Purim

Many Jewish families have also had "family Purims" throughout the centuries, celebrated at home, whereby they celebrate their escape from persecution, an accident, or any other type of misfortune. 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. According to some sources, the influential Rabbi Moses Sofer (the Hatam Sofer), who was born in Frankfurt, celebrated Purim Vintz every year, even when rabbi in Pressburg. 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. This commemorates the Fettmilch uprising (1616-1620), in which one Vincenz Fettmilch attempted to exterminate the Jewish community [1]. The puzzle was carved into a hillside in Chipping Sodbury, near Bristol, England, in view of the M4 motorway. The best known is Purim Vintz, traditionally celebrated in Frankfurt am Main, one week after the regular Purim. 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.

Many cities have until recently had local "Purims", all commemorating the deliverance of the local community from a particular anti-semitic ruler or group. The audience at home was in a separate interactive competition. Shushan Purim, is celebrated by those in Jerusalem the day after Purim. Conferring was permitted although the lack of acquaintance of the players with each other inhibited an analytical discussion. Orah Hayyim, 697). Each player had a hand-held device for entering numbers corresponding to answers for four cells. 46b; comp. Nine teams of nine players (with one celebrity in each team) representing geographical regions competed to solve a puzzle.

i. It was presented by Carol Vorderman. The distinctions between the first and the second Purim in leap years are mentioned in the Mishnah (Meg. As a one-off, the world's first live TV Sudoku show, Sudoku Live, was broadcast on 1 July 2005 on Sky One. The respective days of the first Adar being then called Purim Katan ("Little Purim" in Hebrew), for which there have been set forth certain observances similar to those for Purim proper, with the exception of reading the Megillah, sending gifts to the poor, and fasting on the 13th of the month. On 2 August 2005 the BBC's programme guide Radio Times started to feature a weekly Super Sudoku. In leap years on the Hebrew calendar, Purim is celebrated in the second month of Adar, but by the Karaites in the first month of Adar. From July 2005 Channel 4 included a daily Sudoku game in their Teletext service (at page 391).

The fast on the 13th is still commonly observed; but when that date falls on a Sabbath, the fast is put back to Thursday, Friday being needed to prepare for the Sabbath and the following Purim festival. Recognizing the different psychological appeals of easy and difficult puzzles The Times introduced both side by side on 20 June 2005. Some, however, used to fast three days in commemoration of the fasting of Esther; but as fasting was prohibited during the month of Nisan, the first and second Mondays and the Thursday following Purim were chosen. A simpler explanation is that the puzzle attracts and retains readers—Sudoku players report an increasing sense of satisfaction as a puzzle approaches completion. 2a, "The 13th was the time of gathering", which gathering is explained to have had also the purpose of public prayer and fasting. 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. 18 and Meg. 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]).

ix. Newspapers competed to promote their Sudoku puzzles, with The Times and the Daily Mail each claiming to have been the first to feature Sudoku. The first who mentions it is Rabbi Aḥa of Shabḥa (8th cent.) in "She'eltot", iv.; and the reason there given for its institution is based on an arbitrary interpretation of Esth. As the name Sudoku became well-known in Britain, the Daily Mail adopted it in place of its earlier name "Codenumber". The Fast of Esther, celebrated before Purim, on the 13th of Adar, is not an original part of the Purim celebration, nor was it later instituted "in commemoration of the fasting of Esther, Mordechai, and the people", since this fasting fell, according to rabbinical tradition, in the month of Nisan and lasted three days. 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. This custom is no longer practiced. 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.

The Rabbis themselves, to avoid danger, tried to abolish these customs, often even calling the magistracy to their aid, as in London in 1783. Until then the Times had kept very quiet about the huge daily interest that its daily Sudoku competition had aroused. 309, 317, and Cassel, l.c.). The Telegraph continued to splash the puzzle on its front page, realizing that it was gaining sales simply by its presence. ii. 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. Schudt, l.c. 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".

