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In 1997, retired Hong Kong judge Wayne Gould, 59, a New Zealander, saw a partly completed puzzle in a Japanese bookshop. Over 6 years he developed a computer program to produce puzzles quickly. Knowing that British newspapers have a long history of publishing crosswords and other puzzles, he promoted Sudoku to The Times in Britain, which launched it on 12 November 2004 (calling it su doku). The puzzles by Pappocom, Gould's software house, have been printed daily in the Times ever since. 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. 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. 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. 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 [7] devised by Steve Schaefer has an entire sentence embedded into the puzzle; the Super Wordoku [8] 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. 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] 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.

Here are some of the more notable single-instance variations: In the subscript notation the candidate numerals are written in subscript in the cells. The drawback to this is that original puzzles printed in a newspaper usually are too small to accommodate more than a few digits of normal handwriting. If using the subscript notation, solvers often create a larger copy of the puzzle or employ a sharp or mechanical pencil. In the subscript notation the candidate numerals are written in subscript in the cells. The drawback to this is that original puzzles printed in a newspaper usually are too small to accommodate more than a few digits of normal handwriting. If using the subscript notation, solvers often create a larger copy of the puzzle or employ a sharp or mechanical pencil. For most computer programmers, coding the search for cell values based on elimination, contingencies and multiple contingencies (required for harder Sudoku) is relatively straightforward. These programs emulate the human logic to solve a puzzle without resorting to guesses. Given the self-imposed constraints of most Sudoku publishers, this method generally succeeds. Each numeral in the solution therefore occurs only once in each of three "directions" or "scopes", hence the "single numbers" implied by the puzzle's name. 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] 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.

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For most computer programmers, coding the search for cell values based on elimination, contingencies and multiple contingencies (required for harder Sudoku) is relatively straightforward. These programs emulate the human logic to solve a puzzle without resorting to guesses. Given the self-imposed constraints of most Sudoku publishers, this method generally succeeds. Dr. House was clearly seen working on a Sudoku puzzle on his office computer in one scene of the December 13, 2005 episode of House, M. D.; Sudoku is supposedly now banned on the studio set due to the cast constantly playing it. Three days later The Daily Mail began to publish the puzzle under the name "Codenumber". The Daily Telegraph introduced its first Sudoku by its puzzle compiler Michael Mepham on 19 January 2005 and other Telegraph Group newspapers took it up very quickly. Nationwide News Pty Ltd began publishing the puzzle in The Daily Telegraph of Sydney on 20 May 2005; five puzzles with solutions were printed that day. The immense surge in popularity of Sudoku in British newspapers and internationally has led to it being dubbed in the world media in 2005 the "fastest growing puzzle in the world". Advanced solvers look for "contingencies" while scanning that is, narrowing a numeral's location within a row, column, or region to two or three cells. When those cells all lie within the same row (or column) and region, they can be used for elimination purposes during cross-hatching and counting (Contingency example at Puzzle Japan). Particularly challenging puzzles may require multiple contingencies to be recognized, perhaps in multiple directions or even intersecting—relegating most solvers to marking up (as described below). Puzzles which can be solved by scanning alone without requiring the detection of contingencies are classified as "easy" puzzles; more difficult puzzles, by definition, cannot be solved by basic scanning alone. 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] Other Japanese publishers refer to the puzzle as Number Place, the original U.S. title, or as "Nanpure" for short. Some non-Japanese publishers spell the title as "su doku". 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.

Nikoli Sudoku are hand-constructed, with the author being credited; the givens are always found in a symmetrical pattern. Dell Number Place Challenger (see Variants below) puzzles also list authors. The Sudoku puzzles printed in most UK newspapers are apparently computer-generated but employ symmetrical givens; The Guardian licenses and publishes Nikoli-constructed Sudoku puzzles, though it does not include credits. 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. The challenge to Sudoku programmers is teaching a program how to build clever puzzles, such that they may be indistinguishable from those constructed by humans; Wayne Gould required six years of tweaking his popular program before he believed he achieved that level. In 1997, retired Hong Kong judge Wayne Gould, 59, a New Zealander, saw a partly completed puzzle in a Japanese bookshop. Over 6 years he developed a computer program to produce puzzles quickly. Knowing that British newspapers have a long history of publishing crosswords and other puzzles, he promoted Sudoku to The Times in Britain, which launched it on 12 November 2004 (calling it su doku). The puzzles by Pappocom, Gould's software house, have been printed daily in the Times ever since. The attraction of the puzzle is that the rules are simple, yet the line of reasoning required to reach the solution may be complex 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. Wei-Hwa Huang created a meta-Sudoku, where the object is to finish drawing the 5×5 grid's pentomino-region borders so as to leave a uniquely solvable puzzle with no identically-shaped regions. 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 [7] devised by Steve Schaefer has an entire sentence embedded into the puzzle; the Super Wordoku [8] 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. 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. There is no doubt that it was not until the British Daily Telegraph introduced the puzzle on a daily basis on 23 February 2005 with the full front-page treatment advertising the fact, that the other UK national newspapers began to take real interest. The Telegraph continued to splash the puzzle on its front page, realizing that it was gaining sales simply by its presence. Until then the Times had kept very quiet about the huge daily interest that its daily Sudoku competition had aroused. That newspaper already had plans for taking advantage of their market lead, and a first Sudoku book was already on the stocks before any other national UK papers had realised just how popular Sudoku might be.