The Rubik's Revenge is a 4×4×4 version of Rubik's Cube. It was released in 1981. Invented by Péter Sebestény, the Rubik's Revenge was nearly called the Sebestény Cube until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube. Unlike the original puzzle, it has no fixed facets: the centre facets are free to move to different positions. Methods for solving the 3×3×3 cube work for the edges and corners of the 4×4×4 cube, as long as one has identified the relative positions of the colours — since the centre facets can no longer be used for identification; the puzzle consists of 56 unique miniature cubes on the surface. These consist of 24 centres which show one colour each, 24 edges which show two colours each, 8 corners which show three colours each; the original Rubik's Revenge can be taken apart without much difficulty by turning one side through a 30° angle and prying an edge upward until it dislodges. The original mechanism designed by Sebestény uses a grooved ball to hold the centre pieces in place.
The edge pieces are held in place by the centres and the corners are held in place by the edges, much like the original cube. There are three mutually perpendicular grooves for the centre pieces to slide through; each groove is only wide enough to allow one row of centre pieces to slide through it. The ball is shaped to prevent the centre pieces of the other row from sliding, ensuring that the ball remains aligned with the outside of the cube. Turning one of the centre layers moves either just that layer or the ball as well; the Eastsheen version of the cube, smaller at 6cm to an edge, has a different mechanism. Its mechanism is similar to Eastsheen's version of the Professor's cube, instead of the ball-core mechanism. There are 42 pieces hidden within the cube, corresponding to the centre rows on the Professor's Cube; this design is more durable than the original and allows for screws to be used to tighten or loosen the cube. The central spindle is specially shaped to prevent it from becoming misaligned with the exterior of the cube.
There are 24 edge pieces which show two coloured sides each, eight corner pieces which show three colours. Each corner piece or pair of edge pieces shows a unique colour combination, but not all combinations are present; the location of these cubes relative to one another can be altered by twisting the layers of the cube, but the location of the coloured sides relative to one another in the completed state of the puzzle cannot be altered: it is fixed by the relative positions of the centre squares and the distribution of colour combinations on edge and corner pieces. For most recent Cubes, the colours of the stickers are red opposite orange, yellow opposite white, green opposite blue. However, there exist Cubes with alternative colour arrangements; the Eastsheen version has purple instead of orange. There are 24 edges and 24 centres. Any permutation of the corners is possible, including odd permutations. Seven of the corners can be independently rotated, the orientation of the eighth depends on the other seven, giving 8!×37 combinations.
There are 24 centres, which can be arranged in 24! Different ways. Assuming that the four centres of each colour are indistinguishable, the number of permutations is reduced to 24!/ arrangements. The reducing factor comes about because there are 24 ways to arrange the four pieces of a given colour; this is raised to the sixth power. An odd permutation of the corners implies an odd permutation of the centres and vice versa. There are several ways to make the centre pieces distinguishable, which would make an odd centre permutation visible; the 24 edges can not be flipped. Corresponding edges are distinguishable. Any permutation of the edges is possible, including odd permutations, giving 24! arrangements, independently of the corners or centres. Assuming the cube does not have a fixed orientation in space, that the permutations resulting from rotating the cube without twisting it are considered identical, the number of permutations is reduced by a factor of 24; this is because all 24 possible positions and orientations of the first corner are equivalent because of the lack of fixed centres.
This factor does not appear when calculating the permutations of N×N×N cubes where N is odd, since those puzzles have fixed centres which identify the cube's spatial orientation. This gives a total number of permutations of 8! × 3 7 × 24! 2 24 7 ≈ 7.40 × 10 45. The full number is 7401196841564901869874093974498574336000000000 possible permutations; some versions of Rubik's Revenge have one of the centre pieces marked with a logo, distinguishing it from the other three of the same colour. This increases the number of distinguishable permutations by a factor of four to 2.96×1046, although any of the four
Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Called the Magic Cube, the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer, won the German Game of the Year special award for Best Puzzle that year. As of January 2009, 350 million cubes had been sold worldwide making it the world's top-selling puzzle game, it is considered to be the world's best-selling toy. On the original classic Rubik's Cube, each of the six faces was covered by nine stickers, each of one of six solid colours: white, blue, orange and yellow; the current version of the cube has been updated to coloured plastic panels instead, which prevents peeling and fading. In sold models, white is opposite yellow, blue is opposite green, orange is opposite red, the red and blue are arranged in that order in a clockwise arrangement. On early cubes, the position of the colours varied from cube to cube.
