100-428: Sudoku ( / s uː ˈ d oʊ k uː , - ˈ d ɒ k -, s ə -/ ; Japanese : 数独 , romanized : sūdoku , lit. 'digit-single'; originally called Number Place ) is a logic-based , combinatorial number-placement puzzle . In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose
200-526: A computer program to rapidly produce unique puzzles. 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 daily, published a partially completed 9×9 magic square with 3×3 subsquares on November 19, 1892. 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
300-428: A 7×7 grid with six heptomino regions and a disjoint region. 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
400-455: A Day! . Critically and commercially well-received, it generated particular praise for its Sudoku implementation and sold more than 8 million copies worldwide. Due to its popularity, Nintendo made a second Brain Age game titled Brain Age , which has over 100 new Sudoku puzzles and other activities. In June 2008, an Australian drugs-related jury trial costing over A$ 1 million was aborted when it
500-637: A benefit from the in-group to the out-group) means "[I/we] explained [it] to [him/her/them]". Such beneficiary auxiliary verbs thus serve a function comparable to that of pronouns and prepositions in Indo-European languages to indicate the actor and the recipient of an action. Japanese "pronouns" also function differently from most modern Indo-European pronouns (and more like nouns) in that they can take modifiers as any other noun may. For instance, one does not say in English: The amazed he ran down
600-493: A central axis) like a doughnut ( torus ). An example of approximate spherical symmetry is the Earth (with respect to density and other physical and chemical properties). In 4D, continuous or discrete rotational symmetry about a plane corresponds to corresponding 2D rotational symmetry in every perpendicular plane, about the point of intersection. An object can also have rotational symmetry about two perpendicular planes, e.g. if it
700-414: A distinct language of its own that has absorbed various aspects from neighboring languages. Japanese has five vowels, and vowel length is phonemic, with each having both a short and a long version. Elongated vowels are usually denoted with a line over the vowel (a macron ) in rōmaji , a repeated vowel character in hiragana , or a chōonpu succeeding the vowel in katakana . /u/ ( listen )
800-419: A glide /j/ and either the first part of a geminate consonant ( っ / ッ , represented as Q) or a moraic nasal in the coda ( ん / ン , represented as N). The nasal is sensitive to its phonetic environment and assimilates to the following phoneme, with pronunciations including [ɴ, m, n, ɲ, ŋ, ɰ̃] . Onset-glide clusters only occur at the start of syllables but clusters across syllables are allowed as long as
900-484: A listener depending on the listener's relative social position and the degree of familiarity between the speaker and the listener. When used in different social relationships, the same word may have positive (intimate or respectful) or negative (distant or disrespectful) connotations. Japanese often use titles of the person referred to where pronouns would be used in English. For example, when speaking to one's teacher, it
1000-408: A sentence need not be stated and pronouns may be omitted if they can be inferred from context. In the example above, hana ga nagai would mean "[their] noses are long", while nagai by itself would mean "[they] are long." A single verb can be a complete sentence: Yatta! ( やった! ) "[I / we / they / etc] did [it]!". In addition, since adjectives can form the predicate in a Japanese sentence (below),
1100-428: A single adjective can be a complete sentence: Urayamashii! ( 羨ましい! ) "[I'm] jealous [about it]!". While the language has some words that are typically translated as pronouns, these are not used as frequently as pronouns in some Indo-European languages, and function differently. In some cases, Japanese relies on special verb forms and auxiliary verbs to indicate the direction of benefit of an action: "down" to indicate
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#17327877120901200-616: A standard 81-card Set deck (see Set game ). A three-dimensional Sudoku puzzle was published in The Daily Telegraph in May 2005. The Times also publishes a three-dimensional version under the name Tredoku. Also, a Sudoku version of the Rubik's Cube is named Sudoku Cube . Many other variants have been developed. Some are different shapes in the arrangement of overlapping 9×9 grids, such as butterfly, windmill, or flower. Others vary
1300-680: Is compressed rather than protruded , or simply unrounded. Some Japanese consonants have several allophones , which may give the impression of a larger inventory of sounds. However, some of these allophones have since become phonemic. For example, in the Japanese language up to and including the first half of the 20th century, the phonemic sequence /ti/ was palatalized and realized phonetically as [tɕi] , approximately chi ( listen ) ; however, now [ti] and [tɕi] are distinct, as evidenced by words like tī [tiː] "Western-style tea" and chii [tɕii] "social status". The "r" of
