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Deep Throat

The term Deep Throat has several meanings:

  • Deep Throat is a 1972 pornographic movie. This is the origin of all the other meanings of the term.
  • Deep throating is a sexual act, a type of fellatio depicted in the movie.
  • Deep Throat was the name given to the source in the Washington Post investigation of the Watergate scandal, revealed on May 31, 2005 to be former FBI associate director W. Mark Felt.
  • In general, the term Deep Throat has since been used for secret inside informers or whistleblowers.
  • Deep Throat is the pseudonym of several fictional characters who have acted as a whistleblower:
    • Deep Throat in the television series The X-Files.
    • Deep Throat is the alias of a character in Metal Gear Solid.
  • Deep Throat or Win32.DeepThroat is a computer virus
  • Inside Deep Throat is a 2005 documentary about the 1972 movie.

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The term Deep Throat has several meanings:. CBS has run several stories concerning Sudoku, including on the Early Show in Summer 2005, and on the CBS Evening News that autumn, on October 26. Inside Deep Throat is a 2005 documentary about the 1972 movie. 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. Deep Throat or Win32.DeepThroat is a computer virus. The puzzle was carved into a hillside in Chipping Sodbury, near Bristol, England, in view of the M4 motorway. Deep Throat is the alias of a character in Metal Gear Solid. 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.

Deep Throat in the television series The X-Files. The audience at home was in a separate interactive competition. Deep Throat is the pseudonym of several fictional characters who have acted as a whistleblower:

    . Conferring was permitted although the lack of acquaintance of the players with each other inhibited an analytical discussion. In general, the term Deep Throat has since been used for secret inside informers or whistleblowers. Each player had a hand-held device for entering numbers corresponding to answers for four cells. Mark Felt. Nine teams of nine players (with one celebrity in each team) representing geographical regions competed to solve a puzzle.

    Deep Throat was the name given to the source in the Washington Post investigation of the Watergate scandal, revealed on May 31, 2005 to be former FBI associate director W. It was presented by Carol Vorderman. Deep throating is a sexual act, a type of fellatio depicted in the movie. As a one-off, the world's first live TV Sudoku show, Sudoku Live, was broadcast on 1 July 2005 on Sky One. This is the origin of all the other meanings of the term. On 2 August 2005 the BBC's programme guide Radio Times started to feature a weekly Super Sudoku. Deep Throat is a 1972 pornographic movie. From July 2005 Channel 4 included a daily Sudoku game in their Teletext service (at page 391).

    Recognizing the different psychological appeals of easy and difficult puzzles The Times introduced both side by side on 20 June 2005. A simpler explanation is that the puzzle attracts and retains readers—Sudoku players report an increasing sense of satisfaction as a puzzle approaches completion. 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. 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 [16]).

    Newspapers competed to promote their Sudoku puzzles, with The Times and the Daily Mail each claiming to have been the first to feature Sudoku. As the name Sudoku became well-known in Britain, the Daily Mail adopted it in place of its earlier name "Codenumber". 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. 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.

    Until then the Times had kept very quiet about the huge daily interest that its daily Sudoku competition had aroused. The Telegraph continued to splash the puzzle on its front page, realizing that it was gaining sales simply by its presence. 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 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".

    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 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. Three days later The Daily Mail began to publish the puzzle under the name "Codenumber". The puzzles by Pappocom, Gould's software house, have been printed daily in the Times ever since.

    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). Over 6 years he developed a computer program to produce puzzles quickly. In 1997, retired Hong Kong judge Wayne Gould, 59, a New Zealander, saw a partly completed puzzle in a Japanese bookshop. Sudoku has been called the "Rubik's cube of the 21st century".

    Within the context of puzzle history, parallels are often cited to Rubik's Cube, another logic puzzle popular in the 1980s. It is also often included in puzzle anthologies, such as The Giant 1001 Puzzle Book (under the title Nine Numbers). Additionally, Kappa reprints Nikoli Sudoku in GAMES Magazine under the name Squared Away; the New York Post, USA Today, The Boston Globe, Washington Post, and San Francisco Chronicle now also publish the puzzle. 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.

    Yoshimitsu Kanai published his computerized puzzle generator under the name Single Number for the Apple Macintosh [13] in 1995 in Japanese and English, for the Palm (PDA) [14] in 1996, and for the Mac OS-X [15] in 2005. At least one publisher still uses that title. In 1989, Loadstar/Softdisk Publishing published DigitHunt on the Commodore 64, which was apparently the first home computer version of Sudoku. Within Japan, Nikoli still holds the trademark for the name Sudoku; other publications in Japan use alternative names.

