br> Presumably to mark the 40th anniversary of the iconic puzzle game, Rubik's Cube, Google's homepage today features a virtual Rubik's Cube that you can spend your day today trying to solve. You can rotate the interactive puzzle game by clicking in the area around it. Then click and drag inside the cube to ...
Create Your Own. Excited to make your own creation? Request access to the code used to build these experiments. You will be directed to Rubik's Cube, Ltd. for licensing permission and download. Get the Code. Already made something great and think it should be part of Chrome Cube Lab? Submit Experiment ...
Play Color Cube Puzzle at Math Playground! Can you make each side the same color?. Math Playground · math games logic games math arcade math word problems math videos all games · grade 1 math games. Rotate the rows so that each of the faces of the cube. has only a single colour. Click the arrows to rotate a ... br> Play >>>
Rubik's Cube - Wikipedia
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Play with the 3D Rubik's Cube simulator online. Press the scramble button and try to figure out the solution and practice.
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Rubik's Cube at Cool Math Games: This is a computer version of a Rubik's Cube. You can twist it all around to check for your next moves. Play here >>>
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Rubik's Cube Other names Magic Cube, Speed Cube, Puzzle Cube Type Inventor Company Rubik's Brand Ltd Country Hungary Availability 1977: as Hungarian Magic Cube, first test batches released in Budapest 1980: as Rubik's Cube, worldwide—present Rubik's Cube is a invented in 1974 by Hungarian and of. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by in 1980 via businessman Tibor Laczi and Seven Towns founderand won the special award for Best Puzzle that year. As of January 2009350 million cubes had been sold worldwide making it the world's top-selling puzzle game. It is widely considered to be the world's best-selling toy. On a classic Rubik's Cube, each of the six faces is covered by nine virtual rubiks cube online game, each of one of six solid colours: white, red, blue, orange, green, and yellow. In currently sold models, white is opposite yellow, blue is opposite green, and orange is opposite red, and the red, white 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 independently, 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, dimensions, 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 widely known and used. Many continue to practice it and other twisty puzzles and compete for the fastest times in various categories. Since 2003, Thethe Rubik's Cube's international governing body, has organised competitions worldwide and kept the official world records. Nichols's cube was held together by magnets. Nichols was granted on April 11, 1972, two years before Rubik invented his Cube. On April 9, 1970, Frank Fox applied to patent his "Spherical 3×3×3". He received his UK patent 1344259 on January 16, 1974. Rubik's invention Packaging of Rubik's Cube, Toy of the year 1980—Ideal Toy Corp. Although it is widely 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 then tried to restore it. Rubik obtained Hungarian patent HU170062 for his "" in 1975. Rubik's Cube was first called the Magic Cube Bűvös kocka in Hungary. The first test batches of the Magic Cube were produced in late 1977 and released in toy shops. Magic Cube was held together with interlocking plastic pieces that prevented the puzzle being easily pulled apart, unlike the magnets in Nichols's design. With Ernő Rubik's permission, businessman Tibor Laczi took a Cube to Germany's Toy Fair in February 1979 in 300 online bowling game attempt to popularise it. It was noticed by Seven Towns founder Tom Kremer and they signed a deal with in September 1979 to release the Magic Cube worldwide. Ideal wanted at least a recognisable name to trademark; of french games online language, that arrangement put Rubik in the spotlight because the Magic Cube was renamed after its inventor in 1980. The puzzle made its international debut at the toy fairs of London, Paris, Nuremberg 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 briefly halted so that it could be manufactured to safety and packaging specifications. A lighter Cube was produced, and Ideal decided to rename it. Subsequent history See also: 1980s Cube craze 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 special award, and won similar awards for best toy in the UK, France, and the US. By 1981 Rubik's Cube had become a craze, and it is estimated that in the period from 1980 to 1983 around 200 million Rubik's Cubes were sold worldwide. are olympic summer games online spielen solved />In June 1981 reported that the Rubik's Cube is "a puzzle that's moving like fast food right now. At one stage in 1981 three of the top ten best selling books in the US were books on solving the Rubik's Cube, and the best-selling book of 1981 was James G. Nourse's which sold over 6 million copies. In 1981 the in New York exhibited a Rubik's Cube, and at the in a six-foot Cube was put on display. In June 1982 the took place inand would become the only competition recognized as official until the championship was revived in 2003. In October 1982 