1400-421: Is topic–comment . Sentence-final particles are used to add emotional or emphatic impact, or form questions. Nouns have no grammatical number or gender , and there are no articles . Verbs are conjugated , primarily for tense and voice , but not person . Japanese adjectives are also conjugated. Japanese has a complex system of honorifics , with verb forms and vocabulary to indicate the relative status of
1500-567: Is a half-line . In three dimensions we can distinguish cylindrical symmetry and spherical symmetry (no change when rotating about one axis, or for any rotation). That is, no dependence on the angle using cylindrical coordinates and no dependence on either angle using spherical coordinates . The fundamental domain is a half-plane through the axis, and a radial half-line, respectively. Axisymmetric and axisymmetrical are adjectives which refer to an object having cylindrical symmetry, or axisymmetry (i.e. rotational symmetry with respect to
1600-482: Is a registered trademark in Japan and the puzzle is 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
1700-448: Is also seen in o-medetō "congratulations", from medetaku ). Late Middle Japanese has the first loanwords from European languages – now-common words borrowed into Japanese in this period include pan ("bread") and tabako ("tobacco", now "cigarette"), both from Portuguese . Modern Japanese is considered to begin with the Edo period (which spanned from 1603 to 1867). Since Old Japanese,
1800-527: Is also used in a limited fashion (such as for imported acronyms) in Japanese writing. The numeral system uses mostly Arabic numerals , but also traditional Chinese numerals . Proto-Japonic , the common ancestor of the Japanese and Ryukyuan languages , is thought to have been brought to Japan by settlers coming from the Korean peninsula sometime in the early- to mid-4th century BC (the Yayoi period ), replacing
1900-440: Is appropriate to use sensei ( 先生 , "teacher"), but inappropriate to use anata . This is because anata is used to refer to people of equal or lower status, and one's teacher has higher status. Japanese nouns have no grammatical number, gender or article aspect. The noun hon ( 本 ) may refer to a single book or several books; hito ( 人 ) can mean "person" or "people", and ki ( 木 ) can be "tree" or "trees". Where number
2000-701: Is associated with comedy (see Kansai dialect ). Dialects of Tōhoku and North Kantō are associated with typical farmers. The Ryūkyūan languages, spoken in Okinawa and the Amami Islands (administratively part of Kagoshima ), are distinct enough to be considered a separate branch of the Japonic family; not only is each language unintelligible to Japanese speakers, but most are unintelligible to those who speak other Ryūkyūan languages. However, in contrast to linguists, many ordinary Japanese people tend to consider
2100-466: Is better documentation of Late Middle Japanese phonology than for previous forms (for instance, the Arte da Lingoa de Iapam ). Among other sound changes, the sequence /au/ merges to /ɔː/ , in contrast with /oː/ ; /p/ is reintroduced from Chinese; and /we/ merges with /je/ . Some forms rather more familiar to Modern Japanese speakers begin to appear – the continuative ending - te begins to reduce onto
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#17327877120902200-509: Is correlated with the sex of the speaker and the social situation in which they are spoken: men and women alike in a formal situation generally refer to themselves as watashi ( 私 , literally "private") or watakushi (also 私 , hyper-polite form), while men in rougher or intimate conversation are much more likely to use the word ore ( 俺 "oneself", "myself") or boku . Similarly, different words such as anata , kimi , and omae ( お前 , more formally 御前 "the one before me") may refer to
2300-402: Is homogeneous, and the symmetry group is the whole E ( m ) . With the modified notion of symmetry for vector fields the symmetry group can also be E ( m ) . For symmetry with respect to rotations about a point we can take that point as origin. These rotations form the special orthogonal group SO( m ) , the group of m × m orthogonal matrices with determinant 1. For m = 3 this
2400-417: Is important, it can be indicated by providing a quantity (often with a counter word ) or (rarely) by adding a suffix, or sometimes by duplication (e.g. 人人 , hitobito , usually written with an iteration mark as 人々 ). Words for people are usually understood as singular. Thus Tanaka-san usually means Mx Tanaka . Words that refer to people and animals can be made to indicate a group of individuals through
2500-461: Is 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 version of Sudoku can be played with
2600-404: Is known to be NP-complete . 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. The aim
2700-553: Is left blank and forms a tenth Sudoku puzzle without any cell completed; hence, "clueless". Examples and other variants can be found in the Glossary of Sudoku . This section refers to classic Sudoku, disregarding jigsaw, hyper, and other variants. A completed Sudoku grid is 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). The general problem of solving Sudoku puzzles on n × n grids of n × n blocks
