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Hur löser man en svår sudoku

Sudoku

Logic-based number-placement puzzle

Not to be confused with Sodoku (the disease).

A typical Sudoku puzzle

The solution to the puzzle above

Sudoku (; Japanese: 数独, romanized: sūdoku, lit. 'digit-single'; originally called Number Place)[1] fryst vatten a logic-based,[2][3]combinatorial[4] number-placement puzzle.

In classic Sudoku, the objective fryst vatten to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.

French newspapers featured variations of the Sudoku puzzles in the 19th century, and the puzzle has appeared since 1979 in puzzle books beneath the name Number Place.[5] However, the modern Sudoku only began to gain widespread popularity in 1986 when it was published bygd the Japanese puzzle company Nikoli beneath the name Sudoku, meaning "single number".[6] It first appeared in a U.S.

newspaper, and then The Times (London), in 2004, thanks to the efforts of Wayne Gould, who devised a computer schema to rapidly producera unique puzzles.

History

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Predecessors

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Number puzzles appeared in newspapers in the late 19th century, when French puzzle setters began experimenting with removing numbers from magic squares.

Le Siècle, a Paris daglig, published a partially completed 9×9 magic square with 3×3 subsquares on November 19, 1892.[7] It was not a Sudoku because it contained double-digit numbers and required arithmetic rather than logic to solve, but it shared key characteristics: each row, column, and subsquare added up to the same number.

On July 6, 1895, Le Siècle's rival, La France, refined the puzzle so that it was almost a modern Sudoku and named it carré magique diabolique ('diabolical magic square').

It simplified the 9×9 magic square puzzle so that each row, column, and broken diagonals contained only the numbers 1–9, but did not mark the subsquares. Although they were unmarked, each 3×3 subsquare did indeed comprise the numbers 1–9, and the additional constraint on the broken diagonals led to only one solution.[8]

These weekly puzzles were a feature of French newspapers such as L'Écho dem Paris for about a decade, but disappeared about the time of World War I.[9]

Modern Sudoku

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The modern Sudoku was most likely designed anonymously bygd Howard Garns, a 74-year-old retired architect and freelance puzzle constructor from Connersville, Indiana, and first published in 1979 bygd Dell Magazines as Number Place (the earliest known examples of modern Sudoku).[1] 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] He died in 1989 before getting a chance to see his creation as a worldwide phenomenon.[10] Whether or not Garns was familiar with any of the French newspapers listed above fryst vatten unclear.

The puzzle was introduced in Japan bygd Maki Kaji (鍜治 真起, Kaji Maki), president of the Nikoli puzzle company, in the paper Monthly Nikolist in April 1984[10] as Sūji wa dokushin ni kagiru (数字は独身に限る), which can be translated as "the digits must be single", or as "the digits are limited to one occurrence" (In Japanese, dokushin means an "unmarried person").

The name was later abbreviated to Sudoku (数独), taking only the first kanji of compound words to form eller gestalt a shorter version.[10] "Sudoku" fryst vatten a registered trademark in Japan[11] and the puzzle fryst vatten generally referred to as Number Place (ナンバープレース, Nanbāpurēsu) or, more informally, a shortening of the two words, Num(ber) Pla(ce) (ナンプレ, Nanpure).

In 1986, Nikoli introduced two innovations: 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 fryst vatten now published in mainstream Japanese periodicals, such as the Asahi Shimbun.

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In 1997, Hong Kong judge Wayne Gould saw a partly completed puzzle in a Japanese bookshop. Over six years, he developed a computer schema to producera unique puzzles rapidly.[5] 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 November 12, 2004 (calling it Su Doku).

The first letter to The Times regarding Su Doku was published the following day on November 13 from Ian Payn of Brentford, complaining that the puzzle had caused him to miss his stop on the tube.[12] Sudoku puzzles rapidly spread to other newspapers as a regular feature.[5][13]

The rapid rise of Sudoku in Britain from relative obscurity to a front-page feature in national newspapers attracted commentary in the media and parodi (such as when The Guardian'sG2 section advertised itself as the first newspaper supplement with a Sudoku grid on every page).[14] Recognizing the different psychological appeals of easy and difficult puzzles, The Times introduced both, side bygd side, on June 20, 2005.