An internal pivot mechanism enables each face to turn thus mixing up the colours. For the puzzle to be solved, each face must be returned to have only one colour. Similar puzzles have now been produced with various numbers of sides and stickers, not all of them by Rubik. Although the Rubik's Cube reached its height of mainstream popularity in the 1980s, it is still known and used. Many speedcubers continue to practice similar puzzles. Since 2003, the World Cube Association, the Rubik's Cube's international governing body, has organised competitions worldwide and recognises world records. In March 1970, Larry D. Nichols invented a 2×2×2 "Puzzle with Pieces Rotatable in Groups" and filed a Canadian patent application for it. Nichols's cube was held together by magnets. Nichols was granted U. S. Patent 3,655,201 on 11 April 1972, two years before Rubik invented his Cube. On 9 April 1970, Frank Fox applied to patent an "amusement device", a type of sliding puzzle on a spherical surface with "at least two 3×3 arrays" intended to be used for the game of noughts and crosses.
He received his UK patent on 16 January 1974. In the mid-1970s, Ernő Rubik worked at the Department of Interior Design at the Academy of Applied Arts and Crafts in Budapest. Although it is reported that the Cube was built as a teaching tool to help his students understand 3D objects, his actual purpose was solving the structural problem of moving the parts independently without the entire mechanism falling apart, he did not realise that he had created a puzzle until the first time he scrambled his new Cube and tried to restore it. Rubik applied for a patent in Hungary for his "Magic Cube" on 30 January 1975, HU170062 was granted that year; the first test batches of the Magic Cube were produced in late 1977 and released in Budapest toy shops. Magic Cube was held together with interlocking plastic pieces that prevented the puzzle being pulled apart, unlike the magnets in Nichols's design. With Ernő Rubik's permission, businessman Tibor Laczi took a Cube to Germany's Nuremberg Toy Fair in February 1979 in an attempt to popularise it.
It was noticed by Seven Towns founder Tom Kremer and they signed a deal with Ideal Toys in September 1979 to release the Magic Cube worldwide. Ideal wanted at least a recognisable name to trademark; the puzzle made its international debut at the toy fairs of London, Paris and New York in January and February 1980. After its international debut, the progress of the Cube towards the toy shop shelves of the West was halted so that it could be manufactured to Western safety and packaging specifications. A lighter Cube was produced, Ideal decided to rename it. "The Gordian Knot" and "Inca Gold" were considered, but the company decided on "Rubik's Cube", the first batch was exported from Hungary in May 1980. After the first batches of Rubik's Cubes were released in May 1980, initial sales were modest, but Ideal began a television advertising campaign in the middle of the year which it supplemented with newspaper adverts. At the end of 1980 Rubik's Cube won a German Game of the Year special award, won similar awards for best toy in the UK, the US.
By 1981 Rubik's Cube had become a craze, it is estimated that in the period from 1980 to 1983 around 200 million Rubik's Cubes were sold worldwide. In March 1981 a speedcubing championship organised by the Guinness Book of World Records was held in Munich, a Rubik's Cube was depicted on the front cover of Scientific American that same month. In June 1981 The Washington Post reported that the Rubik's Cube is "a puzzle that's moving like fast food right now... this year's Hoola Hoop or Bongo Board", by September 1981 New Scientist noted that the cube had "captivated the attention of children of ages from 7 to 70 all over the world this summer."As most people could only solve one or two sides, numerous books were published including David Singmaster's Notes on Rubik's "Magic Cube" and Patrick Bossert's You Can Do the Cube. At one stage in 1981 three of the top ten best selling books in the US were books on solving the Rubik's Cube, the best-selling book of 1981 was James G. Nourse's The Simple Solution to Rubik's Cube which sold over 6 million copies.