2800-755: Is less common. In terms of mutual intelligibility , a survey in 1967 found that the four most unintelligible dialects (excluding Ryūkyūan languages and Tōhoku dialects ) to students from Greater Tokyo were the Kiso dialect (in the deep mountains of Nagano Prefecture ), the Himi dialect (in Toyama Prefecture ), the Kagoshima dialect and the Maniwa dialect (in Okayama Prefecture ). The survey
2900-488: Is made up of 'cages', typically depicted by boxes outlined with dashes or colours. The sum of the numbers in a cage is written in the top left corner of the cage, and numbers cannot be repeated in a cage. Puzzles constructed from more than two grids are also common. Five 9×9 grids that 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
3000-564: Is much smaller, 5,472,730,538. Unlike the number of complete Sudoku grids, the number of minimal 9×9 Sudoku puzzles is not precisely known. (A minimal puzzle is one in which no clue can be deleted without losing the uniqueness of the solution.) However, statistical techniques combined with a puzzle generator show that about (with 0.065% relative error) 3.10 × 10 minimal puzzles and 2.55 × 10 nonessentially equivalent minimal puzzles exist. Japanese language Japanese ( 日本語 , Nihongo , [ɲihoŋɡo] )
3100-557: Is now published in mainstream Japanese periodicals, such as the Asahi Shimbun . In 1997, Hong Kong judge Wayne Gould saw a partly completed puzzle in a Japanese bookshop. Over six years, he developed a computer program to produce unique puzzles rapidly. The first newspaper outside of Japan to publish a Sudoku puzzle The Conway Daily Sun (New Hampshire), which published a puzzle by Gould in September 2004. Gould pitched
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3200-420: Is often called a topic-prominent language , which means it has a strong tendency to indicate the topic separately from the subject, and that the two do not always coincide. The sentence Zō wa hana ga nagai ( 象は鼻が長い ) literally means, "As for elephant(s), (the) nose(s) (is/are) long". The topic is zō "elephant", and the subject is hana "nose". Japanese grammar tends toward brevity; the subject or object of
3300-498: Is preserved in words such as matsuge ("eyelash", lit. "hair of the eye"); modern mieru ("to be visible") and kikoeru ("to be audible") retain a mediopassive suffix - yu(ru) ( kikoyu → kikoyuru (the attributive form, which slowly replaced the plain form starting in the late Heian period) → kikoeru (all verbs with the shimo-nidan conjugation pattern underwent this same shift in Early Modern Japanese )); and
3400-514: Is the Cartesian product of two rotationally symmetry 2D figures, as in the case of e.g. the duocylinder and various regular duoprisms . 2-fold rotational symmetry together with single translational symmetry is one of the Frieze groups . A rotocenter is the fixed, or invariant, point of a rotation. There are two rotocenters per primitive cell . Together with double translational symmetry
3500-665: Is the principal language of the Japonic language family spoken by the Japanese people . It has around 123 million speakers, primarily in Japan , the only country where it is the national language , and within the Japanese diaspora worldwide. The Japonic family also includes the Ryukyuan languages and the variously classified Hachijō language . There have been many attempts to group the Japonic languages with other families such as
3600-483: Is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids . Formally
3700-469: Is the rotation group SO(3) . In another definition of the word, the rotation group of an object is the symmetry group within E ( n ) , the group of direct isometries ; in other words, the intersection of the full symmetry group and the group of direct isometries. For chiral objects it is the same as the full symmetry group. Laws of physics are SO(3)-invariant if they do not distinguish different directions in space. Because of Noether's theorem ,
3800-453: Is the rotation group of a regular n -sided polygon in 2D and of a regular n -sided pyramid in 3D. If there is e.g. rotational symmetry with respect to an angle of 100°, then also with respect to one of 20°, the greatest common divisor of 100° and 360°. A typical 3D object with rotational symmetry (possibly also with perpendicular axes) but no mirror symmetry is a propeller . For discrete symmetry with multiple symmetry axes through
3900-402: Is the version of Japanese discussed in this article. Formerly, standard Japanese in writing ( 文語 , bungo , "literary language") was different from colloquial language ( 口語 , kōgo ) . The two systems have different rules of grammar and some variance in vocabulary. Bungo was the main method of writing Japanese until about 1900; since then kōgo gradually extended its influence and
