Sudoku (数独, sūdoku?), also known as Number Place or Nanpure, is a logic-based placement puzzle. The objective is to fill the 9x9 grid so that each column, each row, and each of the nine 3x3 boxes contains the digits 1 to 9. The puzzle setter provides a partially completed grid so that there is only one solution. Completed Sudoku puzzles are a type of Latin square, with an additional constraint on the contents of individual regions. Leonhard Euler is sometimes cited as the source of the puzzle, based on his work with Latin squares. The modern puzzle was invented by an American, Howard Garns, in 1979 and published by Dell Magazines under the name "Number Place". It became popular in Japan in 1986, when it was published by Nikoli and given the name Sudoku. It became an international hit in 2005. Introduction The numerals in Sudoku puzzles are used for convenience; arithmetic relationships between numerals are irrelevant. Any set of distinct symbols will do; letters, shapes, or colours may be used without altering the rules. In fact, ESPN published Sudoku puzzles substituting the positions on a baseball field for the numbers 1–9. Dell Magazines, the puzzle's originator, has been using numerals for Number Place in its magazines since they first published it in 1979. The attraction of the puzzle is that the rules are simple, yet the line of reasoning required to solve the puzzle may be complex. The level of difficulty can be selected to suit the audience. The puzzles are often available free from published sources and may be custom-made using software. There's no right or wrong place to start – but we do have to start somewhere, so let's look at the three boxes at the top of the puzzle.
Look for similar patterns elsewhere. You'll see something similar with the 2s in the stack of boxes down the middle. The top box doesn't have its 2 yet. There is a 2 in each of the center and bottom boxes, so we can rule out five of the seven empty cells in the top box. This is not quite the same situation as before, because there are two places the 2 could go. Some people just guess where the 2 should go, but it is better to use logic. It's best to have a reason why a particular number must go in a particular place. It's time to look in the other direction
– at the rows of the grid, not just the columns. The third grid-row
from the top already has its 2, so we can rule out one extra cell from
the top box. Now there's only one place left for the 2 to go. Sometimes you can build on success. Let's see if that 2 leads us to success in the top-right box. After considering the rows, we can rule out only four of the seven empty cells. Even after considering the columns, we can rule out only five cells, still leaving two places for the 2 to go. Never mind, we learned something about where the 2 can go in the top-right box. In fact, you might like to lightly pencil a small ‘2’ into each of the possible cells. In the Sudoku program these small numbers are called pencilmarks and they can be added and removed very easily. Pencilmarks are useful reminders, but be sparing with them. Using too many can cloud the issues you are trying to clarify.
Solution methods Scanning Cross-hatching: the scanning of rows to
identify which line in a region may contain a certain numeral by a process
of elimination. The process is repeated with the columns. For fastest
results, the numerals are scanned in order of their frequency, from
high to low. It is important to perform this process systematically,
checking all of the digits 1–9. In the subscript notation the candidate
numerals are written in subscript in the cells. Because puzzles printed
in a newspaper are too small to accommodate more than a few subscript
digits of normal handwriting, solvers may create a larger copy of the
puzzle.
In the "what-if" approach (also called "guess-and-check", "bifurcation", "backtracking" and "Ariadne's thread"), a cell with two candidate numerals is selected, and a guess is made. The steps are repeated unless a duplication is found or a cell is left without a possible candidate, in which case the alternative candidate must be the solution. For each cell's candidate, the question is posed: 'will entering a particular numeral prevent completion of the other placements of that numeral?' If the answer is 'yes', then that candidate can be eliminated. The what-if approach requires a pencil and eraser or a good layout memory. There are three kind of conflicts, which can appear during puzzle solving: basic conflicts - there are only N-1 different
candidates in N cell in the area
Many rapid-style solvers employ backtracking searches, with various pruning techniques also being used in order to help reduce the size of the search tree. Rapid solvers are preferred for trial-and-error puzzle-creation algorithms, which allow for testing large numbers of partial problems for validity in a short time; human-style solvers can be employed by hand-crafting puzzlesmiths for their ability to rate the challenge of a created puzzle and show the actual solving process their target audience can be expected to follow. Although vanilla Sudoku puzzles (with 9×9 grid and 3×3 regions) can be solved quickly by computer, the generalization to larger grids is known to be NP-Complete. Various optimisation methods have been proposed for large grids. Details of computer solutions may be found on the page on the Algorithmics of Sudoku.
Most publications sort their Sudoku puzzles into four or five rating levels, although the actual cut-off points and the names of the levels themselves can vary widely. Typically, however, the titles are synonyms of "easy", "intermediate", "hard", and "challenging". An easy puzzle can be solved using only scanning; an intermediate puzzle may take markup to solve; a hard or challenging puzzle will usually take analysis. Another approach is to rely on the experience of a group of human test solvers. Puzzles can be published with a median solving time rather than an algorithmically defined difficulty level.
Nikoli Sudoku are hand-constructed, with the author being credited; the givens are always found in a symmetrical pattern.[13] 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 famously claimed that because they were hand-constructed, their puzzles would contain "imperceptible witticisms" that would be very unlikely in computer-generated Sudoku.
