Sudoku

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. As of January of 2006 Americorps plans to continue to send relief to the affected areas. 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. The crews performed a number of relief tasks free of charge for hurricane survivors in need, including but not limited to support on the Fema/Carnival Cruise Lines shelter ship, tarping damaged roofs, and debris removal. The puzzle was carved into a hillside in Chipping Sodbury, near Bristol, England, in view of the M4 motorway. The crews originated from two main organizations, the National Civilian Community Corps (NCCC) and the Washington Conservation Corps (WCC). 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. Americorps sent several crews to Texas, Mississippi, and Louisiana in response to the Gulf Storms of 2005, namely Hurricanes Katrina and Rita.

The audience at home was in a separate interactive competition. The Red Cross also expanded their Hurricane Katrina internet "Safe List" for use by those affected by Hurricane Rita. Conferring was permitted although the lack of acquaintance of the players with each other inhibited an analytical discussion. The American Red Cross continued to provide disaster relief to Hurricane Katrina affected areas, but as a result of Hurricane Rita, had to open additional shelters in other gulf states. Each player had a hand-held device for entering numbers corresponding to answers for four cells. It is their mission to provide relief support for all of the areas in Texas and Louisiana effected by the two storms and to remove obstructions that might otherwise hinder help to those affected. Nine teams of nine players (with one celebrity in each team) representing geographical regions competed to solve a puzzle. ^{[50] [51]} The 1,400 Oregonian soldiers and airmen, including the 1st Batallion of the 186th Infantry which is designated a quick response unit, are joined by engineers and military police from Louisiana, a Stryker brigade from Pennsylvania, and an engineering batallion from Missouri.

It was presented by Carol Vorderman. Douglas Pritt of the 41st Brigade Combat Team, Oregon Army National Guard, head of Joint Task Force Rita (formally called JTF Ponchartrain). As a one-off, the world's first live TV Sudoku show, Sudoku Live, was broadcast on 1 July 2005 on Sky One. Gen. On 2 August 2005 the BBC's programme guide Radio Times started to feature a weekly Super Sudoku. On September 24, 2005, following the havoc caused by Hurricanes Katrina and Rita, the National Guard named Brig. From July 2005 Channel 4 included a daily Sudoku game in their Teletext service (at page 391). Refineries directly impacted by the storm include:.

Recognizing the different psychological appeals of easy and difficult puzzles The Times introduced both side by side on 20 June 2005. Due to the impending oil shortage and increasing gas prices, Georgia Governor Sonny Perdue declared what he termed "snow days," closing all Georgia public primary and secondary schools on September 26 and 27 to conserve fuel for buses. A simpler explanation is that the puzzle attracts and retains readers—Sudoku players report an increasing sense of satisfaction as a puzzle approaches completion. Some economists argue that the rebuilding effort could buoy the economy in 2006, while others argue that the energy spike could decrease consumer confidence by enough to send the economy into a full-fledged recession when combined with the Federal Reserve's recent increases in interest rates. Sudoku became particularly prominent in newspapers soon after the 2005 general election leading some commentators to suggest that it was filling the gaps previously occupied by election coverage. The most pessimistic projections have GDP growth cut by 1% on an annualized basis in the United States in the second half of 2005, with as many as 500,000 people made unemployed. 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]). With some 200,000 jobless claims attributed to Katrina, Rita could be a further drag on a weakened US economy.

Newspapers competed to promote their Sudoku puzzles, with The Times and the Daily Mail each claiming to have been the first to feature Sudoku. However the oil industry escaped essentially unscathed from the storm and post-storm predictions estimated only minor price rises. As the name Sudoku became well-known in Britain, the Daily Mail adopted it in place of its earlier name "Codenumber". With over half of Gulf production still shut down in the wake of Katrina, some economists have stated that a worst case scenario is for gasoline prices to briefly touch $5/US gallon ($1.30/L), which would be easily the highest real price for gasoline paid in the United States during the internal combustion era. 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. Rita's path takes it through a dense area of offshore pipelines and oil platforms, and on land to an area with large refineries. 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. Currently, there is very little spare crude oil capacity in the United States, and the Gulf of Mexico produces some 2 million barrels per day (300,000 m³) total, as well has having some 30% of the total refining capacity of the United States, which is the world's largest consumer of gasoline and crude oil.