4000-606: Is to add limits on the placement of numbers beyond the usual row, column, and box requirements. Often, the limit takes the form of an extra "dimension"; the most common is 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 Daily Mail , which use 6×6 grids. The killer sudoku variant combines elements of sudoku and kakuro . A killer sudoku puzzle
4100-454: Is to construct a 9-coloring of a particular graph, given a partial 9-coloring. The fewest clues possible for a proper Sudoku is 17. Tens of thousands of distinct Sudoku puzzles have only 17 clues. The number of classic 9×9 Sudoku solution grids is 6,670,903,752,021,072,936,960, or around 6.67 × 10 . The number of essentially different solutions, when symmetries such as rotation, reflection, permutation, and relabelling are taken into account,
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4200-471: Is used for the present and the future. For verbs that represent an ongoing process, the -te iru form indicates a continuous (or progressive) aspect , similar to the suffix ing in English. For others that represent a change of state, the -te iru form indicates a perfect aspect. For example, kite iru means "They have come (and are still here)", but tabete iru means "They are eating". Questions (both with an interrogative pronoun and yes/no questions) have
4300-405: Is why some linguists do not classify Japanese "pronouns" as pronouns, but rather as referential nouns, much like Spanish usted (contracted from vuestra merced , "your ( majestic plural ) grace") or Portuguese você (from vossa mercê ). Japanese personal pronouns are generally used only in situations requiring special emphasis as to who is doing what to whom. The choice of words used as pronouns
4400-563: The Ainu , Austronesian , Koreanic , and the now-discredited Altaic , but none of these proposals have gained any widespread acceptance. Little is known of the language's prehistory, or when it first appeared in Japan. Chinese documents from the 3rd century AD recorded a few Japanese words, but substantial Old Japanese texts did not appear until the 8th century. From the Heian period (794–1185), extensive waves of Sino-Japanese vocabulary entered
4500-462: The Japonic language family, which also includes the Ryukyuan languages spoken in the Ryukyu Islands . As these closely related languages are commonly treated as dialects of the same language, Japanese is sometimes called a language isolate . According to Martine Irma Robbeets , Japanese has been subject to more attempts to show its relation to other languages than any other language in
4600-520: The Nikoli puzzle company, in the paper Monthly Nikolist in April 1984 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 a shorter version. "Sudoku"
4700-514: The Philippines , and various Pacific islands, locals in those countries learned Japanese as the language of the empire. As a result, many elderly people in these countries can still speak Japanese. Japanese emigrant communities (the largest of which are to be found in Brazil , with 1.4 million to 1.5 million Japanese immigrants and descendants, according to Brazilian IBGE data, more than
4800-738: The United States (notably in Hawaii , where 16.7% of the population has Japanese ancestry, and California ), and the Philippines (particularly in Davao Region and the Province of Laguna ). Japanese has no official status in Japan, but is the de facto national language of the country. There is a form of the language considered standard : hyōjungo ( 標準語 ) , meaning "standard Japanese", or kyōtsūgo ( 共通語 ) , "common language", or even "Tokyo dialect" at times. The meanings of
4900-724: The World Puzzle Federation since 2006, except in 2020 and 2021 during the COVID-19 pandemic . In 2006, a Sudoku website published a Sudoku tribute song by songwriter Peter Levy , but the MP3 file for downloading the song was removed due to heavy traffic. The Japanese Embassy to some country nominated the song to receive some kind of award from someone, and the Herald Sun newspaper in Melbourne, Australia , said Levy
5000-806: The de facto standard Japanese had been the Kansai dialect , especially that of Kyoto . However, during the Edo period, Edo (now Tokyo) developed into the largest city in Japan, and the Edo-area dialect became standard Japanese. Since the end of Japan's self-imposed isolation in 1853, the flow of loanwords from European languages has increased significantly. The period since 1945 has seen many words borrowed from other languages—such as German, Portuguese and English. Many English loan words especially relate to technology—for example, pasokon (short for "personal computer"), intānetto ("internet"), and kamera ("camera"). Due to
5100-532: 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 by various software developers , specifically for the iPhone and iPod Touch. One of the most popular video games featuring Sudoku is Brain Age: Train Your Brain in Minutes
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#17327877120905200-437: The rotational symmetry is symmetry with respect to some or all rotations in m -dimensional Euclidean space . Rotations are direct isometries , i.e., isometries preserving orientation . Therefore, a symmetry group of rotational symmetry is a subgroup of E ( m ) (see Euclidean group ). Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space