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. 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, The Age and The Sydney Morning Herald this form of puzzle is known as Samurai SuDoku.[16] 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. 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[17] devised by Steve Schaefer has an entire sentence embedded into the puzzle; the Super Wordoku[18] 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 claims this as a feature designed to defeat solving programs. Here are some of the more notable single-instance variations: A three-dimensional Sudoku puzzle was invented
by Dion Church and published in the Daily Telegraph in May 2005. Similar to Sudoku, the goal of the game is to complete a not-completely filled grid, such that each row, each column, and each of the 16 marked 4x4 squares contains each number between 1 and 16 exactly once. With 256 squares, the hexudoku has more than 3 times as many squares as the regular sudoku. Instead of the numbers 1 to 16, sometimes the hexadecimal digits 0-9, a-f are used, or a variant starting at 1: 1-9, a-g. Also a letter-only variant is sometimes used.
The maximum number of givens 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,[24] [25] and 18 with the givens in rotationally symmetric cells.
Within three years Le Siècle's rival, La France, refined the puzzle so that it was almost a modern Sudoku. It simplified the 9×9 magic square puzzle so that each row and column contained only the numbers 1–9, but did not mark the sub-squares. Although they are unmarked, each 3×3 sub-square does indeed comprise the numbers 1–9. However, the puzzle cannot be considered the first Sudoku because, under modern rules, it has two solutions. The puzzle setter ensured a unique solution by requiring 1–9 to appear in both diagonals. These weekly puzzles were a feature of newspaper titles including L'Echo de Paris for about a decade but disappeared about the time of the First World War.[27] According to Will Shortz, the modern Sudoku was most likely designed anonymously by Howard Garns, a 74-year-old retired architect and freelance puzzle constructor, and first published in 1979 by Dell Magazines as Number Place (the earliest known examples of modern Sudoku), because Garns' name was always present on the list of contributors in issues of Dell Pencil Puzzles and Word Games that included Number Place, and was always absent from issues that did not.[10] Sadly, he died in 1989 before getting a chance to see his creation as a worldwide phenomenon.[10] The puzzle was introduced in Japan by Nikoli in the paper Monthly Nikolist in April 1984[10] as Suuji wa dokushin ni kagiru (数字は独身に限る, Suuji wa dokushin ni kagiru?), which can be translated as "the numbers must be single" or "the numbers must occur only once." At a later date, the name was abbreviated to Sudoku by Maki Kaji (鍜治 真起, Kaji Maki?), taking only the first kanji of compound words to form a shorter version.[10] In 1986, Nikoli introduced two innovations: the number of givens was restricted to no more than 32[citation needed], and puzzles became "symmetrical" (meaning the givens were distributed in rotationally symmetric cells).[9] It is now published in mainstream Japanese periodicals, such as the Asahi Shimbun.
In 1997, retired Hong Kong judge Wayne Gould, 59, a New Zealander, saw a partly completed puzzle in a Japanese bookshop. Over six years he developed a computer program to produce puzzles quickly.[28] 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). It was rapidly introduced by The Daily Telegraph, the Daily Mail and The Independent. By April and May 2005 the puzzle became a national phenomenon and was introduced to several other national British newspapers including The Guardian, The Sun (where it was labelled Sun Doku), and The Daily Mirror.[citation needed] The rapid rise of Sudoku in Britain from relative obscurity to a front-page feature in national newspapers attracted commentary in the media and parody (such as when The Guardian's G2 section advertised itself as the first newspaper supplement with a Sudoku grid on every page [29]). 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. On 2 August, the BBC's programme guide Radio Times featured a weekly Super Sudoku. Later in 2005, the BBC launched SUDO-Q, a game show that combines Sudoku with general knowledge. However, it uses only 4x4 and 6x6 puzzles. Early in 2006, Sudoku was brought to a younger generation for the DS, a handheld game console developed and manufactured by Nintendo. Sudoku made a humble feature in Brain Age: Train Your Brain in Minutes a Day!, an educational game developed by Japanese neuroscientist Ryūta Kawashima. With the popularity of sudoku rising, a game called Sudoku Gridmaster was released focusing solely on the logic-based numerical puzzle. At approximately the same time, Sudoku Mania was released. However, compared to the success of the previous two titles, Sudoku Mania received generally negative reviews from gaming critics and gamers. Sudoku is now also a very popular part of the games available for mobile phones. Gameloft, Guardian Unlimited, World Sudoku League and Playcom are some of the distributors. Web Sudoku - Billions of Free Sudoku Puzzles
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by the name of Howard Garnes. His puzzle, termed 'Number Place', ... Free Sudoku Puzzles to Play Online,Jigsaw
Sudoku, Jigsaw puzzle ...Free Sudoku Puzzles to Play Online,Jigsaw Sudoku,Killer
Sudoku. SudokuIn sudoku there are only a few basic
rules. You have to fill in the 9x9 grid so ... If you like sudoku, you'll
love Flip Words, great puzzle solving fun. ... SudokuSudoku is a logic puzzle. It is typically
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find many free sudoku you can print and use ... Science News for Kids: GameZone: SudokuA
sudoku puzzle usually consists of a nine-by-nine grid. Some of the spaces
contain ... You'll find more Sudoku puzzles at http://www.websudoku.com/.
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