reported that sales had fallen and that "the craze has died", and by 1983 it was clear that sales had plummeted. However, in some Communist countries, such as China and USSR, the craze had started later and demand was still high because of a shortage of Cubes. In the US sales doubled between 2001 and 2003, and remarked that it was "becoming cool to own a Cube again". The 2003 World Rubik's Games Championship was the first speedcubing tournament since 1982. It was held in and was attended by 83 participants. The tournament led to the formation of the in 2004. Annual sales of Rubik branded cubes were said to have reached 15 million worldwide in 2008. Part of the new appeal was ascribed to the advent of Internet video sites, such aswhich allowed fans to share their solving strategies. Following the expiration of Rubik's patent in 2000, other brands of cubes appeared, especially from Chinese companies. Many of these Chinese branded cubes have been engineered for speed and are favoured by. Imitations Taking advantage of an initial shortage of Cubes, many imitations and variations appeared, many of which may have violated one or more patents. Today, the patents have expired and many Chinese companies produce copies of, and in nearly all cases, improvements upon, the Rubik and V-Cube designs. Patent history Nichols assigned his to his employer Moleculon Research Corp. In 1984, Ideal lost the patent infringement suit and 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. Even while Rubik's patent application was being processed, Terutoshi Ishigi, a self-taught engineer and ironworks owner near Tokyo, filed for a Japanese patent for a nearly identical mechanism, which was granted in 1976 Japanese patent publication JP55-008192. Until 1999, when an amended was check this out, Japan's patent office granted Japanese patents for non-disclosed technology within Japan without requiring worldwide. Hence, Ishigi's patent is generally accepted as an independent reinvention at that time. Rubik applied for more patents in 1980, including another Hungarian patent on October 28. In the United States, Rubik was granted on March 29, 1983, for the Cube. This patent expired in 2000. Greek inventor Panagiotis Verdes patented a method of creating cubes beyond the 5×5×5, up to 11×11×11, in 2003. As of 2017, the,and 9×9×9 models are in production in his "V-Cube" line. V-Cube also produces a 2×2×2, 3×3×3 and a 4×4×4. Trademarks Rubik's Brand Ltd. The trademarks have been upheld by a ruling of the General Court of the European Union on 25 November 2014 in a successful defence against a German toy manufacturer seeking to invalidate them. However, European toy manufacturers are allowed to create differently shaped puzzles that have a similar rotating or twisting functionality of component parts such as for exampleor. On 10 November 2016, Rubik's Cube lost a 3d thief games battle over a key trademark issue. The 's highest court, the ruled that the puzzle's shape was not sufficient to grant it trademark protection. Mechanics Rubik's Cube fully disassembled A standard Rubik's Cube measures 5. The puzzle consists of twenty-six virtual rubiks cube online game miniature cubes, also called "cubies" or "cubelets". Each of these includes a concealed inward extension that interlocks with the other cubes while permitting them to move to different locations. However, the centre cube of each of the six faces is merely a single square facade; all six are affixed to the core mechanism. These provide structure for the other pieces to fit into and rotate around. So there are twenty-one pieces: a single core piece consisting of three intersecting axes holding the six centre squares in place but letting them rotate, and twenty smaller plastic pieces which fit into it to form the assembled puzzle. Each of the six centre pieces pivots on a screw fastener held by the centre piece, a "3D cross". A spring between each screw head and its corresponding piece tensions the piece inward, so that collectively, the whole assembly remains compact, but see more still be easily manipulated. The screw can be tightened or loosened to change the "feel" of the Cube. Newer official Rubik's brand cubes have rivets instead of screws and cannot be adjusted. The Cube can be taken apart without much difficulty, typically by rotating learn more here top layer by 45° and then prying one of its edge cubes away from the other two layers. Consequently, it is a simple process to "solve" a Cube by taking it apart and reassembling it in a solved state. There are six central pieces which show one coloured face, twelve edge pieces which show two coloured faces, and eight corner pieces which show three coloured faces. Each piece shows a unique colour combination, but not all combinations are present for example, if red and orange are on opposite sides of the solved Cube, there is no edge piece with both red and orange sides. The location of these cubes relative to one another can be altered by twisting an outer third of the Cube 90°, 180° or 270°, 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. However, Cubes with alternative colour arrangements also exist; for example, with the yellow face opposite the green, the blue face opposite the white, and red and orange remaining opposite each other. Mathematics