5300-527: The 1.2 million of the United States ) sometimes employ Japanese as their primary language. Approximately 12% of Hawaii residents speak Japanese, with an estimated 12.6% of the population of Japanese ancestry in 2008. Japanese emigrants can also be found in Peru , Argentina , Australia (especially in the eastern states), Canada (especially in Vancouver , where 1.4% of the population has Japanese ancestry),
5400-598: The Giant" behemoths. A 100×100-grid puzzle dubbed Sudoku-zilla was published in 2010. Under the name "Mini Sudoku", a 6×6 variant with 3×2 regions appears in the American newspaper USA Today and elsewhere. The object is the same as that of standard Sudoku, but the puzzle only uses the numbers 1 through 6. A similar form, for younger solvers of puzzles, called "The Junior Sudoku", has appeared in some newspapers, such as some editions of The Daily Mail . Another common variant
5500-486: The Japanese language is of particular interest, ranging between an apical central tap and a lateral approximant . The "g" is also notable; unless it starts a sentence, it may be pronounced [ ŋ ] , in the Kanto prestige dialect and in other eastern dialects. The phonotactics of Japanese are relatively simple. The syllable structure is (C)(G)V(C), that is, a core vowel surrounded by an optional onset consonant,
5600-736: The Old Japanese sections are written in Man'yōgana , which uses kanji for their phonetic as well as semantic values. Based on the Man'yōgana system, Old Japanese can be reconstructed as having 88 distinct morae . Texts written with Man'yōgana use two different sets of kanji for each of the morae now pronounced き (ki), ひ (hi), み (mi), け (ke), へ (he), め (me), こ (ko), そ (so), と (to), の (no), も (mo), よ (yo) and ろ (ro). (The Kojiki has 88, but all later texts have 87. The distinction between mo 1 and mo 2 apparently
5700-488: The Ryūkyūan languages as dialects of Japanese. The imperial court also seems to have spoken an unusual variant of the Japanese of the time, most likely the spoken form of Classical Japanese , a writing style that was prevalent during the Heian period , but began to decline during the late Meiji period . The Ryūkyūan languages are classified by UNESCO as 'endangered', as young people mostly use Japanese and cannot understand
5800-543: The addition of a collective suffix (a noun suffix that indicates a group), such as -tachi , but this is not a true plural: the meaning is closer to the English phrase "and company". A group described as Tanaka-san-tachi may include people not named Tanaka. Some Japanese nouns are effectively plural, such as hitobito "people" and wareware "we/us", while the word tomodachi "friend" is considered singular, although plural in form. Verbs are conjugated to show tenses, of which there are two: past and present (or non-past) which
5900-578: The effect of changing Japanese into a mora-timed language. Late Middle Japanese covers the years from 1185 to 1600, and is normally divided into two sections, roughly equivalent to the Kamakura period and the Muromachi period , respectively. The later forms of Late Middle Japanese are the first to be described by non-native sources, in this case the Jesuit and Franciscan missionaries; and thus there
6000-499: The first newspaper supplement with a Sudoku grid on every page). Recognizing the different psychological appeals of easy and difficult puzzles, The Times introduced both, side by side, on June 20, 2005. From July 2005, Channel 4 included a daily Sudoku game in their teletext service. On August 2, the BBC's program guide Radio Times featured a weekly Super Sudoku with a 16×16 grid. The world's first live TV Sudoku show, Sudoku Live ,
6100-455: The flow of loanwords from European languages increased significantly, and words from English roots have proliferated. Japanese is an agglutinative , mora -timed language with relatively simple phonotactics , a pure vowel system, phonemic vowel and consonant length, and a lexically significant pitch-accent . Word order is normally subject–object–verb with particles marking the grammatical function of words, and sentence structure
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#17327877120906200-609: The genitive particle ga remains in intentionally archaic speech. Early Middle Japanese is the Japanese of the Heian period , from 794 to 1185. It formed the basis for the literary standard of Classical Japanese , which remained in common use until the early 20th century. During this time, Japanese underwent numerous phonological developments, in many cases instigated by an influx of Chinese loanwords . These included phonemic length distinction for both consonants and vowels , palatal consonants (e.g. kya ) and labial consonant clusters (e.g. kwa ), and closed syllables . This had
6300-400: 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 similar puzzles in the 19th century, and the modern form of the puzzle first appeared in 1979 puzzle books by Dell Magazines under the name Number Place. However,