These customs often aroused the wrath of Christians, who interpreted them as a disguised attempt to ridicule Jesus and the cross; prohibitions were issued against these displays; e.g., under the reign of Honorius (395-423) and of Theodosius II (408-450; comp. 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. As soon as the reader began to read the Megillah, the house with all its occupants was set on fire to the enjoyment of the spectators. 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. The whole was then put on the almemar, where stood also the wax figures of Zeresh (Haman's wife) and two guards — one to her right and the other to her left — all attired in a flimsy manner and with pipes in their mouths. Three days later The Daily Mail began to publish the puzzle under the name "Codenumber". In Frankfurt am Main, Germany, it was customary to make a house of wax wherein the figures of Haman and his executioner, also of wax, were placed side by side. The puzzles by Pappocom, Gould's software house, have been printed daily in the Times ever since.

In Italy, Jewish children used to range themselves in rows, and pelt one another with nuts; while the adults rode through the streets with fir-branches in their hands, shouted, or blew trumpets round a doll representing Haman and which was finally burned with due solemnity at the stake. 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). As early as the fifth century, and especially in the Geonic period (9th and 10th centuries), it was a custom to burn Haman in effigy on Purim. Over 6 years he developed a computer program to produce puzzles quickly. Some of them date from the Talmudic period. In 1997, retired Hong Kong judge Wayne Gould, 59, a New Zealander, saw a partly completed puzzle in a Japanese bookshop. Outside the synagogue the pranks indulged in on Purim by both children and adults have been carried even to a greater extreme. Sudoku has been called the "Rubik's cube of the 21st century".

In some congregations, people who do not dress up have to perform a forfeit, such as having to sing a song, or being squirted with a water pistol. Within the context of puzzle history, parallels are often cited to Rubik's Cube, another logic puzzle popular in the 1980s. Jews are also encouraged to dress up, with many people dressing up as pop stars, animals or even nuns. It is also often included in puzzle anthologies, such as The Giant 1001 Puzzle Book (under the title Nine Numbers). For example, many congregations will read the prayers in ways which would be considered sacrilegious on any other occasion during the year - for example, asking the congregation to have a race, where the prayers would be read as fast as possible, or singing some prayers to the tune of widely-known songs, which may even be Christian, to add to the stupidity. 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. Purim is also a time for other unusual goings-on. 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.

The custom of using noisemakers in synagogue on Purim is now almost universal. 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. Some of the rabbis protested against these uproarious excesses, considering them a sinful disturbance of public worship, but did so in vain. At least one publisher still uses that title. For noisemaking, others used a noisy rattle, called "gragger" or "greggar" (from Polish grzégarz). In 1989, Loadstar/Softdisk Publishing published DigitHunt on the Commodore 64, which was apparently the first home computer version of Sudoku. Some wrote the name of Haman on the soles of their shoes, and at the mention of the name stamped with their feet as a sign of contempt. Within Japan, Nikoli still holds the trademark for the name Sudoku; other publications in Japan use alternative names.

Ultimately, the stones fell into disuse, with the knocking alone remaining. It is now published in mainstream Japanese periodicals, such as the Asahi Shimbun. 19) is explained to mean "even from wood and stones", the rabbis introduced the custom of writing the name of Haman, the offspring of Amalek, on two smooth stones and of knocking or rubbing them constantly until the name was blotted out. 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). xxv. 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. In accordance with a passage in the Midrash, where the verse "Thou shalt blot out the remembrance of Amalek" (Deut. The puzzle was named by Kaji Maki (鍜治 真起), the president of Nikoli.

For example, during the public service in many congregations, when the reader of the Megillah mentions Haman or his sons, there is boisterous hissing, stamping, and rattling This practice traces its origin to French and German rabbis of the 13th century. 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"). Indeed, Purim was an occasion on which much joyous license was permitted even within the walls of the synagogue itself. 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). This pastry's triangular shape is recognized as a symbol, representing the tri-cornered hat which Haman (Purim's chief villain) wore. 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. These are flattish triangular pastries, with a pocket in the center, traditionally filled with a sweet poppy seed (or sometimes prune) based filling, but more recently made with almost any sweet filling, including fruit or chocolate. The puzzle was designed by Howard Garns, a retired architect and freelance puzzle constructor, and first published in 1979.