In 1981 the Museum of Modern Art in New York exhibited a Rubik's Cube, at the 1982 World's Fair in Knoxville, Tennessee a six-foot Cube was put on display. ABC Television developed a cartoon show called Rubik, the Amazing Cube. In June 1982 the First Rubik's Cube World Championship
The Pocket Cube is the 2×2×2 equivalent of a Rubik's Cube. The cube consists of all corners. In March 1970, Larry D. Nichols invented a 2×2×2 "Puzzle with Pieces Rotatable in Groups" and filed a Canadian patent application for it. Nichols's cube was held together with magnets. Nichols was granted U. S. Patent 3,655,201 on April 11, 1972, two years before Rubik invented his Cube. Nichols assigned his patent to his employer Moleculon Research Corp. which sued Ideal in 1982. In 1984, Ideal appealed. In 1986, the appeals court affirmed the judgment that Rubik's 2×2×2 Pocket Cube infringed Nichols's patent, but overturned the judgment on Rubik's 3×3×3 Cube. Any permutation of the eight corners is possible, seven of them can be independently rotated. There is nothing identifying the orientation of the cube in space, reducing the positions by a factor of 24; this is because all 24 possible positions and orientations of the first corner are equivalent due to the lack of fixed centers. This factor does not appear when calculating the permutations of N×N×N cubes where N is odd, since those puzzles have fixed centers which identify the cube's spatial orientation.
The number of possible positions of the cube is 8! × 3 7 24 = 7! × 3 6 = 3, 674, 160. The maximum number of turns required to solve the cube is up to 11 half or quarter turns, or up to 14 quarter turns only; the number a of positions that require n any turns and number q of positions that require n quarter turns only are: The two-generator subgroup is of order 29,160. A pocket cube can be solved with the same methods as a 3x3x3 Rubik's cube by treating it as a 3x3x3 with solved centers and edges. More advanced methods require more algorithms; these algorithms designed for solving a 2x2x2 cube are significantly shorter and faster than the algorithms one would use for solving a 3x3x3 cube. The Ortega method called the Varasano method, is an intermediate method. First a face is built the last layer is oriented and lastly both layers are permuted; the Ortega method requires a total of 12 algorithms. The CLL method first builds a layer and solves the second layer in one step by using one of 42 algorithms.
The most advanced method is the EG method, named after Eric Gunner. It starts by building a layer, but solves the rest of the puzzle in one step, it requires knowing 128 algorithms. The world record solve is 0.49 seconds, set by Maciej Czapiewski of Poland on 20 March 2016 at Grudziądz Open 2016. The world record average of 5 solves is 1.21 seconds, set by Martin Vædele Egdal on 21 October 2018 at Kjeller Open 2018, with the times, 1.09, 1.47, 1.07 seconds. Rubik's Cube Rubik's Revenge Professor's Cube V-Cube 6 V-Cube 7 V-Cube 8 Combination puzzles WOWCube Methods for speedsolving the 2x2x2
A combination puzzle known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations. The puzzle is solved by achieving a particular combination starting from a random combination; the solution is required to be some recognisable pattern such as'all like colours together' or'all numbers in order'. The most famous of these puzzles is the original Rubik's Cube, a cubic puzzle in which each of the six faces can be independently rotated; each of the six faces is a different colour, but each of the nine pieces on a face is identical in colour, in the solved condition. In the unsolved condition colours are distributed amongst the pieces of the cube. Puzzles like the Rubik's Cube which are manipulated by rotating a layer of pieces are popularly called twisty puzzles; the mechanical construction of the puzzle will define the rules by which the combination of pieces can be altered. This leads to some limitations.