Until then the Times had kept very quiet about the huge daily interest that its daily Sudoku competition had aroused. The heavy concentration of oil infrastructure in the Gulf of Mexico makes hurricanes of Rita's intensity very problematic. The Telegraph continued to splash the puzzle on its front page, realizing that it was gaining sales simply by its presence. Bolivar Peninsula between Galveston and Sabine Pass had only a small ocean surge, in contrast to the eastern side of Rita's center which sent a 20 foot ocean surge through Louisiana's unprotected towns. 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. Rita's ocean surge was easily handled by Port Arthur's extensive levee system. 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". This placed most of the coastal community to the left of the eye and in the least damaging hurricane quadrant.

Nationwide News Pty Ltd began publishing the puzzle in The Daily Telegraph of Sydney on 20 May 2005; five puzzles with solutions were printed that day. The "Golden Triangle" area was spared a more devastating ocean surge by the redirection of Rita's path hours before landfall. 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. Those displaced by Rita were offered up to 60 days of hotel rooms, generators, chainsaws, and monetary assistance by FEMA. Three days later The Daily Mail began to publish the puzzle under the name "Codenumber". A mandatory evacuation was issued before Rita's landfall. The puzzles by Pappocom, Gould's software house, have been printed daily in the Times ever since. Some areas did not have power for more than six weeks.

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). The water treatment plant in Port Neches was heavily damaged. Over 6 years he developed a computer program to produce puzzles quickly. An enormous number of houses and businesses suffered extensive damage due to falling trees and directly from Rita's winds. In 1997, retired Hong Kong judge Wayne Gould, 59, a New Zealander, saw a partly completed puzzle in a Japanese bookshop. In Groves, the home of Texas' Pecan Festival, an equal number of the pecan trees were leveled. Sudoku has been called the "Rubik's cube of the 21st century". In Beaumont an estimated 25% of the trees in the heavily wooded neighborhoods were uprooted.

Within the context of puzzle history, parallels are often cited to Rubik's Cube, another logic puzzle popular in the 1980s. Texas Governor Rick Perry declared a nine county disaster area. It is also often included in puzzle anthologies, such as The Giant 1001 Puzzle Book (under the title Nine Numbers). All communities in the "Golden Triangle" formed by Beaumont, Port Arthur, and Orange sustained enormous damage from Rita's winds. 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. ^[48]. 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. ^[47] After water levels were lowered and an inspection was conducted by national and local experts, the dam was declared stable late on Monday, September 26, 2005.

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. Repairs to the dam are expected to take months to complete. At least one publisher still uses that title. As reported by the a number of news outlets, on Sunday, September 25, 2005, this discharge put lives at risk downstream and threatened a major bridge as well due to a sizable barge coming adrift. In 1989, Loadstar/Softdisk Publishing published DigitHunt on the Commodore 64, which was apparently the first home computer version of Sudoku. North of Houston, the 2.5 mile Lake Livingston dam sustained substantial damage from powerful waves driven by 117 mph winds ^[46] and had to conduct an emergency release in order to lessen pressure on the dam. Within Japan, Nikoli still holds the trademark for the name Sudoku; other publications in Japan use alternative names. ^[45].

It is now published in mainstream Japanese periodicals, such as the Asahi Shimbun. ^[44] Thirty one deaths have been reported in Harris County, of which all of them were indirect (mostly related to the evacuation and cleanup). 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). Some windows blew out of some downtown skyscrapers, and some trees and signals were down. 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. For the most part, Houston escaped major damage, apart from extensive loss of power. The puzzle was named by Kaji Maki (鍜治 真起), the president of Nikoli. ^[43].

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"). Around midnight, a vacant restaurant collapsed nearby, which was reportedly as a result of the fire that weakened the walls. 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). No serious injuries were reported in the fire. 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. However, the fire department was able to fight the blaze and prevent it from spreading through the city. The puzzle was designed by Howard Garns, a retired architect and freelance puzzle constructor, and first published in 1979. In the late evening, a fire broke out in the Strand District of Galveston, Texas, gutting several homes.

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. ^[42]. Since this applies to Latin squares in general, most variants of Sudoku have the same maximum. ^[40][41] Many of the passengers were mobility-impaired making escape difficult or impossible. The maximum number of givens that can be provided while still not rendering the solution unique is four short of a full grid; if two instances of two numbers each are missing and the cells they are to occupy form the corners of an orthogonal rectangle, and exactly two of these cells are within one region, there are two ways the numbers can be assigned. The fire started in the brake system, and the passengers' therapeutic oxygen tanks may have caused the bus to explode. The number of valid Sudoku solution grids for the 16×16 derivation is not known. Twenty three people were killed as a result of that incident.