6400-512: The idea of publishing Sudoku puzzles to newspapers, offering the puzzles for free in exchange for the newspapers' attributing them to him and linking to his website for solutions and other puzzles. 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
6500-430: The language, affecting the phonology of Early Middle Japanese . Late Middle Japanese (1185–1600) saw extensive grammatical changes and the first appearance of European loanwords . The basis of the standard dialect moved from the Kansai region to the Edo region (modern Tokyo ) in the Early Modern Japanese period (early 17th century–mid 19th century). Following the end of Japan's self-imposed isolation in 1853,
6600-458: The languages of the original Jōmon inhabitants, including the ancestor of the modern Ainu language . Because writing had yet to be introduced from China, there is no direct evidence, and anything that can be discerned about this period must be based on internal reconstruction from Old Japanese , or comparison with the Ryukyuan languages and Japanese dialects . The Chinese writing system
6700-449: The languages. Okinawan Japanese is a variant of Standard Japanese influenced by the Ryūkyūan languages, and is the primary dialect spoken among young people in the Ryukyu Islands . Modern Japanese has become prevalent nationwide (including the Ryūkyū islands) due to education , mass media , and an increase in mobility within Japan, as well as economic integration. Japanese is a member of
6800-427: The large quantity of English loanwords, modern Japanese has developed a distinction between [tɕi] and [ti] , and [dʑi] and [di] , with the latter in each pair only found in loanwords. Although Japanese is spoken almost exclusively in Japan, it has also been spoken outside of the country. Before and during World War II , through Japanese annexation of Taiwan and Korea , as well as partial occupation of China ,
6900-403: The logic for solving the grid. One of these is "Greater Than Sudoku". In this, a 3×3 grid of the Sudoku is given with 12 symbols of Greater Than (>) or Less Than (<) on the common line of the two adjacent numbers. Another variant on the logic of the solution is "Clueless Sudoku", in which nine 9×9 Sudoku grids are each placed in a 3×3 array. The center cell in each 3×3 grid of all nine puzzles
7000-465: The notation C n is used, the geometric and abstract C n should be distinguished: there are other symmetry groups of the same abstract group type which are geometrically different, see cyclic symmetry groups in 3D . The fundamental domain is a sector of 360 ∘ n . {\displaystyle {\tfrac {360^{\circ }}{n}}.} Examples without additional reflection symmetry : C n
7100-547: The numbers 1–9, and the additional constraint on the broken diagonals led to only one solution. These weekly puzzles were a feature of French newspapers such as L'Écho de Paris for about a decade, but disappeared about the time of World War I . The modern Sudoku was most likely designed anonymously by Howard Garns , a 74-year-old retired architect and freelance puzzle constructor from Connersville, Indiana , and first published in 1979 by Dell Magazines as Number Place (the earliest known examples of modern Sudoku). Garns' name
7200-400: The object. A "1-fold" symmetry is no symmetry (all objects look alike after a rotation of 360°). The notation for n -fold symmetry is C n or simply n . The actual symmetry group is specified by the point or axis of symmetry, together with the n . For each point or axis of symmetry, the abstract group type is cyclic group of order n , Z n . Although for the latter also
7300-425: The only strict rule of word order is that the verb must be placed at the end of a sentence (possibly followed by sentence-end particles). This is because Japanese sentence elements are marked with particles that identify their grammatical functions. The basic sentence structure is topic–comment . For example, Kochira wa Tanaka-san desu ( こちらは田中さんです ). kochira ("this") is the topic of the sentence, indicated by
7400-470: The out-group gives a benefit to the in-group, and "up" to indicate the in-group gives a benefit to the out-group. Here, the in-group includes the speaker and the out-group does not, and their boundary depends on context. For example, oshiete moratta ( 教えてもらった ) (literally, "explaining got" with a benefit from the out-group to the in-group) means "[he/she/they] explained [it] to [me/us]". Similarly, oshiete ageta ( 教えてあげた ) (literally, "explaining gave" with
7500-415: The particle wa . The verb desu is a copula , commonly translated as "to be" or "it is" (though there are other verbs that can be translated as "to be"), though technically it holds no meaning and is used to give a sentence 'politeness'. As a phrase, Tanaka-san desu is the comment. This sentence literally translates to "As for this person, (it) is Mx Tanaka." Thus Japanese, like many other Asian languages,
7600-481: The proposed larger Altaic family, or to various Southeast Asian languages , especially Austronesian . None of these proposals have gained wide acceptance (and the Altaic family itself is now considered controversial). As it stands, only the link to Ryukyuan has wide support. Other theories view the Japanese language as an early creole language formed through inputs from at least two distinct language groups, or as