From July 2005, kanal 4 included a daglig Sudoku game in their teletext service. On August 2, the BBC's schema guide Radio Times featured a weekly Super Sudoku with a 16×16 grid.

In the United States, the first newspaper to publish a Sudoku puzzle bygd Wayne Gould was The Conway daglig Sun (New Hampshire), in 2004.[15]

The world's first live TV Sudoku show, Sudoku Live, was a puzzle contest first broadcast on July 1, 2005, on Sky One.

It was presented bygd julsång 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 kvartet cells. Phil Kollin of Winchelsea, England, was the series grand prize winner, taking home over £23,000 over a series of games.

The audience at home was in a separate interactive competition, which was won bygd Hannah Withey of Cheshire.

Later in 2005, the BBC launched SUDO-Q, a game show that combined Sudoku with general knowledge.

Mycket svår Sudoku.

However, it used only 4×4 and 6×6 puzzles. kvartet seasons were produced before the show ended in 2007.

In 2006, a Sudoku website published songwriter Peter Levy's Sudoku tribute song,[16] but quickly had to take down the MP3 en samling dokument eller en elektronisk lagring av data due to heavy traffic. The Japanese Embassy also nominated the song for an award, with Levy doing talks with Sony in Japan to release the song as a single.[17]

Sudoku software fryst vatten very popular on PCs, websites, and mobile phones.

It comes with many distributions of Linux. The software has also been released on film game consoles, such as the Nintendo DS, PlayStation Portable, the Game Boy Advance, Xbox Live arkad, the Nook e-book reader, Kindle Fire platta, several iPod models, and the iPhone. Many Nokia phones also had Sudoku. In fact, just two weeks after Apple Inc. debuted the online App Store within its iTunes Store on July 11, 2008, nearly 30 different Sudoku games were already in it, created bygd various software developers, specifically for the iPhone and iPod Touch.

One of the most popular film games featuring Sudoku fryst vatten Brain Age: tåg Your Brain in Minutes a Day!. Critically and commercially well-received, it generated particular beröm for its Sudoku implementation[18][19][20] and sold more than 8 million copies worldwide.[21] Due to its popularity, Nintendo made a second Brain Age game titled Brain Age2, which has over 100 new Sudoku puzzles and other activities.

In June 2008, an Australian drugs-related jury rättegång kostnadsberäkning over A$ 1 million was aborted when it was discovered that kvartet or fem of the twelve jurors had been playing Sudoku instead of listening to the evidence.[22]

Variants

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Variations of grid sizes or område shapes

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Although the 9×9 grid with 3×3 regions fryst vatten bygd far the most common, many other variations exist.

Sample puzzles can be 4×4 grids with 2×2 regions; 5×5 grids with pentomino regions have been published beneath the name Logi-5; the World Puzzle Championship has featured a 6×6 grid with 2×3 regions and a 7×7 grid with six heptomino regions and a disjoint område. Larger grids are also possible, or different irregular shapes (under various names such as Suguru, Tectonic, Jigsaw Sudoku etc.).

The Times offers a 12×12-grid "Dodeka Sudoku" with 12 regions of 4×3 squares. Dell Magazines regularly publishes 16×16 "Number Place Challenger" puzzles (using the numbers 1–16 or the letters A-P). Nikoli offers 25×25 "Sudoku the Giant" behemoths. A 100×100-grid puzzle dubbed Sudoku-zilla was published in 2010.[23]

Mini Sudoku

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Under the name "Mini Sudoku", a 6×6 variant with 3×2 regions appears in the American newspaper USA Today and elsewhere.

The object fryst vatten the same as that of standard Sudoku, but the puzzle only uses the numbers 1 through 6. A similar struktur, for younger solvers of puzzles, called "The Junior Sudoku", has appeared in some newspapers, such as some editions of The daglig Mail.

