplicity and ease of implementation and the availability of documentation and reference source code. In "candidate elimination", progress is made by successively eliminating candidate numerals from one or more cells to leave just one choice. After each answer has been achieved, another scan may be performed—usually checking to see the effect of the contingencies. It is also fairly simple to build a backtracking search. Typically this involves assigning a value (say, 1, or the nearest available number to 1) to the first available cell (say, the top left hand corner) and then moves on to assign the next available value (say, 2) to the next available cell. This continues until a conflict occurs, in which case the next alternative value is used for the last cell changed. If a cell cannot be filled, the program backs up one level (from that cell) and tries the next value at the higher level (hence the name backtracking). Although far from computationally efficient, this "brute force" method will find a solution, given sufficient computation time (even a fairly naive implementation will typically not take a noticeable amount of time). A more efficient program could keep track of potential values for cells, eliminating impossible values until only one value remains for a cell, then filling that cell in and using that information for more eliminations, and so on until the puzzle is solved. sudoku (Japanese) also known as Number Place, 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. It is possible to set starting grids with more than one solution and to set grids with no solution, but such are not considered proper sudoku puzzles; as in most other pure-logic puzzles, a unique solution is expected. During February 7th's episode of the Daily Show, correspondent Jason Jones suggested that to ease the conflict over the Jyllands-Posten Muhammed caricatures, newspapers should be stripped down to only featuring sudoku puzzles. The first principle is based on cells where only matched numerals appear. The second is based on numerals that appear only in matched cells. The validity of either principle is demonstrated by posing the question, 'Would entering the eliminated numeral prevent completion of the other necessary placements?' If the answer to the question is 'Yes,' then the candidate numeral in question can be eliminated. Advanced techniques carry these concepts further to include multiple rows, columns, and regions.

Bringing the process full-circle, 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, The Examiner, 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). A three-dimensional sudoku puzzle was invented by Dion Church and published in the Daily Telegraph in May 2005. The maximum number of givens that can be provided while still not rendering the solution unique is four short of a full grid; if two instances of two numbers each are missing and the cells they are to occupy form the corners of an orthogonal rectangle, and exactly two of these cells are within one region, there are two ways the numbers can be assigned. Since this applies to Latin squares in general, most variants of sudoku have the same maximum. The inverse problem—the fewest givens that render a solution unique—is unsolved, although the lowest number yet found for the standard variation without a symmetry constraint is 17, a number of which have been found by Japanese puzzle enthusiasts [12] [13], and 18 with the givens in rotationally symmetric cells. A second related principle is also true. If, within any set of cells (row, column or region), a set of candidate numerals can only appear within a number of cells equal to the quantity of candidate numerals, the cells and numerals are matched and only those numerals can appear in the matched cells. Other candidates in the matched cells can be eliminated. For example, if the 2 numerals (p,q) can only appear in 2 cells within a specific set of cells (row, column or region), all other candidates in those 2 cells can be eliminated. 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 The numerals in sudoku puzzles are used for convenience; arithmetic relationships between numerals are absolutely irrelevant. Any set of distinct symbols will do; letters, shapes, or colours may be used without altering the rules Bringing the process full-circle, 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, The Examiner, 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). Every puzzle has just one correct solution. The strategy for solving a puzzle may be regarded as comprising a combination of three processes: scanning, marking up, and analysing.