    It is now published in mainstream Japanese periodicals, such as the Asahi Shimbun. 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). At a later date, the name was abbreviated to Sudoku (数独, pronounced SUE-dough-coo; sū = number, doku = single); it is a common practice in Japanese to take only the first kanji of compound words to form a shorter version. The puzzle was named by Kaji Maki (鍜治 真起), the president of Nikoli.

    The puzzle was introduced in Japan by Nikoli in the paper Monthly Nikolist in April 1984 as Suuji wa dokushin ni kagiru (数字は独身に限る), which can be translated as "the numbers must be single" or "the numbers must occur only once" (独身 literally means "single; celibate; unmarried"). 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). 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 designed by Howard Garns, a retired architect and freelance puzzle constructor, and first published in 1979.

    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 [11] [12], and 18 with the givens in rotationally symmetric cells. Since this applies to Latin squares in general, most variants of Sudoku have the same maximum. 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. The number of valid Sudoku solution grids for the 16×16 derivation is not known.

    Russell and Jarvis also showed that when symmetries were taken into account, there were 5,472,730,538 solutions [10] (sequence A109741 in OEIS). The derivation of this result was considerably simplified by analysis provided by Frazer Jarvis and the figure has been confirmed independently by Ed Russell. The result was derived through logic and brute force computation. This number is equal to 9! × 722 × 27 × 27,704,267,971, the last factor of which is prime.

    Nonetheless, the number of valid Sudoku solution grids for the standard 9×9 grid was calculated by Bertram Felgenhauer in 2005 to be 6,670,903,752,021,072,936,960 [9] (sequence A107739 in OEIS). There are significantly fewer valid Sudoku solution grids than Latin squares because Sudoku imposes the additional regional constraint. A valid Sudoku solution grid is also a Latin square. 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.

    In this case, two distinct vertices labelled by and are joined by an edge if and only if:. The vertices can be labelled with the ordered pairs , where x and y are integers between 1 and 9. The graph in question has 81 vertices, one vertex for each cell of the grid. 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.

    Solving Sudoku puzzles (as well as any other NP-hard problem) can be expressed as a graph colouring problem. This gives some indication of why Sudoku is difficult to solve, although on boards of finite size the problem is finite and can be solved by a deterministic finite automaton that knows the entire game tree. The general problem of solving Sudoku puzzles on n2 x n2 boards of n x n blocks is known to be NP-complete [8]. Here are some of the more notable single-instance variations:.

    Top Notch claim this as a feature designed to defeat solving programs. 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. The Code Doku [6] devised by Steve Schaefer has an entire sentence embedded into the puzzle; the Super Wordoku [7] from Top Notch embeds two 9-letter words, one on each diagonal. Recent variants have just that, often in the form of a word reading along a main diagonal once solved; determining the word in advance can be viewed as a solving aid.

    Alphabetical variations have also emerged; there is no functional difference in the puzzle unless the letters spell something. Sequential grids, as opposed to overlapping, are also published, with values in specific locations in grids needing to be transferred to others. Often, no givens are to be found in overlapping regions. [5] Puzzles with twenty or more overlapping grids are not uncommon in some Japanese publications.

    In The Times and The Sydney Morning Herald this form of puzzle is known as Samurai SuDoku. 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. Puzzles constructed from multiple Sudoku grids are common. Some such variants forsake standard givens entirely.

    Other kinds of extra restrictions can be mathematical 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. [3] [4] In this variant, all the numbers must appear in all the concentric rings as well as in all pairs of adjacent wedges. Also found is the Circular Sudoku, also known as Target Sudoku, invented by Essex mathematician Peter Higgins. 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.

    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. 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. 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. Another common variant is for additional restrictions to be enforced on the placement of numbers beyond the usual row, column, and region requirements.

    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. Puzzle Championship had a Sudoku with parallelogram regions that wrapped around the outer border of the puzzle, as if the grid were toroidal. [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. 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.

    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. 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 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. Dell Number Place Challenger (see Variants below) puzzles also list authors .

    Nikoli Sudoku are hand-constructed, with the author being credited; the givens are always found in a symmetrical pattern. 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. 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. They also have no authoring credits — that is, the name of the constructor is not printed with any puzzle.

    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. Building a Sudoku with symmetrical givens is a simple matter of placing the undefined givens in a symmetrical pattern to begin with. (This technique is adaptable to composing puzzles other than Sudoku as well.) Great caution is required, however, as failing to recognize where a number can be logically deduced at any point in construction—regardless of how tortuous that logic may be—can result in an unsolvable puzzle when defining a future given contradicts what has already been built. This technique gives the constructor greater control over the flow of puzzle solving, leading the solver along the same path the compiler used in building the puzzle.

