Rubik's Cube is a 3D combination puzzle invented in 1974^{[1]}^{[2]} by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube,^{[3]} the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980^{[4]} via businessman Tibor Laczi and Seven Towns founder Tom Kremer,^{[5]} and 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^{[6]}^{[7]} making it the world's topselling puzzle game.^{[8]}^{[9]} It is widely considered to be the world's bestselling toy.^{[10]}
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, red, blue, orange, green, and yellow. The current version of the cube has been updated to coloured plastic panels instead, which prevents peeling and fading.^{[11]} 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.^{[12]} On early cubes, the position of the colours varied from cube to cube.^{[13]} 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 speedcubers continue to practice it and similar puzzles; they also compete for the fastest times in various categories. Since 2003, the World Cube Association, the Rubik's Cube's international governing body, has organised competitions worldwide and recognises world records.
Rubik's Cube  

Other names  Magic Cube, Speed Cube, Puzzle Cube 
Type  Combination puzzle 
Inventor(s)  Ernő Rubik 
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 
Official website 
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 (1344259) on 16 January 1974.^{[14]}
In the mid1970s, Ernő Rubik worked at the Department of Interior Design at the Academy of Applied Arts and Crafts in Budapest.^{[15]} 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.^{[16]} Rubik applied for a patent in Hungary for his "Magic Cube" (Bűvös kocka in Hungarian) on 30 January 1975,^{[17]} and HU170062 was granted later 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 easily 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.^{[18]} 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.^{[18]} Ideal wanted at least a recognisable name to trademark; of course, 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. ^{[19]}
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 Western safety and packaging specifications. A lighter Cube was produced, and Ideal decided to rename it. "The Gordian Knot" and "Inca Gold" were considered, but the company finally decided on "Rubik's Cube", and the first batch was exported from Hungary in May 1980.^{[20]}
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.^{[21]} At the end of 1980 Rubik's Cube won a German Game of the Year special award,^{[22]} and won similar awards for best toy in the UK, France, and the US.^{[23]} 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.^{[24]} In March 1981 a speedcubing championship organised by the Guinness Book of World Records was held in Munich,^{[22]} and a Rubik's Cube was depicted on the front cover of Scientific American that same month.^{[25]} 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",^{[26]} and 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."^{[27]}
As most people could only solve one or two sides, numerous books were published including David Singmaster's Notes on Rubik's "Magic Cube" (1980) and Patrick Bossert's You Can Do the Cube (1981).^{[22]} At one stage in 1981 three of the top ten best selling books in the US were books on solving the Rubik's Cube,^{[28]} and the bestselling book of 1981 was James G. Nourse's The Simple Solution to Rubik's Cube which sold over 6 million copies.^{[29]} In 1981 the Museum of Modern Art in New York exhibited a Rubik's Cube, and at the 1982 World's Fair in Knoxville, Tennessee a sixfoot Cube was put on display.^{[22]} ABC Television even developed a cartoon show called Rubik, the Amazing Cube.^{[30]} In June 1982 the First Rubik's Cube World Championship took place in Budapest, and would become the only competition recognized as official until the championship was revived in 2003.^{[31]}
In October 1982 The New York Times reported that sales had fallen and that "the craze has died",^{[32]} and by 1983 it was clear that sales had plummeted.^{[22]} 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.^{[33]}^{[34]}
Rubik's Cubes continued to be marketed and sold throughout the 1980s and 90s,^{[22]} but it was not until the early 2000s that interest in the Cube began increasing again.^{[35]} In the US sales doubled between 2001 and 2003, and The Boston Globe remarked that it was "becoming cool to own a Cube again".^{[36]} The 2003 World Rubik's Games Championship was the first speedcubing tournament since 1982.^{[35]} It was held in Toronto and was attended by 83 participants.^{[35]} The tournament led to the formation of the World Cube Association in 2004.^{[35]} Annual sales of Rubik branded cubes were said to have reached 15 million worldwide in 2008.^{[37]} Part of the new appeal was ascribed to the advent of Internet video sites, such as YouTube, which allowed fans to share their solving strategies.^{[37]} Following the expiration of Rubik's patent in 2000, other brands of cubes appeared, especially from Chinese companies.^{[38]} Many of these Chinese branded cubes have been engineered for speed and are favoured by speedcubers.^{[38]}
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 VCube designs.^{[38]}
Nichols assigned his patent to his employer Moleculon Research Corp., which sued Ideal in 1982. 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.^{[39]}
Even while Rubik's patent application was being processed, Terutoshi Ishigi, a selftaught engineer and ironworks owner near Tokyo, filed for a Japanese patent for a nearly identical mechanism, which was granted in 1976 (Japanese patent publication JP55008192). Until 1999, when an amended Japanese patent law was enforced, Japan's patent office granted Japanese patents for nondisclosed technology within Japan without requiring worldwide novelty.^{[40]}^{[41]} Hence, Ishigi's patent is generally accepted as an independent reinvention at that time.^{[42]}^{[43]}^{[44]} Rubik applied for more patents in 1980, including another Hungarian patent on 28 October. In the United States, Rubik was granted U.S. Patent 4,378,116 on 29 March 1983, for the Cube. This patent expired in 2000.