For instance, in the case of the Rubik's Cube, there are a large number of combinations that can be achieved by randomly placing the coloured stickers on the cube, but not all of these can be achieved by manipulating the cube rotations. Not all the combinations that are mechanically possible from a disassembled cube are possible by manipulation of the puzzle. Since neither unpeeling the stickers nor disassembling the cube is an allowed operation, the possible operations of rotating various faces limit what can be achieved. Although a mechanical realization of the puzzle is usual, it is not necessary, it is only necessary. The puzzle can be realized in virtual space or as a set of mathematical statements. In fact, there are some puzzles. An example is the 4-dimensional 3×3×3×3 tesseract puzzle, simulated by the MagicCube4D software. There have been many different shapes of Rubik type puzzles constructed; as well as cubes, all of the regular polyhedra and many of the semi-regular and stellated polyhedra have been made.
A cuboid is a rectilinear polyhedron. That is. Or in other words, a box shape. A regular cuboid, in the context of this article, is a cuboid puzzle where all the pieces are the same size in edge length. Pieces are referred to as "cubies". There are many puzzles which are mechanically identical to the regular cuboids listed above but have variations in the pattern and colour of design; some of these are custom made in small numbers, sometimes for promotional events. The ones listed in the table below are included because the pattern in some way affects the difficulty of the solution or is notable in some other way. An irregular cuboid, in the context of this article, is a cuboid puzzle where not all the pieces are the same size in edge length; this category of puzzle is made by taking a larger regular cuboid puzzle and fusing together some of the pieces to make larger pieces. In the formulae for piece configuration, the configuration of the fused pieces is given in brackets. Thus, a 2x2x2 is a 2 × 2 × 2 puzzle.
Puzzles which are constructed in this way are called "bandaged" cubes. However, there are many irregular cuboids. N-dimensional sequential move puzzles Puck puzzle WOWCube A large database of twisty puzzles The Puzzle Museum The Magic Polyhedra Patent Page
Wodzisław Śląski is a town in Silesian Voivodeship, southern Poland with 50,493 inhabitants. It is the seat of Wodzisław County, it was in Katowice Voivodeship. Wodzisław Śląski is an urban in the south-eastern part of Upper Silesia, now in Silesian Voivodeship in south Poland, within the south portion of the Upper Silesian Coal Basin, it borders the towns of Pszów, Radlin and villages Marklowice, Godów, Gorzyce and Lubomia. It lies near Czech border in the foreground Moravian Gate. Several rivers flow through the major two being the Leśnica and "Zawadka" rivers. Within 600 km of Wodzisław Śląski are the capital cities of six countries: Berlin, Prague, Bratislava and Warsaw; the climate of the area is continental humid. The average temperature is 8 °C. Yearly rainfall averages at 786 mm, the most rainy month being July; the area's characteristic weak and medium winds blow at about 4 m/s from the south-west. The town is divided into 9 districts that have its own administrative body: Jedłownik Osiedle Jedłownik-Turzyczka-Karkoszka Kokoszyce Nowe Miasto Osiedla XXX-lecia - Piastów - Dąbrówki Radlin II Stare Miasto Wilchwy Zawada Being a borderland town, Wodzisław Śląski is a centre of the Wodzisław County, formed during a historical process lasting many centuries.
Rich excavations the oldest finds dated back to the stone Age give evidence about its ancient inhabitants. The city's name derives from the Piast Duke Władysław of Opole, he located the city and established the Wodzisław monastery about 1257. The city's origins can be traced back into the 10th and 11th century, when three Slavic settlements existed on Wodzisław's present-day territory which merged to form one town. In the course of the medieval eastward migration of Flemish and German settlers, Wodzisław, as many other Polish settlements, was incorporated according to the so-called Magdeburg Law at some point before 1257. This, however, is not to be confused with a change in national affiliation. At that times of Duchess Constance, the town developed fast. Wodzisław was one of the richest towns of Upper Silesia. In 14 and 15th century the city developed into a regional trade centre. In the 15th century, the Hussites devastated the city. From 1526, including the fiefdom of Silesia, which Wodzisław was a part of, came under the authority of the Habsburg crown.