Permutations The current colour scheme of a Rubik's Cube The original 3×3×3 Rubik's Cube has eight corners and twelve edges. There are 40,320 ways to arrange the corner cubes. Each corner has three possible orientations, although only seven of eight can be oriented independently; the orientation of the eighth final corner depends on the preceding seven, giving 3 7 2,187 possibilities. When arrangements of centres are also permitted, as described below, the rule is that the combined arrangement of corners, edges, and centres must be an even permutation. Eleven edges can be flipped independently, with the flip of the twelfth depending on the preceding ones, giving 2 11 2,048 possibilities. The puzzle was originally advertised as having "over 3,000,000,000 three combinations but only one solution". To put this into perspective, if one had as many standard sized Rubik's Cubes as there areone could cover the Earth's surface 275 times. The preceding figure is limited to permutations that can be reached solely by turning the sides of the cube. If one considers permutations reached through disassembly of the cube, the number becomes twelve times as large: 8! } which is approximately 519 quintillion possible arrangements of the pieces that make up the Cube, but only one in twelve of these are actually solvable. This is because there is no sequence of moves that will swap a single pair of pieces or rotate a single corner or edge cube. Thus there are twelve possible sets of reachable configurations, sometimes called "universes" or "", into which the Cube can be placed by dismantling and reassembling it. Centre faces The original Rubik's Cube had no orientation markings on the centre faces although some carried the words "Rubik's Cube" on the centre square of the white faceand therefore solving it does not require any attention to orienting those faces correctly. However, with marker pens, one could, for example, mark the central squares of an unscrambled Cube with four coloured marks on each edge, each corresponding to the colour of the adjacent face; a cube marked in this way is referred to as a "supercube". Some Cubes have also been produced commercially with markings on all of the squares, such as the or. Cubes have also been produced where the nine stickers on a face are used to make a single larger picture, and centre orientation matters on these as well. Thus one can nominally solve a Cube yet have the markings on the centres rotated; it then becomes an additional test to solve the centres as well. Marking the Rubik's Cube's centres increases its difficulty because this expands the set of distinguishable possible configurations. In particular, when the Cube is unscrambled apart from the orientations of the central squares, there will always be an even number of centre squares requiring a quarter turn. Thus orientations of centres increases the total number of possible Cube permutations from 43,252,003,274,489,856,000 4. When turning a cube over is considered to be a change in permutation then we must also count arrangements of the centre faces. Nominally there are 6! When the orientations of centres are also counted, as above, this increases the total number of possible Cube permutations from 88,580,102,706,155,225,088,000 8. Algorithms In Rubik's cubers' parlance, a memorised sequence of moves that has a desired effect on the cube is called an algorithm. This terminology is derived from the mathematical use ofmeaning a list of well-defined instructions for performing a task from a given initial state, through well-defined successive states, to a desired end-state. Each method of solving the Rubik's Cube employs its own set of algorithms, together with descriptions of what effect the algorithm has, and when it can be used to bring the cube closer to being solved. Many algorithms are designed to transform only a small part of the cube without interfering with other parts that have already been solved so that they can be applied repeatedly to different parts of the cube until the whole is solved. For example, there are well-known algorithms for cycling three corners without changing the rest of the puzzle or flipping the orientation of a pair of edges while leaving the others intact. Some algorithms do have a certain desired effect on the cube for example, swapping two corners but may also have the side-effect of changing other parts of the read more such as permuting some edges. Such algorithms are often simpler than the ones without side-effects and are employed early on in the solution when most of the puzzle has not yet been solved and the side-effects are not important. Most are long and difficult to memorise. Towards the end of the solution, the more specific and usually more complicated algorithms are used instead. In addition, the fact that there are well-defined within the enables the puzzle to be learned and mastered by moving up through various self-contained "levels of difficulty". For example, one such "level" could involve solving cubes which have been scrambled using only 180-degree turns. These subgroups are the principle underlying the computer cubing methods by andwhich solve the cube by further reducing it to another subgroup. Solutions Move notation Many 3×3×3 Rubik's Cube enthusiasts use a notation developed