Rubik's Brand Ltd. also holds the registered trademarks for the word Rubik and Rubik's and for the 2D and 3D visualisations of the puzzle. 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 example Skewb, Pyraminx or Impossiball.^{[45]}
On 10 November 2016, Rubik's Cube lost a tenyear battle over a key trademark issue. The European Union's highest court, the Court of Justice ruled that the puzzle's shape was not sufficient to grant it trademark protection.^{[46]}
A standard Rubik's Cube measures 5.7 centimetres (2 ^{1}⁄_{4} in) on each side. The puzzle consists of twentysix unique 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 façade; all six are affixed to the core mechanism. These provide structure for the other pieces to fit into and rotate around. So there are twentyone 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 can 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 the 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.
Douglas Hofstadter, in the July 1982 issue of Scientific American, pointed out that Cubes could be coloured in such a way as to emphasise the corners or edges, rather than the faces as the standard colouring does; but neither of these alternative colourings has ever become popular.^{[42]}
The puzzle was originally advertised as having "over 3,000,000,000 (three billion) combinations but only one solution".^{[47]} Depending on how combinations are counted, the actual number can be significantly higher.
The original (3×3×3) Rubik's Cube has eight corners and twelve edges. There are 8! (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. There are 12!/2 (239,500,800) ways to arrange the edges, restricted from 12! because edges must be in an even permutation exactly when the corners are. (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.^{[48]}
which is approximately 43 quintillion.^{[49]} To put this into perspective, if one had one standardsized Rubik's Cube for each permutation, one could cover the Earth's surface 275 times, or stack them in a tower 261 lightyears high.
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 larger:
which is approximately 519 quintillion^{[49]} 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 "orbits", into which the Cube can be placed by dismantling and reassembling it.
The preceding numbers assume the center faces are in a fixed position. If one considers turning the whole cube to be a different permutation, then each of the preceding numbers should be multiplied by 24. A chosen color can be on one of six sides, and then one of the adjacent colors can be in one of four positions; this determines the positions of all remaining colors.
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 face), and 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 Lo Shu magic square or playing card suits. 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. There are 4^{6}/2 (2,048) ways to orient the centres since an even permutation of the corners implies an even number of quarter turns of centres as well. 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 (4.3×10^{19}) to 88,580,102,706,155,225,088,000 (8.9×10^{22}).^{[50]}
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! ways to arrange the six centre faces of the cube, but only 24 of these are achievable without disassembly of the cube. 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 (8.9×10^{22}) to 2,125,922,464,947,725,402,112,000 (2.1×10^{24}).
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 of algorithm, meaning a list of welldefined instructions for performing a task from a given initial state, through welldefined successive states, to a desired endstate. 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 wellknown 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 sideeffect of changing other parts of the cube (such as permuting some edges). Such algorithms are often simpler than the ones without sideeffects and are employed early on in the solution when most of the puzzle has not yet been solved and the sideeffects 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.
Rubik's Cube lends itself to the application of mathematical group theory, which has been helpful for deducing certain algorithms – in particular, those which have a commutator structure, namely XYX^{−1}Y^{−1} (where X and Y are specific moves or movesequences and X^{−1} and Y^{−1} are their respective inverses), or a conjugate structure, namely XYX^{−1}, often referred to by speedcubers colloquially as a "setup move".^{[51]} In addition, the fact that there are welldefined subgroups within the Rubik's Cube group enables the puzzle to be learned and mastered by moving up through various selfcontained "levels of difficulty". For example, one such "level" could involve solving cubes which have been scrambled using only 180degree turns. These subgroups are the principle underlying the computer cubing methods by Thistlethwaite and Kociemba, which solve the cube by further reducing it to another subgroup.