    Such an undefined given can be assumed to not hold any particular value as long as it is given a different value before construction is completed; the solver will be able to make the same deductions stemming from such assumptions, as at that point the given is very much defined as something else. Building a Sudoku puzzle by hand can be performed efficiently by pre-determining the locations of the givens and assigning them values only as needed to make deductive progress. 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. Some online versions offer several difficulty levels.

    This estimation allows publishers to tailor their Sudoku puzzles to audiences of varied solving experience. Computer solvers can estimate the difficulty for a human to find the solution, based on the complexity of the solving techniques required. It is based on the relevance and the positioning of the numbers rather than the quantity of the numbers. 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.

    Perhaps surprisingly, the number of givens has little or no bearing on a puzzle's difficulty. Published puzzles often are ranked in terms of difficulty. A very fast solver is usually required for most trial-and-error puzzle-creation algorithms. This is the method now preferred by many Sudoku programmers, mainly by virtue of its speed.

    This method can be directly applied to solving Sudoku problems, counting all possible solutions for most puzzles rapidly. A highly efficient way of solving such constraint problems is Donald Knuth's Dancing Links Algorithm. Backtracking may be applied when alternate values cannot otherwise be excluded. 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.

    Another alternative uses finite domain constraint programming. 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. 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). 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).

    This continues until a conflict occurs, in which case the next alternative value is used for the last cell changed. 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. It is also fairly simple to build a backtracking search. Given the self-imposed constraints of most Sudoku publishers, this method generally succeeds.

    These programs emulate the human logic to solve a puzzle without resorting to guesses. For most computer programmers, coding the search for cell values based on elimination, contingencies and multiple contingencies (required for harder Sudoku) is relatively straightforward. The proverbial Holy Grail is to find a technique which minimises counting, marking up, and rubbing out. The what-if approach can be confusing unless you are well organised.

    Writing candidate numbers into empty cells can be time-consuming. The counting of regions, rows, and columns can feel boring. Ideally one needs to find a combination of techniques which avoids some of the drawbacks of the above elements. The two main approaches to analysis are "candidate elimination" and "what-if".

    When using marking, a couple of similar rules applied in a specified order can solve any Sudoku puzzle, without performing any kind of backtracking. 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, additional analysis can be performed. When only one marking is missing, that has to be the value of the cell.

    Thus a cell will start empty and as more constraints become known it will slowly fill. An alternative technique that some find easier is to mark up those numbers that a cell cannot be. There are two popular notations: subscripts and dots. Many find it useful to guide this analysis by marking candidate numbers in the blank cells.

    From this point, it is necessary to engage in some logical analysis. Scanning stops when no further numbers can be discovered. 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. 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).

    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). Advanced solvers look for "contingencies" while scanning—that is, narrowing a number's location within a row, column, or region to two or three cells. Scanning consists of two basic techniques:. Scans may have to be performed several times in between analysis periods.

    Scanning is performed at the outset and periodically throughout the solution. The strategy for solving a puzzle may be regarded as comprising a combination of three processes: scanning, marking up, and analysing. Each number 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 goal is to fill in the empty cells, one number in each, so that each column, row, and region contains the numbers 1–9 exactly once.

    Some cells already contain numbers, known as "givens" (or sometimes as "clues"). The puzzle is most frequently a 9×9 grid, made up of 3×3 subgrids called "regions" (other terms include "boxes", "blocks", and the like when referring to the standard variation; even "quadrants" is sometimes used, despite this being an inaccurate term for a 9×9 grid). The puzzles are often available free from published sources and also may be custom-generated using software. The level of difficulty of the puzzles can be selected to suit the audience.

    Sudoku is recommended by some teachers as an exercise in logical reasoning. The attraction of the puzzle is that the completion rules are simple, yet the line of reasoning required to reach the completion may be complex. Numerals are used throughout this article. Dell Magazines, the puzzle's originator, has been using numerals for Number Place in its magazines since they first published it in 1979.

    Any set of distinct symbols will do; letters, shapes, or colours may be used without altering the rules (Penny Press' Scramblets and Knight Features Syndicate's Sudoku Word both use letters). The numerals in Sudoku puzzles are used for convenience; arithmetic relationships between numerals are absolutely irrelevant. In Japanese, the word is pronounced [sɯːdokɯ]; in English, it is usually spoken with an Anglicised pronunciation, [səˈdəʊkuː] (BrE) [səˈdoʊkuː] (AmE) (suh-DOE-koo) or [ˈsuːdəʊku] (BrE) [ˈsuːdoʊku] (AmE) (SOO-doe-koo). title.