7700-611: The puzzle type only began to gain widespread popularity in 1986 when it was published by the Japanese puzzle company Nikoli under the name Sudoku, meaning "single number". In newspapers outside of Japan, it first appeared in The Conway Daily Sun (New Hampshire) in September 2004, and then The Times (London) in November 2004, both of which were thanks to the efforts of the Hong Kong judge Wayne Gould , who devised
7800-637: The rotation groups are the following wallpaper groups , with axes per primitive cell: Scaling of a lattice divides the number of points per unit area by the square of the scale factor. Therefore, the number of 2-, 3-, 4-, and 6-fold rotocenters per primitive cell is 4, 3, 2, and 1, respectively, again including 4-fold as a special case of 2-fold, etc. 3-fold rotational symmetry at one point and 2-fold at another one (or ditto in 3D with respect to parallel axes) implies rotation group p6, i.e. double translational symmetry and 6-fold rotational symmetry at some point (or, in 3D, parallel axis). The translation distance for
7900-540: The rotational symmetry of a physical system is equivalent to the angular momentum conservation law. Rotational symmetry of order n , also called n -fold rotational symmetry , or discrete rotational symmetry of the n th order , with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of 360 ∘ n {\displaystyle {\tfrac {360^{\circ }}{n}}} (180°, 120°, 90°, 72°, 60°, 51 3 ⁄ 7 °, etc.) does not change
8000-430: 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
8100-578: The same point, there are the following possibilities: In the case of the Platonic solids , the 2-fold axes are through the midpoints of opposite edges, and the number of them is half the number of edges. The other axes are through opposite vertices and through centers of opposite faces, except in the case of the tetrahedron, where the 3-fold axes are each through one vertex and the center of one face. Rotational symmetry with respect to any angle is, in two dimensions, circular symmetry . The fundamental domain
8200-459: The same structure as affirmative sentences, but with intonation rising at the end. In the formal register, the question particle -ka is added. For example, ii desu ( いいです ) "It is OK" becomes ii desu-ka ( いいですか。 ) "Is it OK?". In a more informal tone sometimes the particle -no ( の ) is added instead to show a personal interest of the speaker: Dōshite konai-no? "Why aren't (you) coming?". Some simple queries are formed simply by mentioning
8300-439: The speaker, the listener, and persons mentioned. The Japanese writing system combines Chinese characters , known as kanji ( 漢字 , ' Han characters') , with two unique syllabaries (or moraic scripts) derived by the Japanese from the more complex Chinese characters: hiragana ( ひらがな or 平仮名 , 'simple characters') and katakana ( カタカナ or 片仮名 , 'partial characters'). Latin script ( rōmaji ローマ字 )
8400-817: The state as at the time the constitution was written, many of the elders participating in the process had been educated in Japanese during the South Seas Mandate over the island shown by the 1958 census of the Trust Territory of the Pacific that found that 89% of Palauans born between 1914 and 1933 could speak and read Japanese, but as of the 2005 Palau census there were no residents of Angaur that spoke Japanese at home. Japanese dialects typically differ in terms of pitch accent , inflectional morphology , vocabulary , and particle usage. Some even differ in vowel and consonant inventories, although this
8500-481: The street. (grammatically incorrect insertion of a pronoun) But one can grammatically say essentially the same thing in Japanese: 驚いた彼は道を走っていった。 Transliteration: Odoroita kare wa michi o hashitte itta. (grammatically correct) This is partly because these words evolved from regular nouns, such as kimi "you" ( 君 "lord"), anata "you" ( あなた "that side, yonder"), and boku "I" ( 僕 "servant"). This
8600-611: The topic with an interrogative intonation to call for the hearer's attention: Kore wa? "(What about) this?"; O-namae wa? ( お名前は？ ) "(What's your) name?". Negatives are formed by inflecting the verb. For example, Pan o taberu ( パンを食べる。 ) "I will eat bread" or "I eat bread" becomes Pan o tabenai ( パンを食べない。 ) "I will not eat bread" or "I do not eat bread". Plain negative forms are i -adjectives (see below) and inflect as such, e.g. Pan o tabenakatta ( パンを食べなかった。 ) "I did not eat bread". Rotational symmetry Rotational symmetry , also known as radial symmetry in geometry ,
8700-419: The two consonants are the moraic nasal followed by a homorganic consonant. Japanese also includes a pitch accent , which is not represented in moraic writing; for example [haꜜ.ɕi] ("chopsticks") and [ha.ɕiꜜ] ("bridge") are both spelled はし ( hashi ) , and are only differentiated by the tone contour. Japanese word order is classified as subject–object–verb . Unlike many Indo-European languages ,