During Purim, it is traditional to eat festive meals and to serve hamantaschen (taschen [pockets] of mon [poppy seed]). 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. A popular song is "Ani Purim". Since this applies to Latin squares in general, most variants of Sudoku have the same maximum. For the children's sake certain verses from the Book of Esther have been sung in chorus on Purim. 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. Purim songs have been introduced even into the synagogue. The number of valid Sudoku solution grids for the 16×16 derivation is not known.

In Israel there are Purim parades, and men, women, boys and girls frolic publicly in costumes and masks, and indulge in all kinds of jollity. 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 custom is still practiced today amongst religious Jews of all denominations, and among both religious and non-religious Israelis. The derivation of this result was considerably simplified by analysis provided by Frazer Jarvis and the figure has been confirmed independently by Ed Russell. Although some rigorous authorities issued prohibitions against this custom, the people did not heed them, and the more lenient view prevailed. The result was derived through logic and brute force computation. He expresses the opinion that, since the purpose of the masquerade is only merrymaking, it should not be considered a transgression of the Biblical law regarding dress. This number is equal to 9! × 72² × 2⁷ × 27,704,267,971, the last factor of which is prime.

17, quoted by Moses Isserles on Orah Hayyim, 696:8. 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). 1508 at Venice) in his Responsa, No. There are significantly fewer valid Sudoku solution grids than Latin squares because Sudoku imposes the additional regional constraint. The first among Jewish authors to mention this custom is Judah Minz (d. A valid Sudoku solution grid is also a Latin square. From Italy, this custom spread over all countries where Jews lived, except perhaps the Orient. 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.

The custom of masquerading on Purim was first introduced among the Italian Jews about the close of the fifteenth century under the influence of the Roman carnival. In this case, two distinct vertices labelled by and are joined by an edge if and only if:. In remembrance of how God remained hidden throughout the Purim Miracle, Jews dress up on Purim and many hide their faces. The vertices can be labelled with the ordered pairs , where x and y are integers between 1 and 9. Although Jews believe that everything turned out in the end for the best as a direct result of divine intervention (that is, a series of miracles), the Book of Esther lacks any mention of God's name and seemingly appears to have been nothing more than a result of natural occurrences. The graph in question has 81 vertices, one vertex for each cell of the grid. However, there is also an important concept of hester panim, or "hidden face," a reference to God's role in the Purim miracle. 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.

Many commentaries state that Haman's daughter committed suicide after dumping the rotting contents of a trash bin on her father's head, thinking that he was Mordechai). Solving Sudoku puzzles (as well as any other NP-hard problem) can be expressed as a graph colouring problem. Mistaken identity plays an important role in The Book of Esther, as Esther publically hid her cultural origins from the public, Haman was forced to lead Mordechai on horseback through the capital city Shushan (Haman had thought that the King would order Mordechai to lead Haman around, and this led to confusion among Haman's followers. 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. Costumes and masks are worn to disguise the wearers' identities. The general problem of solving Sudoku puzzles on n² x n² boards of n x n blocks is known to be NP-complete [8]. Children in particular enjoy dressing up as the characters found in the Scroll of Esther, including King Ahasuerus, Queen Vashti, Queen Esther, Mordechai, and the evil Haman. Here are some of the more notable single-instance variations:.

Dressing up in masks and costumes is one of the most entertaining customs of the Purim holiday. Top Notch claim this as a feature designed to defeat solving programs. Some men dress in women's attire and vice versa. The traditional tunes of prayers sung in the synagogue are sometimes altered, always in deliberately humorous ways. 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. Many kinds of merry-making and mockery have been indulged in on Purim, so that among the masses it has become almost a general rule that "on Purim everything is allowed", even transgressions of certain Biblical laws. 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. The Rama effectively pushed a message of moderation, saying that one should only drink a little more that what one is used to drinking and he concludes with "Whether one drinks more or drinks less, the main thing is that his intention is for the sake of Heaven." The Rama encouraged merry-making, but total intoxication was condemned. 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.