Russell and Jarvis also showed that when symmetries were taken into account, there were 5,472,730,538 solutions [10] (sequence A109741 in OEIS). On the morning of September 23, a bus carrying 45 nursing home evacuees from Brighton Gardens in Bellaire, Texas erupted into flames and exploded on Interstate 45 southeast of Dallas in Wilmer. The derivation of this result was considerably simplified by analysis provided by Frazer Jarvis and the figure has been confirmed independently by Ed Russell. This poor area was just getting back of their feet after feeling Category 2 winds when Hurricane Katrina moved through the area. The result was derived through logic and brute force computation. Also Lauderdale County which is in east central Mississippi reported several confirmed and unconfirmed tornado touch downs in and near the cities of Marion and Meridian. This number is equal to 9! × 72² × 2⁷ × 27,704,267,971, the last factor of which is prime. There were several non-life threatening injuries.

Nonetheless, the number of valid Sudoku solution grids for the standard 9×9 grid was calculated by Bertram Felgenhauer in 2005 to be 6,670,903,752,021,072,936,960 [9] (sequence A107739 in OEIS). There were also numerous mobile homes damaged at the University Hills trailer park just off the campus. There are significantly fewer valid Sudoku solution grids than Latin squares because Sudoku imposes the additional regional constraint. MSU officials do not have specific damage assesments available; however, they do note there was significant damage to some buildings. A valid Sudoku solution grid is also a Latin square. A tornado touched down on Mississippi State University's campus. 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. ^[39].

In this case, two distinct vertices labelled by and are joined by an edge if and only if:. Another death was reported in Wilkinson County, although it has not been confirmed if it was storm-related. The vertices can be labelled with the ordered pairs , where x and y are integers between 1 and 9. Another unconfirmed tornado was reported in Bolivar County. The graph in question has 81 vertices, one vertex for each cell of the grid. At least 40 homes and an industrial plant were damaged from one tornado in Humphreys County in central Mississippi, in which one person was killed. 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. Several tornadoes from Rita's outer bands affected the state.

Solving Sudoku puzzles (as well as any other NP-hard problem) can be expressed as a graph colouring problem. ^[38]. 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. 250 people were rescued on Saturday, September 24. The general problem of solving Sudoku puzzles on n² x n² boards of n x n blocks is known to be NP-complete [8]. In Vermilion Parish south of Abbeville, rescue efforts were undertaken for up to 1,000 people stranded by local flooding. Here are some of the more notable single-instance variations:. ^[37].

Top Notch claim this as a feature designed to defeat solving programs. Louisiana Governor Kathleen Blanco reported that 700,000 homes had lost power in 41 of the state's 64 parishes. 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. ^[36]. 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. It has been reported that at least 100 people needed to be rescued from rooftops, and at least 25 more remain stranded. 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. ^[35] Some people were stranded in flooded communities, and boats had to be used for rescues.

Alphabetical variations have also emerged; there is no functional difference in the puzzle unless the letters spell something. In Terrebonne Parish, virtually every levee was breached. Sequential grids, as opposed to overlapping, are also published, with values in specific locations in grids needing to be transferred to others. Widespread flooding was reported in coastal parishes. Often, no givens are to be found in overlapping regions. In Vinton, several fires were burning, the roof was torn off the town's recreation center and many homes were damaged by fallen trees. [5] Puzzles with twenty or more overlapping grids are not uncommon in some Japanese publications. ^[34] Damage to the city's electrical system was so severe that authorities warned that power would not return for two weeks, if not longer.

In The Times and The Sydney Morning Herald this form of puzzle is known as Samurai SuDoku. There was also extensive damage to its regional airport. 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. At a hotel on the Contraband Bayou, water was reportedly up to the second floor. Puzzles constructed from multiple Sudoku grids are common. Lake Charles experienced severe flooding, with reports of water rising 6-8 feet in areas around the lake itself. Some such variants forsake standard givens entirely. A casino boat and several barges were floating loose in Lake Charles and damaged a bridge spanning Interstate 10 across the Calcasieu River.