Many 3×3×3 Rubik's Cube enthusiasts use a notation developed by David Singmaster to denote a sequence of moves, referred to as "Singmaster notation".^{[52]} Its relative nature allows algorithms 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.
When a prime symbol ( ′ ) follows a letter, it denotes an anticlockwise face turn; while a letter without a prime symbol denotes a clockwise turn. These directions are as one is looking at the specified face. A letter followed by a 2 (occasionally a superscript ^{2}) denotes two turns, or a 180degree turn. R is right side clockwise, but R′ is right side anticlockwise. 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.^{[53]}
For methods using middlelayer turns (particularly cornersfirst 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.g. in Marc Waterman's Algorithm.^{[54]}
The 4×4×4 and larger cubes use an extended notation to refer to the additional middle layers. 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). An asterisk (L*), a number in front of it (2L), or two layers in parentheses (Ll), means to turn the two layers at the same time (both the inner and the outer left faces) For example: (Rr)' l2 f' means to turn the two rightmost layers anticlockwise, then the left inner layer twice, and then the inner front layer anticlockwise. By extension, for cubes of 6×6×6 and larger, moves of three layers are notated by the number 3, for example, 3L.
An alternative notation, Wolstenholme notation,^{[55]} 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 (top), so that all are consonants. The key difference is the use of the vowels O, A and I for clockwise, anticlockwise and 180degree turns, which results in wordlike sequences such as LOTA RATO LATA ROTI (equivalent to LU′R′UL′U′RU2 in Singmaster notation). 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 180degree turn of the middle layer adjacent to the R face.
Another notation appeared in the 1981 book The Simple Solution to Rubik's Cube. Singmaster notation was not widely known at the time of publication. The faces were named Top (T), Bottom (B), Left (L), Right (R), Front (F) and Posterior (P), with + for clockwise, – for anticlockwise and 2 for 180degree turns.
Another notation appeared in the 1982 "The Ideal Solution" book for Rubik's Revenge. Horizontal 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 anticlockwise.
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. David Singmaster first published his solution in the book Notes on Rubik's "Magic Cube" in 1981.^{[51]} 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".^{[56]} 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.^{[57]}^{[58]}^{[59]} In 2008, Tomas Rokicki lowered that number to 22 moves,^{[60]}^{[61]}^{[62]} and in July 2010, a team of researchers including Rokicki, working with Google, proved the socalled "God's number" to be 20.^{[63]}^{[64]} 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 Θ(n^{2} / log(n)) moves.^{[65]}
A solution commonly used by speedcubers was developed by Jessica Fridrich. This method is called CFOP standing for "cross, F2L, OLL, PLL". It is similar to the layerbylayer 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 secondlayer edge piece, thus completing the first two layers (F2L). This is then followed by orienting the last layer, then permuting the last layer (OLL and PLL respectively). Fridrich's solution requires learning roughly 120 algorithms but allows the Cube to be solved in only 55 moves on average.
A now wellknown method was developed by Lars Petrus. 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 threemove algorithm, which eliminates the need for a possible 32move algorithm later. The principle behind this is that in layerbylayer, one must constantly break and fix the completed layer(s); the 2×2×2 and 2×2×3 sections allow three or two layers (respectively) to be turned without ruining progress. One of the advantages of this method is that it tends to give solutions in fewer moves. For this reason, the method is also popular for fewest move competitions.^{[66]}
The Roux Method, developed by Gilles Roux, is similar to the Petrus method in that it relies on block building rather than layers, but derives from cornersfirst 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.^{[67]}
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.^{[68]}^{[69]}
In 1981, thirteenyearold Patrick Bossert developed a solution for solving the cube, along with a graphical notation, designed to be easily understood by novices.^{[70]} It was subsequently published as You Can Do The Cube and became a bestseller.^{[71]}
In 1997, Denny Dedmore published a solution described using diagrammatic icons representing the moves to be made, instead of the usual notation.^{[72]}
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.^{[73]}
The most move optimal online Rubik's Cube solver programs use Herbert Kociemba's TwoPhase Algorithm 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.^{[74]}
Speedcubing (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.
A speedcubing championship organised by the Guinness Book of World Records was held in Munich on 13 March 1981.^{[75]} The contest used standardised scrambling and fixed inspection times, and the winners were Ronald Brinkmann and Jury Fröschl with times of 38.0 seconds.^{[75]} The first world championship was the 1982 World Rubik's Cube Championship held in Budapest on 5 June 1982, which was won by Minh Thai, a Vietnamese student from Los Angeles, with a time of 22.95 seconds.^{[76]}
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 World Cube Association maintains a history of world records.^{[77]} In 2004, the WCA made it mandatory to use a special timing device called a Stackmat timer.
In addition to the main 3x3x3 event, the WCA also holds events where the cube is solved in different ways:^{[78]}
In Blindfolded Solving, the contestant first studies the scrambled cube (i.e., looking at it normally with no blindfold), and is then blindfolded before beginning to turn the cube's faces. Their recorded time for this event includes both the time spent memorizing the cube and the time spent manipulating it.
In Multiple Blindfolded, all of 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 points achieved after the one hour time limit has elapsed. The number of points achieved is equal to the number of cubes solved correctly, minus the number of cubes unsolved after the end of the attempt, where a greater number of points is better. If multiple competitors achieve the same number of points, rankings are assessed based on the total time of the attempt, with a shorter time being better.
In Fewest Moves solving, the contestant is given one hour to find a solution and must write it down.
Name  Fastest solve  Competition 

Yusheng Du (杜宇生)  3.47s  Wuhu Open 2018 
Feliks Zemdegs  4.22s  Cube for Cambodia 2018 
Patrick Ponce  4.24s  Northeast Championship 2019 
Max Park  4.40s  SacCubing V 2018 
Jakub Kipa  4.59s  Polish Championship 2018 
SeungBeom Cho (조승범)  4.59s  ChicaGhosts 2017 
Name  Fastest average  Competition 

Feliks Zemdegs  5.69s  Koalafication Brisbane 2019 
Max Park  5.83s  Bay Area Speedcubin' 15 2019 
Philipp Weyer  6.06s  Swisscubing Cup Final 2018 
Patrick Ponce  6.14s  Lower Moreland Winter 2019 
Lucas Etter  6.24s  Indianapolis Cubes 2019 
There are different variations of Rubik's Cubes with up to thirtythree layers: the 2×2×2 (Pocket/Mini Cube), the standard 3×3×3 cube, the 4×4×4 (Rubik's Revenge/Master Cube), and the 5×5×5 (Professor's Cube) being the most well known. As of 1981, the official Rubik's Brand has licensed twisty puzzle cubes only up to the 5×5×5. The 17×17×17 "Over The 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,^{[98]} and a 33x33 in December 2017.^{[99]} Chinese manufacturer ShengShou has been producing cubes in all sizes from 2×2×2 to 10×10×10 (as of late 2013),^{[100]} and have also come out with an 11x11x11, and 13x13x13.
Nonlicensed physical cubes as large as 17×17×17 based on the VCube patents are commercially available to the massmarket; these represent about the limit of practicality for the purpose of "speedsolving" competitively (as the cubes become increasingly ungainly and solvetimes increase quadratically).
There are many variations^{[101]} 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 selfsolving, and it includes a charging stand. The TouchCube was introduced at the American International Toy Fair in New York on 15 February 2009.^{[102]}^{[103]}
The Cube has inspired an entire category of similar puzzles, commonly referred to as twisty puzzles, which includes the cubes of different sizes mentioned above as well as various other geometric shapes. Some such shapes include the tetrahedron (Pyraminx), the octahedron (Skewb Diamond), the dodecahedron (Megaminx), the icosahedron (Dogic). There are also puzzles that change shape such as Rubik's Snake and the Square One.
In 2011, Guinness World Records awarded the "largest order Rubiks magic cube" to a 17×17×17 cube, made by Oskar van Deventer.^{[104]}^{[105]} On 2 December 2017, Grégoire Pfennig announced that he had broken this record, with a 33×33×33 cube, and that his claim had been submitted to Guinness for verification.^{[99]} On 8 April 2018, Grégoire Pfennig announced another world record, the 2x2x50 cube.^{[106]} Whether this is a replacement for the 33x33x33 record, or an additional record, remains to be seen.
Some puzzles have also been created in the shape of the KeplerPoinsot polyhedra, such as Alexander's Star (a great dodecahedron). Grégoire Pfennig has also created at least one puzzle in the shape of a small stellated dodecahedron.
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.^{[107]} 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 v1.5v2, Bevel Cube, SuperX, Toru, Rua, and 1×2×3. These puzzles usually have a set of masters 3D printed, which then are copied using moulding and casting techniques to create the final puzzle.
Other Rubik's Cube modifications include cubes that have been extended or truncated to form a new shape. An example of this is the Trabjer's Octahedron, which can be built by truncating and extending portions of a regular 3×3. Most shape mods can be adapted to higherorder cubes. In the case of Tony Fisher's Rhombic Dodecahedron, there are 3×3, 4×4, 5×5, and 6×6 versions of the puzzle.
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 5dimensional analogues of the cube.^{[108]}^{[109]}
Google has released the Chrome Cube Lab in association with^{[110]} Ernő Rubik. The site has various interactive objects based on Rubik's Cube. Customised versions of Rubik's Cube can be created and uploaded.^{[111]}
Hofstadter gives the name as 'Ishige'.
The 1982 World Rubik's Cube Championship was a competition for speedsolving the 3×3×3 Rubik's Cube.
It was held in Budapest, Hungary, on 5 June 1982. Contestants selected from 19 countries took part. Minh Thai from the United States of America was the winner with a best time of 22.95 after three attempts for each contestant. The top attempt of three was taken as the competitor's score. First prize was a goldplated Rubik's Cube.Writing shortly afterwards, David Singmaster who was one of the judges, described the competition as being efficiently organized, although at one point power for the TV and the display timer failed in the middle of a trial. The cubes were selected by Ernő Rubik himself, and according to Singmaster "competitors described them as pretty good". However, writing around 20 years later, Jessica Fridrich who had participated in the contest, criticised the cubes for being "really hard to turn and were not prepared for serious speed cubing".This competition was the first officially recognised competition of its kind. The next competition was held in 2003 in Canada, with many differences to the competition structure and many other puzzles being added other than the Rubik's Cube.
CFOP MethodThe CFOP Method (Cross – F2L – OLL – PLL), sometimes known as the Fridrich method, is one of the most commonly used methods in speedsolving a 3×3×3 Rubik's Cube. This method was first developed in the early 1980s combining innovations by a number of speed cubers. Czech speedcuber Jessica Fridrich is generally credited for popularizing it by publishing it online in 1997.The method works on a layerbylayer system, first solving a cross typically on the bottom, continuing to solve the first two layers (F2L), orienting the last layer (OLL), and finally permuting the last layer (PLL).
Chris Hardwick (speedcuber)Christopher Michael Hardwick (born December 6, 1983) is an American competitive speedcuber.
Born in Merritt Island, Florida, he attended the North Carolina School of Science and Mathematics (class of 2002) and University of North Carolina at Chapel Hill (class of 2005).
He is known especially for his blindfolded world record solution times of Rubik's Revenge and Rubik's Professor's Cube puzzles, though he started out as a top onehanded cuber. Chris holds the former world record for the blindfolded solve time of the Rubik's Professor's Cube with 15 minutes 22 seconds.
Hardwick has made a number of television appearances demonstrating the Rubik's Cube, including MTV in 2002, Canada AM and Much Music in the fall of 2003, discussing the 2003 Rubik's Cube World Championships. His home videos have also appeared on numerous online video sites including CollegeHumor and Digg. A home video of Hardwick solving a 3x3x3 Rubik's Cube onehanded appeared on VH1 in 2006 for Web Junk 20. Axe deodorant parodied another one of Hardwick's home videos in their 2006 South African "Get a Girlfriend" commercial campaign.
Chris Hardwick, the comedian, referenced this particular Chris Hardwick on Web Soup in 2009 when a comment about the Rubik's Cube was made. The two met during the comedian's show at the Barrymore Theatre in Madison, Wisconsin, on April 11, 2015.
Ernő RubikErnő Rubik (Hungarian: [ˈrubik ˈɛrnøː]; born 13 July 1944) is a Hungarian inventor, architect and professor of architecture. He is best known for the invention of mechanical puzzles including Rubik's Cube (1974), Rubik's Magic, Rubik's Magic: Master Edition, and Rubik's Snake.While Rubik became famous for inventing the Rubik's Cube and his other puzzles, much of his recent work involves the promotion of science in education. Rubik is involved with several organizations such as Beyond Rubik's Cube, the Rubik Learning Initiative and the Judit Polgar Foundation all of whose aim is to engage students in science, mathematics, and problem solving at a young age.
God's algorithmGod's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles and mathematical games. It refers to any algorithm which produces a solution having the fewest possible moves, the idea being that an omniscient being would know an optimal step from any given configuration.
Layer by LayerThe Layer by Layer method is a method of solving the 3x3x3 Rubik's Cube. Many beginners' methods use this approach, but it also forms the basis of the CFOP speedcubing technique.
MegaminxThe Megaminx or Mégaminx (, ) is a dodecahedronshaped puzzle similar to the Rubik's Cube. It has a total of 50 movable pieces to rearrange, compared to the 20 movable pieces of the Rubik's Cube.
Optimal solutions for Rubik's CubeOptimal solutions for Rubik's Cube refer to solutions that are the shortest. There are two common ways to measure the length of a solution. The first is to count the number of quarter turns. The second is to count the number of outerlayer twists, called "face turns". A move to turn an outer layer two quarter (90°) turns in the same direction would be counted as two moves in the quarter turn metric (QTM), but as one turn in the face metric (FTM, or HTM "Half Turn Metric", or OBTM "Outer Block Turn Metric").The maximum number of face turns needed to solve any instance of the Rubik's Cube is 20, and the maximum number of quarter turns is 26. These numbers are also the diameters of the corresponding Cayley graphs of the Rubik's Cube group. In STM (slice turn metric) it's unknown.
There are many algorithms to solve scrambled Rubik's Cubes. An algorithm that solves a cube in the minimum number of moves is known as God's algorithm.
Pocket CubeThe Pocket Cube (also known as the Mini Cube) is the 2×2×2 equivalent of a Rubik's Cube. The cube consists of 8 pieces, all corners.
PyraminxThe Pyraminx () is a regular tetrahedron puzzle in the style of Rubik's Cube. It was made and patented by Uwe Mèffert after the original 3 layered Rubik's Cube by Erno Rubik, and introduced by Tomy Toys of Japan (then the 3rd largest toy company in the world) in 1981.
Rubik's 360Rubik's 360 is a 3D mechanical puzzle released in 2009 by Ernő Rubik, the inventor of Rubik's Cube and other puzzles. Rubik's 360 was introduced on February 5, 2009 at the Nürnberg International Toy Fair ahead of its worldwide release in August.In contrast to most of Rubik's puzzles, Rubik's 360 is a physical challenge requiring manual dexterity, rather than learning of algorithms. The puzzle involves moving of six balls, each a different color, from a central sphere to six colorcoded compartments in the outer sphere. This is done by maneuvering them through a middle sphere that only has two holes. There are three spheres that make up the puzzle.
Like Rubik's Cube, Rubik's 360 has only one solution, but it cannot be solved by being broken apart. It is considered suitable for all ages and, according to first reviews, it is very addictive and engaging.The unofficial world record for solving this puzzle at a competition is 35.02 seconds, a record held by Martin Smith of the UK.
Rubik's Cube groupThe Rubik’s Cube group is a group that represents the structure of the Rubik's Cube mechanical puzzle. Each element of the set corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces. With this representation, not only can any cube move be represented, but also any position of the cube as well, by detailing the cube moves required to rotate the solved cube into that position. Indeed with the solved position as a starting point, there is a onetoone correspondence between each of the legal positions of the Rubik's Cube and the elements of . The group operation is the composition of cube moves, corresponding to the result of performing one cube move after another.
The Rubik's Cube group is constructed by labeling each of the 48 noncenter facets with the integers 1 to 48. Each configuration of the cube can be represented as a permutation of the labels 1 to 48, depending on the position of each facet. Using this representation, the solved cube is the identity permutation which leaves the cube unchanged, while the twelve cube moves that rotate a layer of the cube 90 degrees are represented by their respective permutations. The Rubik's Cube group is the subgroup of the symmetric group generated by the six permutations corresponding to the six clockwise cube moves. With this construction, any configuration of the cube reachable through a sequence of cube moves is within the group. Its operation refers to the composition of two permutations; within the cube, this refers to combining two sequences of cube moves together, doing one after the other. The Rubik’s Cube group is nonabelian as composition of cube moves is not commutative; doing two sequences of cube moves in a different order can result in a different configuration.
Rubik's Cube in popular cultureThe Rubik's Cube, a 1974 invention of Ernő Rubik of Hungary, fascinated people around the globe and became one of the most popular games in America in the early 1980s, having been initially released as the Magic Cube in Hungary in late 1977, and then remanufactured and released in the western world as Rubik's Cube in 1980. As of January 2009, 350 million cubes have been sold worldwide making it the world's topselling puzzle game. It earned a place as a permanent exhibit in New York’s Museum of Modern Art and entered the Oxford English Dictionary in 1982. The Cube retains a dedicated following, with almost 40,000 entries on YouTube featuring tutorials and video clips of quick solutions.
Rubik, the Amazing CubeRubik, the Amazing Cube is a 30minute Saturday morning animated series based on the puzzle created by Ernő Rubik, produced by RubySpears Enterprises and broadcast as part of The PacMan/Rubik, the Amazing Cube Hour block on ABC from September 10, to December 10, 1983. The Rubik half hour was broadcast in reruns as a standalone series on ABC from May 4 to August 31, 1985.The program features a magic Rubik's Cube named Rubik who can fly through the air and has other special powers. Rubik can only come alive when the colored squares on his sides had been matched up. The voice of Rubik, Ron Palillo, told TV Guide in 1983 that for the role, he spoke very slowly and then technicians sped up the tapes and raised the pitch. Palillo said Rubik's giggle is very different from the trademark laugh of Horshack, his character on the TV series Welcome Back, Kotter, and that it is pretty "for an inanimate object".
SpeedcubingSpeedcubing (also known as speedsolving) is the hobby involving solving a variety of twisty puzzles, the most famous being the 3x3x3 puzzle or Rubik's Cube, as quickly as possible. For most puzzles, solving entails performing a series of moves that alters a scrambled puzzle into a state in which every face of the puzzle is a single, solid color. Some puzzles have different requirements to be considered solved, such as the Clock, for which all the dials must be moved into the 12 'o clock position.
The standard puzzle sizes are 2x2x2, 3x3x3, 4x4x4, 5x5x5, 6x6x6, and 7x7x7. There are also different shapes of the famous puzzles, including Pyraminx, Megaminx, Skewb, and Square1. An individual who competes in speedcubing is known as a speedcuber.
Sudoku CubeThe Sudoku Cube or Sudokube is a variation on a Rubik's Cube in which the faces have numbers one to nine on the sides instead of colours. The aim is to solve Sudoku puzzles on one or more of the sides. The toy was created in 2006 by Jay Horowitz in Sebring, Ohio.
SuperflipThe superflip or 12flip is a Rubik's Cube configuration in which all 20 of the movable subcubes (or "cubies") are in the correct permutation, and the eight corners are correctly oriented, but all twelve of the edges are oriented incorrectly ("flipped"). It has been shown that the shortest path between a solved cube and the Superflip position requires 20 moves under the usual halfturn metric (HTM, in which rotating a face 180° counts as a single move), and that no position requires more (although there are many other positions that also require 20 moves).
Under the more restrictive quarterturn metric (QTM), only 90° face turns are allowed, so 180° turns count as two "moves". In those terms, the Superflip requires 24 moves, and is not maximally distant from the solved state. Instead, when Superflip is composed with the "fourdot" or "fourspot" position, in which four faces have their centers exchanged with the centers on the opposite face, the resulting position may be unique in requiring 26 moves under QTM.
The Simple Solution to Rubik's CubeThe Simple Solution to Rubik's Cube by James G. Nourse is a book that was published in 1981. The book explains how to solve the Rubik's Cube. The book became the bestselling book of 1981, selling 6,680,000 copies that year. It was the fastestselling title in the 36year history of Bantam Books.
Void CubeThe Void Cube is a 3D mechanical puzzle similar to a Rubik's Cube, with the notable difference being that the center pieces are missing, which causes the puzzle to resemble a level 1 Menger sponge. The core used on the Rubik's Cube is also absent, creating holes straight through the cube on all three axes. Due to the restricted volume of the puzzle it employs an entirely different structural mechanism from a regular Rubik's Cube, though the possible moves are the same. The Void Cube was invented by Katsuhiko Okamoto. Gentosha Education, in Japan, holds the license to manufacture Void Cubes.
Rubik's Cube  

Puzzle inventors  
Rubik's Cubes  
Cubic variations  
Noncubic variations 
 
Virtual variations (>3D)  
Derivatives  
Renowned solvers 
 
Solutions 
 
Mathematics  
Official organization  
Related articles  

This page is based on a Wikipedia article written by authors
(here).
Text is available under the CC BYSA 3.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.