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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. Scanning stops when no further numerals can be discovered. From this point, it is necessary to engage in some logical analysis. Many find it useful to guide this analysis by marking candidate numerals in the blank cells. There are two popular notations: subscripts and dots The puzzle was designed anonymously by Howard Garns, a 74-year-old retired architect and freelance puzzle constructor, and first published in 1979.[14] Although likely inspired by the Latin square invention of Leonhard Euler, Garns added a third dimension (the regional restriction) to the mathematical construct and (unlike Euler) presented the creation as a puzzle, providing a partially-completed grid and requiring the solver to fill in the rest. The puzzle was first published in New York by the specialist puzzle publisher Dell Magazines in its magazine Dell Pencil Puzzles and Word Games, under the title Number Place (which we can only assume Garns named it). By April and May 2005 the puzzle had become popular in these publications and it was rapidly introduced to several other national British newspapers including The Independent, The Guardian, The Sun (where it was labelled Sun Doku), and The Daily Mirror. As the name sudoku became well-known in Britain, the Daily Mail adopted it in place of its earlier name "Codenumber". Newspapers competed to promote their sudoku puzzles, with The Times and the Daily Mail each claiming to have been the first to feature sudoku. Fill in the grid so that every row, every column, and every 3x3 box contains the digits 1 through 9. Yoshimitsu Kanai published his computerized puzzle generator under the name Single Number for the Apple Macintosh [15] in 1995 in Japanese and English, for the Palm (PDA) [16] in 1996, and for the Mac OS-X [17] in 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. 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. Published puzzles often are ranked in terms of difficulty. Surprisingly, the number of givens has little or no bearing on a puzzle's difficulty. A puzzle with a minimum number of givens may be very easy to solve, and a puzzle with more than the average number of givens can still be extremely difficult to solve. The difficulty of a puzzle is based on the relevance and the positioning of the given numbers rather than the quantity of the numbers.

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. 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. Computer solvers can estimate the difficulty for a human to find the solution, based on the complexity of the solving techniques required. This estimation allows publishers to tailor their sudoku puzzles to audiences of varied solving experience. Some online versions offer several difficulty levels. By April and May 2005 the puzzle had become popular in these publications and it was rapidly introduced to several other national British newspapers including The Independent, The Guardian, The Sun (where it was labelled Sun Doku), and The Daily Mirror. As the name sudoku became well-known in Britain, the Daily Mail adopted it in place of its earlier name "Codenumber". Newspapers competed to promote their sudoku puzzles, with The Times and the Daily Mail each claiming to have been the first to feature sudoku. Ideally one needs to find a combination of techniques which avoids some of the drawbacks of the above elements. The counting of regions, rows, and columns can feel boring. Writing candidate numerals into empty cells can be time-consuming. The what-if approach can be confusing unless you are well organised. The proverbial Holy Grail is to find a technique which minimizes counting, marking up, and rubbing out. 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 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. 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.

sudoku puzzle game and solver by MuddyFunksters

Scanning is performed at the outset and throughout the solution. Scans only have to be performed one time in between analysis periods. Scanning consists of two basic techniques: 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. The world's first live TV sudoku show, 1 July 2005, Sky One.As a one-off, the world's first live TV sudoku show, sudoku Live, was broadcast on 1 July 2005 on Sky One. It was presented by Carol Vorderman. Nine teams of nine players (with one celebrity in each team) representing geographical regions competed to solve a puzzle. Each player had a hand-held device for entering numbers corresponding to answers for four cells. Conferring was permitted although the lack of acquaintance of the players with each other inhibited an analytical discussion. The audience at home was in a separate interactive competition. A Sky One publicity stunt to promote the programme with the world's largest sudoku puzzle went awry when the 275 foot (84 m) square puzzle was found to have 1,905 correct solutions. The puzzle was carved into a hillside in Chipping Sodbury, near Bristol, England, in view of the M4 motorway. The stunt was cleverly timed to coincide with a major road expansion, where an imposed 40 mph speed restriction allowed drivers to safely view the puzzle whilst driving. Another alternative uses finite domain constraint programming. A constraint program specifies the constraints of the puzzle (the fact that every number in each row, each column, and each 3×3 region must be unique, and the provided "givens"); a finite domain solver applies the constraints successively to narrow down the solution space until a solution is found. Backtracking may be applied when alternate values cannot otherwise be excluded. Fill in the grid so that every row, every column, and every 3x3 box contains the digits 1 through 9. In Japanese, the word is pronounced [s??dok?]; in English, it is usually spoken with an Anglicised pronunciation, [s?'d??ku?] (BrE) [s?'do?ku?] (AmE) or ['su?d??ku] (BrE) ['su?do?ku] (AmE) (See IPA, International Phonetic Alphabet for notation usage.) 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] Although the 9×9 grid with 3×3 regions is by far the most common, numerous 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; Daily sudoku features new 4×4, 6×6, and simpler 9×9 grids every day as Daily sudoku for Kids. [1] Even the 9×9 grid is not always standard, with Ebb regularly publishing some of those with nonomino regions (also known as a jigsaw variation); the 2005 U.S. Puzzle Championship had a sudoku with parallelogram regions that wrapped around the outer border of the puzzle, as if the grid were toroidal. Larger grids are also possible, with Daily sudoku's 12×12-grid Monster sudoku [2], 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.

This is a column, 9 cells tall. A filled-in column must have one of each digit. That means that each digit appears only once in the column. There are 9 columns in the grid, and the same applies to each of them. When using marking, additional analysis can be performed. For example, if a digit appears only one time in the mark-ups written inside one region, then it is clear that the digit should be there, even if the cell has other digits marked as well. When using marking, a couple of similar rules applied in a specified order can solve any sudoku puzzle, without performing any kind of backtracking. Here are some of the more notable single-instance variations: 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 strategy for solving a puzzle may be regarded as comprising a combination of three processes: scanning, marking up, and analysing. 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 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.