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It is commonly believed that Dell Number Place puzzles are computer-generated; they typically have over 30 givens placed in an apparently random scatter, some of which can possibly be deduced from other givens. They also have no authoring credits — that is, the name of the constructor is not printed with any puzzle. Wei-Hwa Huang claims that he was commissioned by Dell to write a Number Place puzzle generator in the winter of 2000; prior to that, he was told, the puzzles were hand-made. The puzzle generator was written with Visual C++, and although it had options to generate a more Japanese-style puzzle, with symmetry constraints and fewer numbers, Dell opted not to use those features, at least not until their recent publication of Sudoku-only magazines. 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 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. 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. Sudoku is recommended by some teachers as an exercise in logical reasoning. 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. 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.

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. Fill in the grid so that every row, every column, and every 3x3 box contains the digits 1 through 9. The attraction of the puzzle is that the rules are simple, yet the line of reasoning required to reach the solution may be complex The attraction of the puzzle is that the rules are simple, yet the line of reasoning required to reach the solution may be complex 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. The Daily Mail also features Super Sudoku X in its Weekend magazine: an 8×8 grid in which rows, columns, main diagonals, 2×4 blocks and 4×2 blocks contain each number once. Another dimension in use is digits with the same relative location within their respective regions; such puzzles are usually printed in colour, with each disjoint group sharing one colour for clarity. Also found is the Circular Sudoku, also known as Target Sudoku, invented by Essex mathematician Peter Higgins. [3] [4] In this variant, all the numbers must appear in all the concentric rings as well as in all pairs of adjacent wedges. Fill in the grid so that every row, every column, and every 3x3 box contains the digits 1 through 9. Solving Sudoku puzzles (as well as any other NP-hard problem) can be expressed as a graph colouring problem. The aim of the puzzle in its standard form is to construct a proper 9-colouring of a particular graph, given a partial 9-colouring. The graph in question has 81 vertices, one vertex for each cell of the grid. The vertices can be labelled with the ordered pairs , where x and y are integers between 1 and 9. In this case, two distinct vertices labelled by and are joined by an edge if and only if:or, or, and There's no math involved, the grid has numbers, but nothing has to add up to anything else.

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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. 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. 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. 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". 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. 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: 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 Solving Sudoku puzzles (as well as any other NP-hard problem) can be expressed as a graph colouring problem. The aim of the puzzle in its standard form is to construct a proper 9-colouring of a particular graph, given a partial 9-colouring. The graph in question has 81 vertices, one vertex for each cell of the grid. The vertices can be labelled with the ordered pairs , where x and y are integers between 1 and 9. In this case, two distinct vertices labelled by and are joined by an edge if and only if:or, or, and 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.

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 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). The two main approaches to analysis are "candidate elimination" and "what-if". 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. 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. 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. The Daily Mail also features Super Sudoku X in its Weekend magazine: an 8×8 grid in which rows, columns, main diagonals, 2×4 blocks and 4×2 blocks contain each number once. Another dimension in use is digits with the same relative location within their respective regions; such puzzles are usually printed in colour, with each disjoint group sharing one colour for clarity. Also found is the Circular Sudoku, also known as Target Sudoku, invented by Essex mathematician Peter Higgins. [3] [4] In this variant, all the numbers must appear in all the concentric rings as well as in all pairs of adjacent wedges. Other kinds of extra restrictions can be arithmetical in nature, such as requiring the numbers in delineated segments of the grid to have specific sums or products (an example of the former being Killer su doku in The Times), demarcating all places arithmetically adjacent digits appear orthogonally adjacent in the grid, providing the parity of all cells, requiring the Lo Shu Square to appear in the solution, and so on. Some such variants forsake standard givens entirely. Others like Magic Sudoku [5] adds some restrictions (diagonals from 1 to 9, and colors) to the standard sudoku to solve it with less numbers. Michael Metcalf reportedly created a 100×100 Sudoku puzzle, published to the "Sudokuworld" Yahoo! group.