    S. Other Japanese publishers refer to the puzzle as Nanpure (Number Place), the original U. Ltd in Japan. The name Sudoku is the Japanese abbreviation of a longer phrase, "suji wa dokushin ni kagiru (数字は独身に限る)," meaning "the digits must remain single"; it is a trademark of puzzle publisher Nikoli Co.

    . The first world championship will be in Lucca(Italy) from 10 to 12 March 2006. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. S.

    Although first published in a U. Completing the puzzle requires patience and logical ability. Each row, column, and region must contain only one instance of each numeral. The aim of the canonical 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").

    Sudoku (Japanese: 数独, sūdoku), sometimes spelled Su Doku, is a logic-based placement puzzle, also known as Number Place in the United States. and . or,. or,.

    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. 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. The 2005 U.S. A three-dimensional Sudoku puzzle was invented by Dion Church and published in the Daily Telegraph in May 2005.

    This approach may be frowned on by logical purists as trial and error (and most published puzzles are built to ensure that it will never be necessary to resort to this tactic,) but it can arrive at solutions fairly rapidly. The what-if approach requires a pencil and eraser. Nishio is a limited form of this approach: for each candidate for a cell, the question is posed: will entering a particular number prevent completion of the other placements of that number? If the answer is yes, then that candidate can be eliminated. In logical terms, this is known as reductio ad absurdum.

    The steps above are repeated unless a duplication is found or a cell is left with no possible candidate, in which case the alternative candidate is the solution. In the what-if approach, a cell with only two candidate numbers is selected, and a guess is made. For example, if (p,q) can only appear in 2 cells (within a specific row, column, region scope), other candidates in the 2 cells can be eliminated. Other candidates in the matched cells can be eliminated.

    A second related principle is also true — if each cell within a set of cells (in a row, column or region scope) contains the same set of candidate numbers, and if the number of cells is equal to the quantity of candidate numbers, the cells and numbers are matched and only those numbers can appear in matched cells. The principle is true for all quantities of candidate numbers. This principle also works with candidate number subsets—if three cells have candidates (p,q,r), (p,q), and (q,r) or even just (p,r), (q,r), and (p,q), all of the set (p,q,r) elsewhere in the scope can be deleted. The placement of these numbers anywhere else in the matching scope would make a solution for the matched cells impossible; thus, the candidate numbers (p,q,r) appearing in unmatched cells in the row, column or region scope can be deleted.

    For example, cells are said to be matched within a particular row, column, or region (scope) if two cells contain the same pair of candidate numbers (p,q) and no others, or if three cells contain the same triplet of candidate numbers (p,q,r) and no others. Cells with identical sets of candidate numbers are said to be matched if the quantity of candidate numbers in each is equal to the number of cells containing them; essentially, these are perfectly coincident contingencies. One of the most common elimination tactics is "unmatched candidate deletion". If these patterns can be identified, elimination of candidate possibilities external to the grid framework can sometimes be achieved.

    Only certain "closed circuit" or "n×n grid" possibilities exist (which have acquired peculiar names such as "X-wing" and "Swordfish", among others; see List of Sudoku terms and jargon for more information). Each set of candidate numbers, 1–9, must ultimately be in an independently self-consistent pattern. This is the basis for advanced analysis techniques that require inspection of the entire set of possibilities for a given candidate number. A given set of n cells in any particular block, row, or column can only accommodate n different numbers. This is the basis for the "unmatched candidate deletion" technique, discussed below. There are a number of elimination tactics, all of which are based on the simple rules given above, which have important and useful corollaries, including:


      After each answer has been achieved, another scan may be performed—usually checking to see the effect of the latest number. In elimination, progress is made by successively eliminating candidate numbers from one or more cells to leave just one choice. Using a pencil would then be recommended. Dexterity is required in placing the dots, since misplaced dots or inadvertent marks inevitably lead to confusion and may not be easy to erase without adding to the confusion.

      The dot notation has the advantage that it can be used on the original puzzle. The second notation is a pattern of dots with a dot in the top left hand corner representing a 1 and a dot in the bottom right hand corner representing a 9. If using the subscript notation, solvers often create a larger copy of the puzzle or employ a sharp or mechanical pencil. 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.

      In the subscript notation the candidate numbers are written in subscript in the cells. 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. Counting 1–9 in regions, rows, and columns to identify missing numbers. Counting based upon the last number discovered may speed up the search. It is important to perform this process systematically, checking all of the digits 1–9.

      For fastest results, the numbers are scanned in order of their frequency. This process is then repeated with the columns (or rows). Cross-hatching: the scanning of rows (or columns) to identify which line in a particular region may contain a certain number by a process of elimination.

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