by to denote a sequence of moves, referred to as "Singmaster notation". Its relative nature allows to be written in such a way that they can be applied regardless of which side is designated the top or how the colours are organised on a particular cube. A letter followed by a 2 occasionally a superscript 2 denotes two turns, or a 180-degree turn. R is right side clockwise, but R' is right side counter-clockwise. The letters x, y, and z are used to indicate that the entire Cube should be turned about one of its axes, corresponding to R, U, and F turns respectively. When x, y or z are primed, it is an indication that the cube must be rotated in the opposite direction. When they are squared, the cube must be rotated 180 degrees. The most common deviation from Singmaster notation, and in fact the current official standard, is to use "w", for "wide", instead of lowercase letters to represent moves of two layers; thus, a move of Rw is equivalent to one of r. For methods using middle-layer turns particularly corners-first methods there is a generally accepted "MES" extension to the notation where letters M, E, and S denote middle layer turns. It was used e. Generally speaking, uppercase letters F B U D L R refer to the outermost portions of the cube called faces. Lowercase letters f b u d l r refer to the inner portions of the cube called slices. By extension, for cubes of 6x6 and larger, moves of three in english games online japanese are notated by the number 3, for example, 3L. An alternative notation, Wolstenholme notation, is designed to make memorising sequences of moves easier for novices. This notation uses the same letters for faces except it replaces U with T topso that all are consonants. Addition of a C implies rotation of the entire cube, so ROC is the clockwise rotation of the cube around its right face. Middle layer moves are denoted by adding an M to corresponding face move, so RIM means a 180-degree turn of the middle layer adjacent to the R face. Another notation appeared in the 1981 book. Singmaster notation was not widely known at the time of publication. The faces were named Top TBottom BLeft LRight RFront F and Posterior Pwith + for clockwise, - for anticlockwise and 2 for 180-degree turns. Another notation appeared in the 1982 "The Ideal Solution" book for Rubik's Revenge. jai ho online planes were noted as tables, with table 1 or T1 starting at the top. Vertical front to back planes were noted as book, with book 1 or B1 starting from the left. Vertical left to right planes were noted as windows, with window 1 or W1 starting at the front. Using the front face as a reference view, table moves were left or right, book moves were up or down, and window moves were clockwise or counter-clockwise. Optimal solutions solving Rubik's Cube during 1982 expedition in to peak Although there are a significant number of possible permutations for the Rubik's Cube, a number of solutions have been developed which allow solving the cube in well under 100 moves. Many general solutions for the Rubik's Cube have been discovered independently. This solution involves solving the Cube layer by layer, in which one layer designated the top is solved first, followed by the middle layer, and then the final and bottom layer. After sufficient practice, solving the Cube layer by layer can be done in under one minute. Other general solutions include "corners first" methods or combinations of several other methods. In 1982, David Singmaster and Alexander Frey hypothesised that the number of moves needed to solve the Rubik's Cube, given an ideal algorithm, might be in "the low twenties". In 2007, Daniel Kunkle and Gene Cooperman used computer search methods to demonstrate that any 3×3×3 Rubik's Cube configuration can be solved in 26 moves or fewer. In 2008, Tomas Rokicki lowered that number to 22 moves, and in July 2010, a team of researchers including Rokicki, working withproved the so-called "" to be 20. This is optimal, since there exist some starting positions which require a minimum of 20 moves to solve. More generally, it has been shown that an n× n× n Rubik's Cube can be solved optimally in moves. Speedcubing methods In 1981, thirteen-year-old Patrick Bossert developed a solution for solving the cube, along with a graphical notation, designed to be easily understood by novices. It was subsequently published as You Can Do The Cube and became a best-seller. A solution commonly used by speed cubers was developed by. This method is called "CFOP," standing for "cross, F2L, OLL, PLL". It is similar to the layer-by-layer method but employs the use of a large number of algorithms, especially for orienting and permuting the last layer. The cross is done first, followed by first layer corners and second layer edges simultaneously, with each corner paired up with a second-layer edge piece, thus completing the first two layers F2L. This is then followed by the last layer, then the last layer OLL and PLL respectively. Philip Marshall's The Ultimate Solution to Rubik's Cube takes a different approach, averaging only 65 twists yet requiring the memorisation of only two algorithms. The cross is solved first, followed by the remaining edges, then five corners, and finally the last three corners. A now well-known method was developed by. In this