In response, some commentators like Moses Isserles (The Rama) who worried about the abuse of this rule, developed less literal ways to understand this invitation. Alphabetical variations have also emerged; there is no functional difference in the puzzle unless the letters spell something. While Jews have long been noted for a lack of alcohol abuse, drunkenness was licensed on this holiday. Sequential grids, as opposed to overlapping, are also published, with values in specific locations in grids needing to be transferred to others. 7b) that one should drink on Purim until he can no longer distinguish "Cursed be Haman" from "Blessed be Mordechai", a saying which was codified in the authoritative code of Jewish law, the Shulkhan Arukh. Often, no givens are to be found in overlapping regions. The jovial character of the feast was illustrated in the saying of the Talmud (Meg. [5] Puzzles with twenty or more overlapping grids are not uncommon in some Japanese publications.

Thus Ashkenazi Jews eat Hamantaschen and Hamanohren (in Italy, orrechi d'Aman), Kreppchen, Kindchen, etc. In The Times and The Sydney Morning Herald this form of puzzle is known as Samurai SuDoku. Jews developed special pastries for this holiday; cakes were shaped into special forms and were given names having some symbolic bearing on the historical events of Purim. 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. Hence it was the rule to have at least one festive meal, called Seudat Purim, toward the evening of the 14th. Puzzles constructed from multiple Sudoku grids are common. The national rather than the religious character of the festival made it appear appropriate to celebrate the occasion by feasting. Some such variants forsake standard givens entirely.

In some congregations, it is customary to place a charity box in the vestibule of the synagogue. 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. It was obligatory upon the poorest Jew, even on one who was himself dependent on charity, to give to other poor — at least to two people. [3] [4] In this variant, all the numbers must appear in all the concentric rings as well as in all pairs of adjacent wedges. No distinction was to be made among the poor; anyone who was willing to accept charity, even a non-Jew, was to be allowed to participate. Also found is the Circular Sudoku, also known as Target Sudoku, invented by Essex mathematician Peter Higgins. In the synagogue, regular collections may be made on the festival, and the money is distributed among the needy. 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.

Jews send gifts of food (called "Mishloach manot"), especially pastries, to one another, and Jews give charity to the poor. 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. Over time, this became one of the most prominent features of the celebration of Purim. 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 Book of Esther prescribes "the sending of portions one to another, and gifts to the poor". Often the restriction takes the form of an extra "dimension"; the most common is for the numbers in the main diagonals of the grid to also be required to be unique. The Bobov purimspiel is still performed annually, at midnight, inside the Bobov main synagogue in Brooklyn. Another common variant is for additional restrictions to be enforced on the placement of numbers beyond the usual row, column, and region requirements.

The Bobov Hassidic group has never ceased performing its Purimspiel. 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. Because satire was deemed inappropriate for the synagogue itself, they were usually performed outdoors in its court. Puzzle Championship had a Sudoku with parallelogram regions that wrapped around the outer border of the puzzle, as if the grid were toroidal. By the 18th century in eastern Romania and some other parts of Eastern Europe, Purim plays -- Purimspiels -- had evolved into broad-ranging satires with music and dance, precursors to Yiddish theater, for which the story of Esther was little more than a pretext: indeed, by the mid-19th century, some were even based on other stories, such as Joseph sold by his brothers, Daniel, or the Sacrifice of Isaac. [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. Other writings (dramas, plays, etc.) intended for general edification, both in Hebrew and in other languages, have been composed as well. 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.

These include a large number of hymns intended for the public service. 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. Purim gave rise to many religious compositions, some of which were incorporated into the liturgy. 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. 8-16, the story of the attack on the Jews by Amalek, the progenitor of Haman, is also to be read. 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. xvii. Dell Number Place Challenger (see Variants below) puzzles also list authors .

30b), Ex. Nikoli Sudoku are hand-constructed, with the author being credited; the givens are always found in a symmetrical pattern. According to the Mishnah (Meg. 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. According to Jewish law the Megillah may be read in any language intelligible to the audience. 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. It has been also customary since the time of the Geonim (early medieval era) to unroll the whole Megillah before reading it, in order to give it the appearance of an epistle. They also have no authoring credits — that is, the name of the constructor is not printed with any puzzle.

26, 29) to the Book of Esther. 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. ix. Building a Sudoku with symmetrical givens is a simple matter of placing the undefined givens in a symmetrical pattern to begin with. In some places, however, it is not chanted, but is read like a letter, because of the name "iggeret" (epistle) which is applied (Esth. (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. The Megillah is read with a traditional chant differing from that used in the customary reading of the Torah. 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.

3, which relate the origin of Mordechai and his triumph. 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. 15-16, and x. 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. 5, viii. 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. The congregation was to recite aloud with the reader the verses ii. Some online versions offer several difficulty levels.

7-10) in one breath, to indicate their simultaneous death. This estimation allows publishers to tailor their Sudoku puzzles to audiences of varied solving experience. ix. Computer solvers can estimate the difficulty for a human to find the solution, based on the complexity of the solving techniques required. For example, the reader is to pronounce the names of the ten sons of Haman (Esth. It is based on the relevance and the positioning of the numbers rather than the quantity of the numbers. The Talmud added other provisions. 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.

However, the Talmud, a later work, prescribed three benedictions before the reading and one benediction after the reading. Perhaps surprisingly, the number of givens has little or no bearing on a puzzle's difficulty. In the Mishnah, the recitation of a benediction on the reading of the Megillah is not yet a universally recognized obligation. Published puzzles often are ranked in terms of difficulty. Further, he obliged women to attend the reading of the Megillah, inasmuch as it was a woman, Queen Esther, through whom the miraculous deliverance of the Jews was accomplished. A very fast solver is usually required for most trial-and-error puzzle-creation algorithms. Originally this enactment was for the 14th of Adar only; later, however, Rabbi Joshua ben Levi (3d cent.) prescribed that the Megillah should be read on the eve of Purim also. This is the method now preferred by many Sudoku programmers, mainly by virtue of its speed.

2a) to the "Men of the Great Synod", of which Mordechai is reported to have been a member. This method can be directly applied to solving Sudoku problems, counting all possible solutions for most puzzles rapidly. The first religious ceremony ordained for the celebration of Purim is the reading of the Book of Esther (the "Megillah") in the synagogue, a regulation ascribed in the Talmud (Meg. A highly efficient way of solving such constraint problems is Donald Knuth's Dancing Links Algorithm. The siddur (Jewish prayer book) has a special prayer to be said on this festival. Backtracking may be applied when alternate values cannot otherwise be excluded. The Book of Esther enjoins the annual celebration of the feast among the Jews on the 14th and 15th of Adar, commanding that they should "make them days of feasting and joy, and of sending portions one to another, and gifts to the poor". 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.

5a; Maimonides, "Yad", Megillah). Another alternative uses finite domain constraint programming. i. 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. Purim has been held in high esteem by Judaism at all times; some have held that when all the prophetical and hagiographical works are forgotten, the Book of Esther will still be remembered, and, accordingly, the Feast of Purim will continue to be observed (Jerusalem Talmud, Meg. 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). Accordingly, business transactions and even manual labor are allowed on Purim, although in certain places restrictions have been imposed on work (Shulkhan Arukh, Orach Chayim, 696). 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).

Like Hanukkah, Purim's status as a holiday is on a lesser level than those ordained holy by the Torah. 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. (In a small number of cities that were walled in ancient times, it is instead celebrated on the 15th.) As with all Jewish holidays, Purim begins at sundown on the previous day. It is also fairly simple to build a backtracking search. Purim is celebrated annually on the 14th of the Hebrew month of Adar. Given the self-imposed constraints of most Sudoku publishers, this method generally succeeds.

According to that book, the feast was instituted as a national one by the book's protagonists, Mordechai and Esther. These programs emulate the human logic to solve a puzzle without resorting to guesses. Purim (פּוּרִים "Lots", Standard Hebrew Purim, Tiberian Hebrew Pûrîm: plural of פּוּר pûr "Lot", from Akkadian pūru) is a Jewish holiday that commemorates the deliverance of the Persian Jews from the plot of the evil Haman to exterminate them, as recorded in the biblical Book of Esther. 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: