Rubik's Cube

Diagram from Nichols' patent showing a cube held together with magnets

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.[15]

Packaging of Rubik's Cube, Toy of the year 1980–Ideal Toy Corp., made in Hungary

In the mid-1970s, Ernő Rubik worked at the Department of Interior Design at the Academy of Applied Arts and Crafts in Budapest.[16] 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.[17] Rubik applied for a patent in Hungary for his "Magic Cube" (Bűvös kocka in Hungarian) on 30 January 1975,[4] 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; 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 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 solve only 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 Rubik's Cube,[28] and the best-selling 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 six-foot 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 the 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] On 27 October 2020, Spin Master said it will pay $50 million to buy the Rubik's Cube brand.[39]

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.[40]

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 Japanese patent law was enforced, Japan's patent office granted Japanese patents for non-disclosed technology within Japan without requiring worldwide novelty.[41][42] Hence, Ishigi's patent is generally accepted as an independent reinvention at that time.[43][44][45] 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.[46]

On 10 November 2016, Rubik's Cube lost a ten-year 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.[47]

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 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 3⁷ (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 2¹¹ (2,048) possibilities.[49]

${\displaystyle {8!\times 3^{7}\times {\frac {12!}{2}}\times 2^{11}}=43{,}252{,}003{,}274{,}489{,}856{,}000}$

which is approximately 43 quintillion.[50] To put this into perspective, if one had one standard-sized Rubik's Cube for each permutation, one could cover the Earth's surface 275 times, or stack them in a tower 261 light-years 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:

${\displaystyle {8!\times 3^{8}\times 12!\times 2^{12}}=519{,}024{,}039{,}293{,}878{,}272{,}000}$

which is approximately 519 quintillion[50] 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 12 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 centre 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 colour can be on one of six sides, and then one of the adjacent colours can be in one of four positions; this determines the positions of all remaining colours.

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 Rubik's Cube's centres increases its difficulty, because this expands the set of distinguishable possible configurations. There are 4⁶/2 (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 (4.3×10¹⁹) to 88,580,102,706,155,225,088,000 (8.9×10²²).[51]

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 (8.9×10²²) to 2,125,922,464,947,725,402,112,000 (2.1×10²⁴).

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 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 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 cube (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.

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⁻¹Y⁻¹ (where X and Y are specific moves or move-sequences 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".[52] In addition, the fact that there are well-defined subgroups within the Rubik's Cube group 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 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".[53] 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.

• F (Front): the side currently facing the solver
• B (Back): the side opposite the front
• U (Up): the side above or on top of the front side
• D (Down): the side opposite the top, underneath the Cube
• L (Left): the side directly to the left of the front
• R (Right): the side directly to the right of the front
• ƒ (Front two layers): the side facing the solver and the corresponding middle layer
• b (Back two layers): the side opposite the front and the corresponding middle layer
• u (Up two layers): the top side and the corresponding middle layer
• d (Down two layers): the bottom layer and the corresponding middle layer
• l (Left two layers): the side to the left of the front and the corresponding middle layer
• r (Right two layers): the side to the right of the front and the corresponding middle layer
• x (rotate): rotate the entire Cube on R
• y (rotate): rotate the entire Cube on U
• z (rotate): rotate the entire Cube on F

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 180-degree 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.[54]

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.g. in Marc Waterman's Algorithm.[55]

• M (Middle): the layer between L and R, turn direction as L (top-down)
• E (Equator): the layer between U and D, turn direction as D (left-right)
• S (Standing): the layer between F and B, turn direction as F

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,[56] 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 twice (180-degree) turns, which results in word-like 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 180-degree 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 180-degree 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 books, 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.

Mountaineer solving Rubik's Cube during a 1982 expedition to Tartu Ülikool 350 in the Pamir Mountains

Although there are a significant number of possible permutations for 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 Cube have been discovered independently. David Singmaster first published his solution in the book Notes on Rubik's "Magic Cube" in 1981.[52] 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 Cube, given an ideal algorithm, might be in "the low twenties".[57] 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.[58][59][60] In 2008, Tomas Rokicki lowered that number to 22 moves,[61][62][63] and in July 2010, a team of researchers including Rokicki, working with Google, proved the so-called "God's number" to be 20.[64][65] 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(n² / log(n)) moves.[66]

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 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 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 well-known 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 three-move algorithm, which eliminates the need for a possible 32-move algorithm later. The principle behind this is that in layer-by-layer, 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.[67]

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 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.[68]

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.[69][70]

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.[71] It was subsequently published as You Can Do The Cube and became a best-seller.[72]

In 1997, Denny Dedmore published a solution described using diagrammatic icons representing the moves to be made, instead of the usual notation.[73]

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.[74]

The most move optimal online Rubik's Cube solver programs use Herbert Kociemba's Two-Phase Algorithm which can typically determine a solution of 20 moves or fewer. The user has to set the colour configuration of the scrambled cube, and the program returns the steps required to solve it.[75]

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.[76] The contest used standardised scrambling and fixed inspection times, and the winners were Ronald Brinkmann and Jury Fröschl with times of 38.0 seconds.[76] 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.[77]

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.[78] 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:[79]

• Blindfolded solving[80]
• Multiple Blindfolded solving, or "multi-blind", in which the contestant solves any number of cubes blindfolded in a row[81]
• Solving the cube using a single hand[82]
• Solving the cube in the fewest possible moves[83]

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.

• Single time: The world record time for solving a 3×3×3 Rubik's Cube is 3.47 seconds, held by Du Yusheng (杜宇生) of China, on 24 November 2018 at Wuhu Open 2018.[84]
• Average time: The world record average of the middle three of five solve times (which excludes the fastest and slowest) is 5.53 seconds, set by Feliks Zemdegs of Australia at Odd Day at Sydney 2019.[85]
• One-handed solving: The world record fastest one-handed solve is 6.82 seconds, set by Max Park of the United States on 12 October 2019 at Bay Area Speedcubin' 20 2019. The world record fastest average of five one-handed solves is 9.42 seconds, also set by Max Park at Berkeley Summer 2018.[86]
• Feet solving: The world record fastest Rubik's Cube solve with one's feet is 15.56 seconds, set by Mohammed Aiman Koli of India on 27 December 2019 at VJTI Mumbai Cube Open 2019. The world record average of five feet solves is 19.90 seconds, set by Lim Hung (林弘) of Malaysia on 21 December 2019 at Medan 10th Anniversary 2019.[87] Since 1 January 2020, 3x3x3 With Feet is no longer an event recognized by the WCA, and no results are being accepted.[88]
• Blindfold solving: The world record fastest Rubik's Cube solve blindfolded is 15.50 seconds (including memorization), set by Max Hilliard of the United States on 1 August 2019 at CubingUSA Nationals 2019. The world record mean of three for blindfold solving is 18.18 seconds, set by Jeff Park of the United States on 14 December at OU Winter 2019.[89]
• Multiple blindfold solving: The world record for multiple Rubik's Cube solving blindfolded is 59 out of 60 cubes, set by Graham Siggins of the United States on 9 November 2019 at OSU Blind Weekend 2019. Siggins inspected 60 cubes, donned a blindfold, and solved successfully 59 of them, all under the time limit of one hour.[90]
• Fewest moves solving: The world record of fewest moves to solve a cube, given one hour to determine one's solution, is 16, which was achieved by Sebastiano Tronto of Italy on 15 June 2019 at FMC 2019. The world record mean of three for the fewest moves challenge (with different scrambles) is 22.00, also set by Sebastiano Tronto of Italy on 15 June 2019 at FMC 2019.[91]

• Non-human solving: The fastest non-human Rubik's Cube solve was performed by Rubik's Contraption, a robot made by Ben Katz and Jared Di Carlo. A YouTube video shows a 0.38-second solving time using a Nucleo with the min2phase algorithm.[92]
• Highest order physical n×n×n cube solving: Jeremy Smith solved a 17x17x17 in 45 minutes and 59.40 seconds.[93][94]

• Group solving (12 minutes): The record for most people solving a Rubik's Cube at once in twelve minutes is 134, set on 17 March 2010 by schoolboys from Dr Challoner's Grammar School, Amersham, England, breaking the previous Guinness World Record of 96 people at once.[95]
• Group solving (30 minutes): On 21 November 2012, at the O2 Arena in London, 1414 people, mainly students from schools across London, solved Rubik's Cube in under 30 minutes, breaking the previous Guinness World Record of 937. The event was hosted by Depaul UK.[96]

On 4 November 2012, 3248 people, mainly students of the College of Engineering Pune, successfully solved Rubik's cube in 30 minutes on college ground. The successful attempt is recorded in the Limca Book of Records. The college will submit the relevant data, witness statements and video of the event to Guinness authorities.[97]

Novelty keychain

Puzzles have been built resembling Rubik's Cube, or based on its inner workings. For example, a cuboid is a puzzle based on Rubik's Cube, but with different functional dimensions, such as 2×2×4, 2×3×4, and 3×3×5.[109] Many cuboids are based on 4×4×4 or 5×5×5 mechanisms, via building plastic extensions or by directly modifying the mechanism.

Some custom puzzles are not derived from any existing mechanism, such as the Gigaminx v1.5-v2, 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 3×3×3. Most shape modifications can be adapted to higher-order cubes. In the case of Tony Fisher's Rhombic Dodecahedron, there are 3×3×3, 4×4×4, 5×5×5, and 6×6×6 versions of the puzzle.

Puzzles, like Rubik's Cube, can be simulated by computer software, which provides 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.[110][111]

• 
  Magic Cube 4D, a 4×4×4×4 virtual puzzle
• 
  Magic Cube 5D, a 3×3×3×3×3 virtual puzzle
• 
  high-dimensional Octagon Magic Cube Puzzle simulated phone application
• 
  4D virtual 2x2x2x2 sequential move puzzle

Google has released the Chrome Cube Lab in association with[112] Ernő Rubik. The site has various interactive objects based on Rubik's Cube. Customised versions of Rubik's Cube can be created and uploaded.[113]