method, a 2×2×2 section is solved first, followed by a 2×2×3, and then the incorrect edges are solved using a three-move algorithm, which eliminates the need for a possible 32-move algorithm later. The principle behind this is that in layer-by-layer you must constantly break and fix the first layer; the 2×2×2 and 2×2×3 sections allow three or two layers to be turned without ruining progress. One of the advantages of this method is that it tends to give solutions in fewer moves. The Roux Method, developed byis similar to the Petrus method in that it relies on block building rather than layers, but derives from corners-first methods. In Roux, a 3×2×1 block is solved, followed by another 3×2×1 on the opposite side. Next, the corners of the top layer are solved. The cube can then be solved using only moves of the U layer and M slice. In 1997, Denny Dedmore published a solution described using diagrammatic icons representing the moves to be made, instead of the usual notation. Beginner's method Most beginner solution methods involve solving the cube one layer at a time, using algorithms that preserve what has already been solved. The easiest layer by layer methods require only 3-8 algorithms. Rubik's Cube solver program The most move optimal online Rubik's Cube solver programs use which can typically determine a solution of 20 moves or less. The user has to set the colour configuration of the scrambled cube and the program returns the steps required to solve it. Competitions and records Speedcubing competitions Main article: or speedsolving is the practice of trying to solve a Rubik's Cube in the shortest time possible. There are a number of speedcubing competitions that take place around the world. The first world championship organised by the was held in on March 13, 1981. All Cubes were moved 40 times and lubricated with. The official winner, with a record of 38 seconds, was Jury Froeschl, born in. The first international world championship was held in on June 5, 1982, and was won bya Vietnamese student fromwith a time of 22. Since 2003, the winner of a competition is determined by taking the average time of the middle three of five attempts. However, the single best time of all tries is also recorded. The maintains a history of world records. In virtual rubiks cube online game, the Visit web page made it mandatory to use a special timing device called a. Their recorded time for this event includes both the time spent memorizing the cube and the time spent manipulating it. In multiple blindfolded, all rage games online the cubes are memorised, and then all of the cubes are solved once blindfolded; thus, the main challenge is memorising many — often ten or more — separate cubes. The event is scored not by time but by the number of solved cubes minus the number of unsolved cubes after one hour has elapsed. In fewest moves solving, the contestant is given one hour to find his or her solution and must write it down. The world record fastest average of five one-handed solves is 9. The world record mean of 3 feet solves is 26. The world record mean of three blindfold solves is 22. Kowalczyk inspected 41 cubes, donned a blindfold, and solved them, all under the time limit of one hour. This has been achieved by Tim Wong of the United States on 11 October 2015 at Irvine Fall 2015, by Marcel Peters of on 9 January 2016 at Cubelonia 2016, and by Vladislav Ushakov of on 27 August 2016 at PSU Open 2016. The world record mean of three fewest moves challenges with different scrambles is 24. A YouTube video shows a 0. Next record is 3. This beats the prior 5. This had in turn broken the previous record of 10. The event was hosted by Depaul UK. On November 4, 2012, 3248 people, mainly students ofsuccessfully solved the Rubik's cube in 30 minutes on college ground. The successful attempt is recorded in the. The college will submit the relevant data, witness statements and video of the event to Guinness authorities. Variations Variations of Rubik's Cubes. Top row:. Bottom row:original Rubik's Cube. Clicking on a cube in the picture will redirect to the respective cube's page. An 11×11×11 cube There are different variations of Rubik's Cubes with up to thirty-three layers: the 2×2×2the standard 3×3×3 cube, the 4×4×4and the 5×5×5 being the most well known. The 17×17×17 "Over Customer service online games Top" cube available late 2011 was until December 2017 the largest and most expensive, costing more than two thousand dollars commercially sold cube. A working design for a 22×22×22 cube exists and was demonstrated in January 2016, and a 33x33 in December 2017. Chinese manufacturer ShengShou has been producing cubes in all sizes from 2×2×2 to 10×10×10 as of late 2013and have also come out with an 11x11x11. Non-licensed physical cubes as large as 13×13×13 based on the V-Cube patents are commercially available to the mass-market circa 2015 in China; these represent about the limit of practicality for the purpose of "speed-solving" competitively as the cubes become increasingly ungainly and solve-times increase quadratically. Rubik's TouchCube There are many variations of the original cube, some of which are made by Rubik. The mechanical products include the Rubik's Magic, 360, and Twist. Also, electronics like the Rubik's Revolution and Slide were also