8800-577: The two methods were both used in writing until the 1940s. Bungo still has some relevance for historians, literary scholars, and lawyers (many Japanese laws that survived World War II are still written in bungo , although there are ongoing efforts to modernize their language). Kōgo is the dominant method of both speaking and writing Japanese today, although bungo grammar and vocabulary are occasionally used in modern Japanese for effect. The 1982 state constitution of Angaur , Palau , names Japanese along with Palauan and English as an official language of
8900-480: The two terms (''hyōjungo'' and ''kyōtsūgo'') are almost the same. Hyōjungo or kyōtsūgo is a conception that forms the counterpart of dialect. This normative language was born after the Meiji Restoration ( 明治維新 , meiji ishin , 1868) from the language spoken in the higher-class areas of Tokyo (see Yamanote ). Hyōjungo is taught in schools and used on television and in official communications. It
9000-407: The verb (e.g. yonde for earlier yomite ), the -k- in the final mora of adjectives drops out ( shiroi for earlier shiroki ); and some forms exist where modern standard Japanese has retained the earlier form (e.g. hayaku > hayau > hayɔɔ , where modern Japanese just has hayaku , though the alternative form is preserved in the standard greeting o-hayō gozaimasu "good morning"; this ending
9100-548: The world. Since Japanese first gained the consideration of linguists in the late 19th century, attempts have been made to show its genealogical relation to languages or language families such as Ainu , Korean , Chinese , Tibeto-Burman , Uralic , Altaic (or Ural-Altaic ), Austroasiatic , Austronesian and Dravidian . At the fringe, some linguists have even suggested a link to Indo-European languages , including Greek , or to Sumerian . Main modern theories try to link Japanese either to northern Asian languages, like Korean or
9200-456: Was a puzzle contest first broadcast on July 1, 2005, on the British pay-television channel 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. Phil Kollin of Winchelsea, England ,
9300-500: 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. He died in 1989 before getting a chance to see his creation as a worldwide phenomenon. Whether or not Garns was familiar with any of the French newspapers listed above is unclear. The puzzle was introduced in Japan by Maki Kaji ( 鍜治 真起 , Kaji Maki ) , president of
9400-539: Was based on 12- to 20-second-long recordings of 135 to 244 phonemes , which 42 students listened to and translated word-for-word. The listeners were all Keio University students who grew up in the Kanto region . There are some language islands in mountain villages or isolated islands such as Hachijō-jima island , whose dialects are descended from Eastern Old Japanese . Dialects of the Kansai region are spoken or known by many Japanese, and Osaka dialect in particular
9500-497: Was discovered that four or five of the twelve jurors had been playing Sudoku instead of listening to the evidence. Although the 9×9 grid with 3×3 regions is by 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 under the name Logi-5; the World Puzzle Championship has featured a 6×6 grid with 2×3 regions and
9600-735: Was imported to Japan from Baekje around the start of the fifth century, alongside Buddhism. The earliest texts were written in Classical Chinese , although some of these were likely intended to be read as Japanese using the kanbun method, and show influences of Japanese grammar such as Japanese word order. The earliest text, the Kojiki , dates to the early eighth century, and was written entirely in Chinese characters, which are used to represent, at different times, Chinese, kanbun , and Old Japanese. As in other texts from this period,
9700-607: Was in discussions with Sony in Japan to release the song as a single on a Sony label. Sudoku software is very popular on PCs, websites, and mobile phones. It comes with many distributions of Linux . The software has also been released on video game consoles, such as the Nintendo DS , PlayStation Portable , the Game Boy Advance , Xbox Live Arcade , the Nook e-book reader, Kindle Fire tablet, several iPod models, and
9800-474: Was lost immediately following its composition.) This set of morae shrank to 67 in Early Middle Japanese , though some were added through Chinese influence. Man'yōgana also has a symbol for /je/ , which merges with /e/ before the end of the period. Several fossilizations of Old Japanese grammatical elements remain in the modern language – the genitive particle tsu (superseded by modern no )
9900-448: 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 . Sudoku puzzles rapidly spread to other newspapers as a regular feature. 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
10000-518: 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 by Hannah Withey of Cheshire . Later in 2005, the BBC launched SUDO-Q , a game show that combined Sudoku with general knowledge. However, it used only 4×4 and 6×6 puzzles. Four seasons were produced before the show ended in 2007. An annual World Sudoku Championship series has been organized by
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