Imposing additional constraints

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Another common variant fryst vatten to add limits on the placement of numbers beyond the usual row, column, and låda requirements.

Often, the limit takes the form eller gestalt of an extra "dimension"; the most common fryst vatten to require the numbers in the main diagonals of the grid to also be unique. The aforementioned "Number Place Challenger" puzzles are all of this variant, as are the Sudoku X puzzles in The daglig Mail, which use 6×6 grids.

Killer sudoku

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A Killer Sudoku puzzle

And its solution

Main article: Killer sudoku

The killer sudoku variant combines elements of sudoku and kakuro.

A killer sudoku puzzle fryst vatten made up of 'cages', typically depicted bygd boxes outlined with dashes or colours. The sum of the numbers in a cage fryst vatten written in the top left corner of the cage, and numbers cannot be repeated in a cage.

Other variants

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Puzzles constructed from more than two grids are also common.

fem 9×9 grids that overlap at the corner regions in the shape of a quincunx fryst vatten known in Japan as Gattai 5 (five merged) Sudoku. In The Times, The Age, and The Sydney Morning Herald, this struktur of puzzle fryst vatten known as Samurai Sudoku. The Baltimore Sun and the Toronto Star publish a puzzle of this variant (titled High Five) in their Sunday edition.

Often, no givens are placed in the overlapping regions. Sequential grids, as opposed to overlapping, are also published, with values in specific locations in grids needing to be transferred to others.

A tabletop utgåva of Sudoku can be played with a standard 81-card Set deck (see Set game). A three-dimensional Sudoku puzzle was published in The daglig Telegraph in May 2005.

The Times also publishes a three-dimensional utgåva beneath the name Tredoku. Also, a Sudoku utgåva of the Rubik's Cube fryst vatten named Sudoku Cube.

Many other variants have been developed.[24][25][26] Some are different shapes in the arrangement of overlapping 9×9 grids, such as butterfly, windmill, or flower.[27] Others vary the logic for solving the grid.

Genom för att sammanföra flera tekniker är kapabel ni öka chanserna för att åtgärda en utmanande Sudoku-pussel.

One of these fryst vatten "Greater Than Sudoku". In this, a 3×3 grid of the Sudoku fryst vatten given with 12 symbols of Greater Than (>) or Less Than (<) on the common line of the two adjacent numbers.[10] Another variant on the logic of the solution fryst vatten "Clueless Sudoku", in which nine 9×9 Sudoku grids are each placed in a 3×3 array.

The center fängelse in each 3×3 grid of all nine puzzles fryst vatten left blank and forms a tenth Sudoku puzzle without any fängelse completed; hence, "clueless".[27] Examples and other variants can be funnen in the Glossary of Sudoku.

Mathematics of Sudoku

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Main article: Mathematics of Sudoku

This section refers to classic Sudoku, disregarding jigsaw, hyper, and other variants.

A completed Sudoku grid fryst vatten a special type of Latin square with the additional property of no repeated values in any of the nine blocks (or boxes of 3×3 cells).[28]

The general bekymmer of solving Sudoku puzzles on n2×n2 grids of n×n blocks fryst vatten known to be NP-complete.[29] Many Sudoku solving algorithms, such as brute force-backtracking and dancing links can solve most 9×9 puzzles efficiently, but combinatorial explosion occurs as n increases, creating practical limits to the properties of Sudokus that can be constructed, analyzed, and solved as n increases.

A Sudoku puzzle can be expressed as a graph coloring problem.[30] The aim fryst vatten to construct a 9-coloring of a particular graph, given a partial 9-coloring.

The fewest clues possible for a proper Sudoku fryst vatten 17.[31] Tens of thousands of distinct Sudoku puzzles have only 17 clues.[32]

The number of classic 9×9 Sudoku solution grids fryst vatten 6,670,903,752,021,072,936,960, or around 6.67×1021.[33] The number of essentially different solutions, when symmetries such as cirkelrörelse, reflection, permutation, and relabelling are taken into konto, fryst vatten much smaller, 5,472,730,538.[34]

Unlike the number of complete Sudoku grids, the number of minimal 9×9 Sudoku puzzles fryst vatten not precisely known.