inspired by the original. One of the newest 3×3×3 Cube variants is the Rubik's TouchCube. Sliding a finger across its faces causes its patterns of coloured lights to rotate the same way they would on a mechanical cube. The TouchCube also has buttons for hints and self-solving, and it includes a charging stand. The TouchCube was introduced at the in New York on February 15, 2009. The Cube has inspired an entire category of similar puzzles, commonly referred to aswhich includes the cubes of different sizes mentioned above as well as various other geometric shapes. Some such shapes include thethethethe. There are also puzzles that change shape such as and the. In 2011, awarded the "largest order Rubiks magic cube" to a 17×17×17 cube, made by. On 2 December 2017, announced that he had broken this record, with a 33×33×33 cube, and that his claim had been submitted to Guinness for verification. All five platonic solid versions of Rubik's cube Since 2015, with the mass production of the Icosaix, all five analogous to Rubik's cube face-turning with cuts one-third from each face, except the Pyraminx, which also has turnable tips became available. Besides Rubik's cube, the tetrahedron is available as the Pyraminx, the octahedron as the Face Turning Octahedron, the dodecahedron as the Megaminx, and the icosahedron as the Icosaix. Some puzzles have also been created in the shape of thesuch as a. Custom-built puzzles Novelty keychain Puzzles have been built resembling the Rubik's Cube or based on its inner workings. For example, a cuboid is a puzzle based on the Rubik's Cube, but with different functional dimensions, such as 2×2×4, 2×3×4, and 3×3×5. Many cuboids are based on 4×4×4 or 5×5×5 mechanisms, via building plastic extensions or by directly modifying the mechanism itself. Some custom puzzles are not derived from any existing mechanism, such as the Gigaminx v1. These puzzles usually have a set of masters 3D printed, which then are copied using moulding and casting techniques to create the final puzzle. An example of this is the Trabjer's Octahedron, which can be built by truncating and extending portions of a regular 3×3. Most click here mods can be adapted to higher-order cubes. In the case of Rhombic Dodecahedron, there are 3×3, 4×4, 5×5, and 6×6 versions of the puzzle. Rubik's Cube software Puzzles like the Rubik's Cube can be simulated by computer software, which provide functions such as recording of player metrics, storing scrambled Cube positions, conducting online competitions, analysing of move sequences, and converting between different move notations. Software can also simulate very large puzzles that are impractical to build, such as 100×100×100 and 1,000×1,000×1,000 cubes, as well as virtual puzzles that cannot be physically built, such as 4- and 5-dimensional analogues of the cube. The site has various interactive objects based on Rubik's Cube. Customised versions of Rubik's Cube can be created and uploaded. Retrieved 28 April 2014. A Biographical Encyclopedia of Scientists. Bristol: Institute of Physics Pub. Retrieved July 26, 2012. Archived from on 2009-02-01. Retrieved August 15, 2005. Growing up with science: The illustrated encyclopedia of invention. Cambridge: Press Syndicate of the University of Cambridge. Retrieved 19 May 2014. Retrieved virtual rubiks cube online game June 2012. The 1970s American Popular Culture Through History. Westport, Conn: Greenwood Press. The New York Times. Encyclopedia of Play in Today's Society. Retrieved 26 October 2016. In Guy, Richard K. The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and Its History. Singmaster the numbers sold were between 100 and 300 million. His estimate is based on sales of 50 to 100 million legitimate cubes and perhaps a higher number of imitations. In Guy, Richard K. The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and Its History. Encyclopedia of Television Shows, 1925 through 2010. The New York Times. The New York Times. The Wall Street Journal. Archived from PDF on 2012-02-16. Metamagical Themas: Questing for the Essence of Mind and Pattern. New York: Basic Books. Hofstadter gives the name as 'Ishige'. Retrieved March 22, 2015. Retrieved 10 October 2017 — via YouTube. discussion hitman online games apologise on Rubik's Magic Cube. Harmondsworth, Eng: Penguin Books. Adventures in group theory: Rubik's Cube, Merlin's machine, and Other Mathematical Toys. Baltimore: Johns Hopkins University Press. Retrieved 5 May 2012. Marc Waterman's Algorithm, Part 2. Cubism For Fun 15. Handbook of Cubik Math. Proceedings of the International Symposium on Symbolic and Algebraic Computation ISSAC '07. Archived from on 2007-10-11. Retrieved 28 June 2016. Retrieved 17 July 2017. Retrieved 28 June 2016. Retrieved 10 October 2017. Retrieved 6 July 2017. Retrieved 12 December 2017. Retrieved 25 May 2012. Retrieved 10 February 2018 — via YouTube. Retrieved 30 December 2012. Archived from on 2009-04-22. Retrieved 10 February 2018 — via YouTube. The College Mathematics Journal. Retrieved 19 May 2014. Handbook of Cubic Math. Mathematics of the Rubik's Cube Design. Pittsburgh, Pa: Dorrance Pub. The Cube: The Ultimate Guide to the World's Bestselling Puzzle. By using this site, you agree to the and. Wikipedia® is a registered trademark of thea non-profit organization.