In 16th and 17th century and during the time of the Thirty Years' War, Wodzisław been part of the Habsburg Empire. After the end of the Thirty Years' War Wodzisław was destroyed. Never back to Middle Ages' "golden time". At the beginning of the War of the Austrian Succession between King Frederick II of Prussia and the Habsburg empress Maria Theresa of Austria, the greatest part of Silesia, including Wodzisław, was annexed by the Kingdom of Prussia in 1740, which Austria recognized in 1763. In 1815 the city became part of the Prussian Province of Silesia. Coal mining gained importance for Wodzisław's economy as early as the 19th century. After the end of World War I in 1918, Polish statehood was restored. Amidst an atmosphere of ethnic unrest, a referendum was organized to determine the future national affiliation of Upper Silesia. Although an overall majority had opted for Germany, the area was divided in an attempt to satisfy both parties. Although both parties considered the territory they were assigned insufficient, the division was justified insofar as in the German and Polish parts a majority had voted in favour of the respective nation.
The lowest amount of pro-German votes was registered in the districts of Pszczyna. The city and the largest part of the district of Rybnik were attached to the territory of the Second Polish Republic; the Upper Silesia plebiscite and eventual division of Upper Silesia were accompanied by three Silesian Uprisings of Polish milicians. Within the Second Polish Republic of the interwar period, Wodzisław was part of the Silesian Voivodeship, which enjoyed far-reaching political and financial autonomy. With the outbreak of World War II in 1939, the border city Wodzisław returned under the rule of Germany, being in the part of Poland, directly incorporated into the German state; the population was ethnically categorized and either "re-Germanized" or disfranchised and deported into the General Government as Poles. On 22 January 1945 a death march from Nazi German's death camp Auschwitz, 35 mi away, ended in Wodzisław Śląski, where the prisoners were put on freight trains to other camps; when the Soviet army advanced on Poland, nine days before the Soviets arrived, the Schutzstaffel had marched 60,000 prisoners out of the camp.
15,000 prisoners died on the way. There is a memorial to the victims of the Holocaust from Wodzisław in the Baron Hirsch Cemetery Staten Island, New York where the Wodzisław landsmanshaft has a section. In March 1945 the Soviet army arrived near Wodzisław. 80% of the town was destroyed in the war. From 26 March 194
Bełchatów is a town in central Poland with a population of 58,326. It is located in 160 kilometres from Warsaw; the Elektrownia Bełchatów, located in Bełchatów, is the largest coal fueled power plant in Europe and one of the largest in the world. It produces 20 % of the total power generation in Poland. One municipal division of Bełchatów comprises numerous housing estates including the Budowlanych housing estate located in the central part of the town; the estate is close to the "Rakówka" river and Olszewski Park. Other municipal divisions of Bełchatów include Dobrzelów District and the following housing estates: GKS Bełchatów - men's football team Skra Bełchatów - men's volleyball team playing in Polish Volleyball League Championship of Poland in seasons 2004/05 and 05/06, Winner of Polish Cup in 2004 and 2005, 3rd place in season 2001/02, 4th place in season 2003/2004, Zjednoczeni Bełchatów - men's football team Harry Haft, survivor of the Auschwitz concentration camp and a professional boxer in the United States during 1948–1949 Bełchatów is twinned with: Aubergenville in France Myślenice in Poland Csongrád in Hungary Alcobaça in Portugal Tauragė in Lithuania Sovetsk in Russia Official page of the town
The V-Cube 7 is a combination puzzle in the form of a 7×7×7 cube. The first mass-produced 7×7×7 was invented by Panagiotis Verdes and is produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a number of Chinese companies, some of which have mechanisms which improve on the original. Like the 5 × 5 × 5, the V-Cube 7 has both movable center facets; the puzzle consists of 218 unique miniature cubes on the surface. Six of these are attached directly to the internal "spider" frame and are fixed in position relative to one another; the V-Cube 6 uses the same mechanism, except that on the latter the central rows, which hold the rest of the pieces together, are hidden. There are 150 center pieces which show one color each, 60 edge pieces which show two colors each, eight corner pieces which show three colors each; each piece shows a unique color combination. The location of these cubes relative to one another can be altered by twisting the outer layers of the Cube 90°, 180° or 270°, but the location of the colored sides relative to one another in the completed state of the puzzle cannot be altered: it is fixed by the relative positions of the fixed center squares and the distribution of color combinations on edge and corner pieces.