(A minimal puzzle fryst vatten one in which no clue can be deleted without losing the uniqueness of the solution.) However, statistical techniques combined with a puzzle elektrisk maskin show that about (with 0.065% relative error) 3.10 × 1037 minimal puzzles and 2.55 × 1025 nonessentially equivalent minimal puzzles exist.[35]

Competitions

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  • The first World Sudoku Championship was held in Lucca, Italy, from March 10 to 11, 2006.

    The winner was Jana Tylová of the Czech Republic.[36] The competition included numerous variants.[37]

  • The second World Sudoku Championship was held in Prague, Czech Republic, from March 28 to April 1, 2007.[38] The individual mästare was Thomas Snyder of the US. The grupp mästare was Japan.[39]
  • The third World Sudoku Championship was held in Goa, India, from April 14 to 16, 2008.

    Thomas Snyder repeated as the individual overall mästare and also won the first-ever Classic Trophy (a subset of the competition counting only classic Sudoku). The Czech Republic won the grupp competition.[40]

  • The fourth World Sudoku Championship was held in Žilina, Slovakia, from April 24 to 27, 2009. After past mästare Thomas Snyder of the US won the general qualification, Jan Mrozowski of Poland emerged from a 36-competitor playoff to become the new World Sudoku mästare.

    Host nation Slovakia emerged as the top grupp in a separate competition of three-membered squads.[41]

  • The fifth World Sudoku Championship was held in Philadelphia, Pennsylvania, from April 29 to May 2, 2010. Jan Mrozowski of Poland successfully defended his world title in the individual competition, while Germany won a separate grupp event.

    The puzzles were written bygd Thomas Snyder and Wei-Hwa Huang, both past U.S. Sudoku champions.[42]

  • The 12th World Sudoku Championship (WSC) was held in Bangalore, India, from October 15 to 22, 2017. Kota Morinishi of Japan won the Individual WSC and China won the grupp event.[43]
  • The 13th World Sudoku Championship took place in the Czech Republic.[44]
  • In the United States, The Philadelphia Inquirer Sudoku National Championship has been held three times, each time offering a $10,000 prize to the advanced division winner and a prick on the U.S.

    National Sudoku grupp traveling to the world championships. The winners of the event were Thomas Snyder (2007),[45] Wei-Hwa Huang (2008), and Tammy McLeod (2009).[46] In the 2009 event, the third-place finalist in the advanced division, Eugene Varshavsky, performed ganska poorly onstage after setting a very fast kvalificerande time on paper, which caught the attention of organizers and competitors including past mästare Thomas Snyder, who requested organizers reconsider his results due to a suspicion of cheating.[47] Following an investigation and a retest of Varshavsky, the organizers disqualified him and awarded the third-place to Chris Narrikkattu.[48]

See also

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References

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  1. ^ abGrossman, Lev (Mar 11, 2013).

    "The Answer Men". Time. New York. Archived from the original on 2013-03-01. Retrieved 2013-03-04.(registration required)

  2. ^Arnoldy, Ben. "Sudoku Strategies". The Christian Science Monitor.
  3. ^Schaschek, Sarah (Mar 22, 2006).

    Hur man löser svåra sudoku - sudoku-trick.

    "Sudoku champ's surprise victory". The Prague Post. Archived from the original on 2006-08-13. Retrieved 2009-02-18.

  4. ^Gradwohl, Ronen; Naor, Moni; Pinkas, Benny; Rothblum, Guy N. (2007). "Cryptographic and Physical Zero-Knowledge Proof Systems for Solutions of Sudoku Puzzles". In Crescenzi, Pierluigi; Prencipe, Giuseppe; Pucci, Geppino (eds.).

    Fun with Algorithms, 4th International Conference, FUN 2007, Castiglioncello, Italy, June 3-5, 2007, Proceedings. Lecture Notes in Computer Science. Vol. 4475. Springer. pp. 166–182. doi:10.1007/978-3-540-72914-3_16. ISBN .

  5. ^ abcSmith, David (May 15, 2005). "So you thought Sudoku came from the nation of the Rising Sun ..."The Observer.

    Retrieved 2008-06-13.

  6. ^Hayes, Brian (2006). "Unwed Numbers". American Scientist. 94 (1): 12–15. doi:10.1511/2006.57.3475.
  7. ^Boyer, Christian (May 2006). "Supplément dem l'article "Les ancêtres français ni sudoku""(PDF). Pour la Science (in French): 1–6. Archived from the original(PDF) on 2006-12-10.

    Retrieved 2009-08-03.

  8. ^Boyer, Christian (2007). "Sudoku's French ancestors" (in French). (personal webpage). Archived from the original on 2007-10-10. Retrieved 2009-08-03.
  9. ^Malvern, Jack (Jun 3, 2006). "Les fiendish French beat us to Su Doku". The Times. Retrieved 2024-10-02.
  10. ^ abcdePegg, Ed Jr.

    (Sep 15, 2005). "Ed Pegg Jr.'s Math Games: Sudoku Variations". MAA Online. The Mathematical Association of amerika. Retrieved 2006-10-03.

  11. ^"Reg. No. 5056856". Japanese Trademark 5056856. Japan Platform for Trademark upplysning. Retrieved 2018-10-03.
  12. ^Payn, Ian (Nov 13, 2004). "Deep in thought". The Times.
  13. ^Devlin, Keith (Jan 28–29, 2012).

    "The Numbers Game (book review of Taking Sudoku Seriously bygd Jason Rosenhouse et al.)". The vägg Street Journal. Weekend Edition. p. C5.

  14. ^"G2, home of the discerning Sudoku addict". The Guardian. London.

    Njut från spelet!

    May 13, 2005. Retrieved 2006-09-16.

  15. ^"Correction attached to "Inside Japan's Puzzle Palace"". The New York Times. Mar 21, 2007.
  16. ^"Sudoku the song, bygd Peter Levy". Sudoku.org.uk. Aug 17, 2006. Retrieved 2008-10-05.
  17. ^"Hit Song Has the Numbers".

    The Herald Sun. Aug 17, 2006. Retrieved 2008-10-05.

  18. ^"Brain Age: tåg Your Brain in Minutes a Day!". Gamerankings.com.
  19. ^"Brain Age: ... Review". Gamespot.com.
  20. ^Harris, Craig (Apr 18, 2006). "Brain Age: lära Your Brain in Minutes a Day". IGN. Retrieved 2023-02-08.
  21. ^Thorsen, Tor (Oct 26, 2006).

    "Nintendo posts $456.6 million profit". GameSpot. Retrieved 2013-03-29.

  22. ^Knox, Malcolm (Jun 11, 2008). "The game's up: jurors playing Sudoku abort trial". The Sydney Morning Herald. Retrieved 2008-06-11.
  23. ^Eisenhauer, William (2010). Sudoku-zilla. CreateSpace. p. 220. ISBN .
  24. ^Snyder, Thomas; Huang, Wei-Hwa (2009).

    Mutant Sudoku. Puzzlewright Press. ISBN .

  25. ^Conceptis, Puzzles (2013). Amazing Sudoku Variants. Puzzlewright. ISBN . OCLC 700343731.
  26. ^Murali, A V (2014). A Collection of Fascinating Games and Puzzles. CreateSpace Independent Publishing. ISBN . OCLC 1152132274.
  27. ^ ab"Zahlenraetsel".

    janko.at.

  28. ^Keedwell, A. D. (Nov 2006). "Two remarks about Sudoku squares". The Mathematical Gazette. 90 (519): 425–430. doi:10.1017/s0025557200180234. JSTOR 40378190.
  29. ^Yato, Takayuki; Seta, Takahiro (2003). "Complexity and completeness of finding another solution and its application to puzzles"(PDF).

    IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences. E86-A (5): 1052–1060. Archived from the original(PDF) on 2020-03-03.

  30. ^Lewis, R. (2015). A Guide to Graph Colouring: Algorithms and Applications. Springer. doi:10.1007/978-3-319-25730-3. ISBN . OCLC 990730995.

    Lös din Sudoku snabbt samt pålitligt.

    S2CID 26468973.

  31. ^McGuire, G.; Tugemann, B.; Civario, G. (2014). "There fryst vatten no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem". Experimental Mathematics. 23 (2): 190–217. arXiv:1201.0749. doi:10.1080/10586458.2013.870056.
  32. ^Royle, Gordon. "Minimum Sudoku". Archived from the original on 2006-11-26.

    Retrieved 2012-02-28.

  33. ^Sloane, N. J. A. (ed.). "Sequence A107739 (Number of (completed) sudokus (or Sudokus) of storlek n^2 X n^2)".

    Detta existerar den maximalt elementär metoden för att börja tillsammans då ni löser en sudoku.

    The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

  34. ^Sloane, N. J. A. (ed.). "Sequence A109741 (Number of inequivalent (completed) n^2 X n^2 sudokus (or Sudokus))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  35. ^Berthier, Denis (Dec 4, 2009).

    "Unbiased Statistics of a CSP – A Controlled-Bias Generator". In Elleithy, Khaled (ed.). Innovations in Computing Sciences and Software Engineering. Springer. pp. 165–70. Bibcode:2010iics.book.....S. doi:10.1007/978-90-481-9112-3. ISBN . Retrieved 2009-12-04.

  36. ^"Sudoku title for Czech accountant".

    BBC News. Mar 11, 2006. Retrieved 2006-09-11.

  37. ^"World Sudoku Championship 2006 Instructions Booklet"(PDF). BBC News. Archived(PDF) from the original on 2006-06-10. Retrieved 2010-05-24.
  38. ^"Report on the 8th General Assembly of the World Puzzle Federation". World Puzzle Federation. October 30, 2006.

    Archived from the original on September 26, 2007. Retrieved November 15, 2006.

  39. ^"Thomas Snyder wins World Sudoku Championship". US Puzzle Team. Mar 31, 2007. Retrieved 2008-04-18.
  40. ^Harvey, Michael (Apr 17, 2008). "It's a puzzle but sun, sea, and beer can't compete with Sudoku for British team".

    TimesOnline. London. Archived from the original on 2008-07-20. Retrieved 2008-04-18.

  41. ^Malvern, Jack (Apr 27, 2009). "Su Doku battle goes a little off the wall". TimesOnline. London. Archived from the original on 2011-06-15. Retrieved 2009-04-27.
  42. ^"Pole, 23, repeats as Sudoku world champ". PhillyInquirer.

    May 2, 2009. Archived from the original on 2010-05-05. Retrieved 2013-08-03.

  43. ^"WSPC 2017 - Logic Masters India".

    För för att åtgärda detta måste ni koncentrera dig samt nyttja logiskt tänkande.

    wspc2017.logicmastersindia.com.

  44. ^"World Sudoku Championships | WPF". orldpuzzle.org.
  45. ^"Thomas Snyder, World Sudoku champion". The Philadelphia Inquirer. Oct 21, 2007. Retrieved 2007-10-21.
  46. ^Shapiro, Howard (Oct 25, 2009). "Going for 2d, she wins 1st".

    The Philadelphia Inquirer. Archived from the original on 2009-11-02. Retrieved 2013-08-03.

  47. ^Timpane, John (Oct 27, 2009). "Possible cheating probed at Sudoku National Championship". The Philadelphia Inquirer. Archived from the original on 2009-11-01. Retrieved 2013-08-03.
  48. ^"3rd-place winner disqualified in Sudoku scandal".

    The Philadelphia Inquirer. Nov 24, 2009. Archived from the original on 2009-11-27. Retrieved 2013-08-03.

Further reading

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External links

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