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. In Cameron Parish, the communities of Hackberry ^[33], Cameron, Creole, Grand Chenier, and Holly Beach were heavily damaged or entirely destroyed. [3] [4] In this variant, all the numbers must appear in all the concentric rings as well as in all pairs of adjacent wedges. Damage in southwestern Louisiana was extensive. Also found is the Circular Sudoku, also known as Target Sudoku, invented by Essex mathematician Peter Higgins. ^[32]. 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. As of Saturday night, September 24, water from a 150-foot gap in the Industrial Canal levee had some areas of the Ninth Ward under eight feet of water.

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. Some pumping stations were abandoned. 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. CDT, water had begun gushing through another leak in the patched London Avenue Canal into the surrounding Gentilly neighborhood. 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. By approximately 5 p.m. Another common variant is for additional restrictions to be enforced on the placement of numbers beyond the usual row, column, and region requirements. CDT on Friday.

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. Water in the Ninth Ward was reported to be waist-deep at 11 a.m. Puzzle Championship had a Sudoku with parallelogram regions that wrapped around the outer border of the puzzle, as if the grid were toroidal. CDT on Friday, September 23. [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. Water entered the Ninth Ward over two 32-foot (10 m) wide patches in the levee as of about 9 a.m. 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. On Friday, September 23, the day prior to landfall, rising water due to Hurricane Rita was pouring through breaches in the patched Industrial Canal levee in New Orleans' already hard-hit Ninth Ward, as reported by the Army Corps of Engineers.

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. New Orleans levee system had already sustained heavy damage from Hurricane Katrina before Rita's outer bands of rain fell on the city. 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. ^[31]. 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. Both were due to high surf and rip currents caused by Rita's distant waves. Dell Number Place Challenger (see Variants below) puzzles also list authors . While the Florida Panhandle escaped most of the land effects from Rita, two deaths were reported on beaches.

Nikoli Sudoku are hand-constructed, with the author being credited; the givens are always found in a symmetrical pattern. No deaths were reported in either Florida or Cuba from the initial impact. 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. ^[30]. 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. More than 2,000 National Guard troops and dozens of law enforcement officers were brought in and are on standby. They also have no authoring credits — that is, the name of the constructor is not printed with any puzzle. Bush in four counties: Broward, Collier, Miami-Dade and Monroe.

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. A state of emergency was declared by Florida Governor Jeb Bush and a federal emergency by President George W. Building a Sudoku with symmetrical givens is a simple matter of placing the undefined givens in a symmetrical pattern to begin with. ^[29]. (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. EDT on Tuesday, September 20, about 25,000 customers were without electricity in Broward and Miami-Dade counties, plus another 2,100 in the Keys. 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. As of 8 p.m.

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. The Overseas Highway (US 1) connecting the islands was impassable in some sections as a result of the flooding. 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. Flooding was reported along the Florida Keys as a result of the storm surge. 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. More than 340,000 people were under voluntary or mandatory evacuation orders in Florida and Cuba. Some online versions offer several difficulty levels. No deaths were reported in Arkansas due to Rita.

This estimation allows publishers to tailor their Sudoku puzzles to audiences of varied solving experience. ^[28]. Computer solvers can estimate the difficulty for a human to find the solution, based on the complexity of the solving techniques required. Most tornadoes move northeast. It is based on the relevance and the positioning of the numbers rather than the quantity of the numbers. The tornadoes were unusual in that they moved in a northwestern direction due to the direction in which Rita was moving. 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. ^[27].

Perhaps surprisingly, the number of givens has little or no bearing on a puzzle's difficulty. In addition, significant flooding has been reported in several areas. Published puzzles often are ranked in terms of difficulty. While Rita weakened to a tropical depression, the outer bands continued to spawn numerous tornadoes in Arkansas, including one in Lonoke County and another in Conway County, damaging many homes and businesses in several communities. A very fast solver is usually required for most trial-and-error puzzle-creation algorithms. poisoning, illnesses, waiting for help). This is the method now preferred by many Sudoku programmers, mainly by virtue of its speed. Indirect deaths indicate those caused by hurricane-related accidents (including car accidents, fires or other incidents), as well as clean-up and evacuation incidents and health issues (i.e.

This method can be directly applied to solving Sudoku problems, counting all possible solutions for most puzzles rapidly. Direct deaths indicate those caused by the direct effects of the winds, flooding, tornadoes, storm surge or oceanic effects of Rita. A highly efficient way of solving such constraint problems is Donald Knuth's Dancing Links Algorithm. The two Florida deaths were both in rip currents on beaches caused by Rita's distant waves. Backtracking may be applied when alternate values cannot otherwise be excluded. One was caused by a hurricane-related tornado in the outer bands, and three others were caused by fallen trees during the storm. 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. Only six of them were direct deaths.