The V-Cube 7 is produced with white plastic as a base, with red opposite orange, blue opposite green, yellow opposite black. Verdes and other manufacturers sell cubes with black plastic and a white face, with the other colors remaining the same, solid plastic versions with the plastic the colour itself and no stickers; the fixed black or white center piece is branded with the logo of the manufacturer, V on cubes by Verdes. Flag variations of 7×7s including Germany and Russia, are sold by Verdes. Unlike the flat-sided V-Cube 6, the V-Cube 7 is noticeably rounded; this departure from a true cube shape is necessary, since the mechanism used on this puzzle would not function properly with layers of identical thickness. Other means would be required. Note from the image at right that if a 7×7×7 were to be constructed with layers of identical thickness the corner pieces would lose contact with the rest of the puzzle when a side was rotated 45 degrees; the V-Cube 6 and V-Cube 7 both solve the problem by using thicker outer layers.
The rounded shape of the V-Cube 7 results in corner stickers that are similar in size to the center stickers, which helps hide the unequal thickness. Cubes from other manufacturers can be found with rounded or flat sides, but all use thicker outer layers. There are 60 edges and 150 centers. Any permutation of the corners is possible, including odd permutations. Seven of the corners can be independently rotated, the orientation of the eighth depends on the other seven, giving 8!×37 combinations. There are 144 movable centers. Within each set there are four centers of each color. Centers from one set cannot be exchanged with those from another set; each set can be arranged in 24! Different ways. Assuming that the four centers of each color in each set are indistinguishable, the number of permutations of each set is reduced to 24!/ arrangements, all of which are possible. The reducing factor comes about because there are 24 ways to arrange the four pieces of a given color; this is raised to the sixth power.
The total number of permutations of all movable centers is the permutations of a single set raised to the sixth power, 24!6/. There are 60 edge pieces, consisting of 12 central, 24 intermediate, 24 outer edges; the central edges can be flipped but the rest cannot, nor can an edge from one set exchange places with one from another set. The five edges in each matching quintet are distinguishable, since corresponding non-central edges are mirror images of each other. There are 12!/2 ways to arrange the central edges, since an odd permutation of the corners implies an odd permutation of these pieces as well. There are 211 ways that they can be flipped, since the orientation of the twelfth edge depends on the preceding eleven. Any permutation of the intermediate and outer edges is possible, including odd permutations, giving 24! Arrangements for each set or 24!2 total, regardless of the position or orientation any other pieces. This gives a total number of permutations of 8! × 3 7 × 12! × 2 10 × 24! 8 24 36 ≈ 1.95 × 10 160 The entire number is 19 500 551 183 731 307 835 329 126 754 019 748 794 904 992 692 043 434 567 152 132 912 323 232 706 135 469 180 065 278 712 755 853 360 682 328 551 719 137 311 299 993 600 000 000 000 000 000 000 000 000 000 000 000.
One of the fixed center pieces is marked with the logo of the manufacturer, such as V in a cube by V-Cube. This center piece can be oriented in four different ways, which increases the number of patterns by a factor of four to 7.80×10160. Any orientation of the fixed ce