Another alternative uses finite domain constraint programming. CDT on October 3 (0300 UTC October 4) stands at 119. 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. The reported death toll as of 10 p.m. 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). Also gas prices fell in the U.S instead of rising as feared. 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). ^[9].

This continues until a conflict occurs, in which case the next alternative value is used for the last cell changed. ^[8] Total damage is estimated $9.4 billion, which makes Rita the ninth costliest storm in US history. 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 total, it is estimated that well over 2 million customers were without electricity. It is also fairly simple to build a backtracking search. ^[7] Calcasieu Parish, with the communities of Lake Charles, Sulphur, Westlake and Vinton also suffered heavy damage. Given the self-imposed constraints of most Sudoku publishers, this method generally succeeds. Cameron Parish was heavily damaged, with the communities of Holly Beach, Hackberry and Cameron being essentially destroyed.

These programs emulate the human logic to solve a puzzle without resorting to guesses. However, local storm surges of 15 to 20 feet (4.5-6.1 m) in southwestern Louisiana were reported, and in from coastal parishes, damage was extensive. 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 5 inches (130 mm) of rain expected to fall overnight in New Orleans also did not happen, and the pressure on the levee system was eased. The proverbial Holy Grail is to find a technique which minimises counting, marking up, and rubbing out. The storm surge feared in Galveston did not materialize, as the city was well to the west of the storm's center; the strong winds actually flattened the surge, which was only seven feet (2 m), and the seawall was easily able to handle it. The what-if approach can be confusing unless you are well organised. The effects of Hurricane Rita were not nearly as severe as expected.

Writing candidate numbers into empty cells can be time-consuming. Valero Energy Corp, the nation's largest refiner, stated on September 21 that Rita could have caused gasoline prices to rise well above $3 per US gallon ($0.79/L). The counting of regions, rows, and columns can feel boring. While no potential storm path would threaten all of the capacity at once, a direct strike on Houston could disable up to 8% of the nation's refining capacity. Ideally one needs to find a combination of techniques which avoids some of the drawbacks of the above elements. The Texas Gulf Coast is home to 23% of the United States' refining capacity, and numerous offshore production platforms were in Rita's path. The two main approaches to analysis are "candidate elimination" and "what-if". The storm threatened a large amount of oil infrastructure that was left undamaged by Katrina.

When using marking, a couple of similar rules applied in a specified order can solve any Sudoku puzzle, without performing any kind of backtracking. Concerns had been raised over the state of the oil industry in response to Rita. 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. As part of the evacuation, Johnson Space Center in Houston handed off control of the International Space Station to their Russian counterparts. When using marking, additional analysis can be performed. Many motorists ran out of gas despite turning off their air conditioners in the 98 degree record temperatures. When only one marking is missing, that has to be the value of the cell. Evacuees fought traffic all day and only moved about one hundred to one-hundred and fifty miles.

Thus a cell will start empty and as more constraints become known it will slowly fill. The Texas Department of Transportation was unprepared to execute this in an efficient way and in many cases without a release point to the North traffic would only speed up for a short time. An alternative technique that some find easier is to mark up those numbers that a cell cannot be. Contraflow lanes were instigated after it was realized that a the state's highway system had become gridlocked. There are two popular notations: subscripts and dots. Distances that usually took 2-3 hours of travel time took some passengers upwards of 24 hours. Many find it useful to guide this analysis by marking candidate numbers in the blank cells. Designated evacuation routes slowed to a pace far worse than with any previous hurricane.

From this point, it is necessary to engage in some logical analysis. By the time Jefferson County began their mandatory evacuation up Highway 69, 96 and others, Houstonians had already clogged up these highway arteries to the North. Scanning stops when no further numbers can be discovered. During the Rita evacuation these preperations and their execution were overwhelmed by the enormous and unprecedented numbers of people fleeing from the Houston area prior to the residents of the "Golden Triangle". 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. Plans were put in place to open up these intersections. 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). After Lili, citizens came back with complaints of long lines of cars caused by stop lights and stop signs along evacuation routes unattended by anyone from law enforcement.

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). Highway 73 between Port Arthur and Winnie was also widened to facilitate future evacuations in response to an even earlier hurricane. 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. Officials in the "Golden Triangle" area had set up evacuation routes and a shelter system of sorts in response to the slow evacuation of residents prior to Hurricane Lili. Scanning consists of two basic techniques:. "If you're not in the evacuation zone, follow the news," he said, advising people to use common sense. Scans may have to be performed several times in between analysis periods. After heavy traffic snarled roads leading out of town and gas shortages left numerous vehicles stranded, he backed off on this.

Scanning is performed at the outset and periodically throughout the solution. On Wednesday, Houston mayor Bill White urged residents to evacuate the city, telling residents, "Don't wait; the time for waiting is over," and reminding residents of the disaster in New Orleans. The strategy for solving a puzzle may be regarded as comprising a combination of three processes: scanning, marking up, and analysing. These evacuation-destination cities included Austin, College Station, San Antonio, Dallas, Huntsville, and Lufkin, Texas. 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. Also, different zones were to be forced to go to certain cities in Texas and were not allowed to exit their designated routes except for food and gas - another feature of the evacuation plan which hoped to keep traffic and flow orderly throughout this timeframe. 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. Officials of Harris County hoped that the designation of zones A, B, and C would be able to prevent bottlenecks leaving the area such as those seen out of New Orleans prior to Katrina and Hurricane Dennis this year.

Some cells already contain numbers, known as "givens" (or sometimes as "clues"). Nonetheless, many residents remained in the county because they were either unaware of the danger of the storm or believed that it was more important to protect their belongings, particularly in the wake of looting following Hurricane Katrina. 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). Officials in Galveston County (which includes the city of Galveston), which was devastated by the Galveston Hurricane of 1900, ordered mandatory evacuations, effective September 21 at 6 p.m., in a staggered sequence setting different zones in the area which were due to leave at different times over 24 hours, well in advance of the storm's possible landfall later in the week but not enough in advance to ensure that all residents could evacuate safely in advance of the storm. The puzzles are often available free from published sources and also may be custom-generated using software. Highway 290 northwest to Bryan/College Station. The level of difficulty of the puzzles can be selected to suit the audience. ^[6] On September 22, Governor Perry and the Texas Department of Transportation implemented a contraflow lane reversal on Interstate 45 north towards Dallas, on Interstate 10 west towards San Antonio and U.S.

Sudoku is recommended by some teachers as an exercise in logical reasoning. Texas Governor Rick Perry recalled all emergency personnel, including almost 1,200 Texas National Guard from Katrina recovery efforts, in anticipation of Hurricane Rita's arrival. 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. In addition, residents of Cameron Parish, Calcasieu Parish, and parts of Jefferson Davis Parish and Vermillion Parish were told to evacuate ahead of the storm. Numerals are used throughout this article. ^[5]. Dell Magazines, the puzzle's originator, has been using numerals for Number Place in its magazines since they first published it in 1979. The original breaches had occurred a month earlier as a result of Hurricane Katrina.

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). Although Rita remained well to the south and west of New Orleans, a pre-landfall storm surge overwhelmed a levee protecting the lower 9th Ward ^[3], a part of a fragile and already compromised levee system as repairs continued ^[4] At landfall, more parts of the levee wall were breached causing major reflooding in New Orleans. The numerals in Sudoku puzzles are used for convenience; arithmetic relationships between numerals are absolutely irrelevant. ^[2] However, as Rita developed in the Gulf of Mexico, the reopening was cancelled and a re-evacuation of the city was initiated on September 21 as the storm was initially forecast to make landfall much closer to the city. 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). Before Rita, the mayor of New Orleans, Ray Nagin, had planned to begin reopening the city after the damage caused by Hurricane Katrina on September 19. title. Hurricane Rita was the third (now fourth) most intense hurricane on record in the Atlantic basin and the most intense hurricane on record in the Gulf of Mexico, taking over the latter record set by Hurricane Katrina only three weeks earlier.

S. Rita has broken multiple records, being the earliest 17th named storm, the third (now fourth) most intense storm, and quickest drop of pressure in one hour. Other Japanese publishers refer to the puzzle as Nanpure (Number Place), the original U. The Hydrometeorological Prediction Center ceased monitoring Tropical Depression Rita early on September 26. Ltd in Japan. Rita's remnants -- technically an extensive low pressure area -- moved quickly out of the lower Mississippi Valley region and were absorbed by a cold front. 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. Rita lost both hurricane and tropical storm status on the same day as its landfall.

. Rita's wind field was so intense that it destroyed or disabled several weather buoys. The first world championship will be in Lucca(Italy) from 10 to 12 March 2006. "Rita is the strongest storm that I've ever been in," he commented. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. Warren Madden, a Hurricane Hunter and meteorologist for The Weather Channel, recorded a peak wind gust of 235 mph (380 km/h) while in the eye of the storm. S. Col.

Although first published in a U. Lt. Completing the puzzle requires patience and logical ability. (NASA clip depicting the history of the storm before landfall). Each row, column, and region must contain only one instance of each numeral. Hurricane Rita's rapid intensification may in part be attributed to its encounter with the Gulf Loop Current and Eddy Vortex. 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"). CDT, the advisory said that Rita's maximum sustained winds had increased to 175 mph (280 km/h) with an estimated minimum pressure of 897 mbar (hPa), (26.59 inHg).

Sudoku (Japanese: 数独, sūdoku), sometimes spelled Su Doku, is a logic-based placement puzzle, also known as Number Place in the United States. At 10:00 p.m. and . CDT, a reconnaissance aircraft recorded a pressure reading of 899 mbar (hPa), but it was thought to actually be lower since the reading was not from the center. or,. At 6:50 p.m. or,. CDT (19:55 UTC), another update was issued, saying Rita had strengthened into a Category 5 storm with maximum wind speeds of 165 mph (265 km/h).

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. Less than two hours later, at 3:55 p.m. 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. CDT (1815 UTC) said that Rita's maximum winds had increased to 150 mph (240 km/h) and a minimum pressure of 920 mbar (hPa). The 2005 U.S. An update issued at 2:15 p.m. A three-dimensional Sudoku puzzle was invented by Dion Church and published in the Daily Telegraph in May 2005. Rita continued to gain strength unabated.

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. At that advisory, Rita's maximum sustained winds increased to 140 mph (225 km/h). The what-if approach requires a pencil and eraser. EDT on September 21. 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. EDT on September 20 to 11 a.m. In logical terms, this is known as reductio ad absurdum. The National Hurricane Center's official advisories, issued every three hours, showed strengthening at every single advisory from 5 p.m.

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. As Hurricane Rita entered the Gulf of Mexico, it rapidly increased in intensity. In the what-if approach, a cell with only two candidate numbers is selected, and a guess is made. The warm water in the Gulf of Mexico, which was at the time 1 °F (0.5 °C) above average, was very favorable for hurricane development. 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. Four hours later, another special update stated that Rita had reached Category 2 strength with 100 mph (160 km/h) maximum sustained winds. Other candidates in the matched cells can be eliminated. EDT that morning showed that Rita had closed the eyewall and winds clearly reached hurricane strength.

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. Aerial reconnaissance data released at 9:45 a.m. The principle is true for all quantities of candidate numbers. Rita was slow to become a hurricane; discussions early on September 20 showed that wind translations to surface level were indeed at 75 mph (120 km/h), however, the lack of a complete eyewall meant that the National Hurricane Center kept Rita as a tropical storm with 70 mph (110 km/h) winds overnight. 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. A mandatory evacuation had been ordered for the entire Florida Keys. 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. It became the 17th tropical storm of the season on September 18, less than a day after forming.

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. A surface low formed near it, and the season's 18th tropical depression formed soon thereafter east of the Turks and Caicos Islands. 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. The storm formed at the tail end of an old frontal boundary, where convection and low level circulation around an upper level low steadily developed for over two days. One of the most common elimination tactics is "unmatched candidate deletion". Rita was in fact the third seventeenth storm of any season to form since naming of tropical storms began in 1950, but in the 1969 season many tropical storms went unnamed due to the lack of sophisticated forecasting systems; the seventeenth storm of 1969 was Hurricane Martha. If these patterns can be identified, elimination of candidate possibilities external to the grid framework can sometimes be achieved. Rita's name itself is a significant indicator of the activity of the 2005 hurricane season: only once before had a name starting with 'R' been used for an Atlantic storm, in 1995 for Hurricane Roxanne.

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. The storm killed just 6 people but caused 113 indirect deaths; damage estimates are around $9 billion (2005 US dollars). 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. Post-landfall damage was extensive in the coastal areas in southwestern Louisiana and extreme southeastern Texas. 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: