rubik's cube 3d drawing

3-D combination puzzle

Rubik's Cube

Other names	Magic Cube, Speed Cube, Puzzle Cube, Cube
Blazon	Combination puzzle
Inventor(s)	Ernő Rubik
Company	Rubik'south Brand Ltd (Spin Master)[i]
Country	Hungary
Availability	1977: as Hungarian Magic Cube, starting time exam batches released in Budapest 1980: as Rubik's Cube, worldwide–present
Official website

The Rubik'due south Cube is a three-D combination puzzle invented in 1974^{[2] [three]} by Hungarian sculptor and professor of architecture Ernő Rubik. Originally chosen the Magic Cube,^[4] the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980^[5] via businessman Tibor Laczi and Seven Towns founder Tom Kremer.^[six] Rubik'southward Cube won the 1980 German Game of the Year special honour for Best Puzzle. As of Jan 2009^[update], 350 million cubes had been sold worldwide,^{[seven] [8] [ needs update ]} making it the earth'due south bestselling puzzle game^{[9] [10]} and bestselling toy.^[11]

On the original archetype Rubik'southward Cube, each of the six faces was covered by nine stickers, each of one of six solid colours: white, red, blue, orange, light-green, and yellow. Some later versions of the cube have been updated to employ coloured plastic panels instead, which prevents peeling and fading.^[12] In models as of 1988^[update], white is opposite yellow, blue is opposite green, and orangish is opposite ruby-red, and the red, white, and bluish are bundled in that order in a clockwise organization.^[13] On early cubes, the position of the colours varied from cube to cube.^[fourteen] An internal pivot machinery enables each confront to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must exist returned to have merely i color. 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, information technology is however widely known and used. Many speedcubers continue to practise it and similar puzzles; they also compete for the fastest times in various categories. Since 2003, the World Cube Association, the international governing body of the Rubik's Cube, has organised competitions worldwide and recognises world records.

History

Precursors

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

In March 1970, Larry D. Nichols invented a two×2×2 "Puzzle with Pieces Rotatable in Groups" and filed a Canadian patent application for information technology. Nichols's cube was held together past magnets. Nichols was granted U.Due south. Patent 3,655,201 on xi April 1972, two years earlier Rubik invented his Cube.

On ix April 1970, Frank Fob applied to patent an "amusement device", a type of sliding puzzle on a spherical surface with "at to the lowest degree two 3×3 arrays" intended to exist used for the game of noughts and crosses. He received his U.k. patent (1344259) on 16 January 1974.^[15]

Rubik's invention

Packaging of Rubik'southward Cube, Toy of the twelvemonth 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 Craft in Budapest.^[16] Although it is widely reported that the Cube was built as a education 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 beginning time he scrambled his new Cube so tried to restore information technology.^[17] Rubik applied for a patent in Hungary for his "Magic Cube" (Bűvös kocka in Hungarian) on thirty January 1975,^[iv] and HU170062 was granted after that yr.

The outset 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 existence hands pulled autonomously, unlike the magnets in Nichols's blueprint. With Ernő Rubik'southward permission, businessman Tibor Laczi took a Cube to Germany's Nuremberg Toy Fair in February 1979 in an attempt to popularise it.^[18] Information technology was noticed by Vii Towns founder Tom Kremer, and they signed a deal with Ideal Toys in September 1979 to release the Magic Cube worldwide.^[xviii] Ideal wanted at to the lowest degree a recognisable proper noun 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 rubber and packaging specifications. A lighter Cube was produced, and Ideal decided to rename it. "The Gordian Knot" and "Inca Aureate" were considered, only the company finally decided on "Rubik's Cube", and the start batch was exported from Hungary in May 1980.^[20]

1980s Cube craze

Afterward the first batches of Rubik's Cubes were released in May 1980, initial sales were pocket-sized, just Ideal began a television set advertising campaign in the eye of the twelvemonth which it supplemented with newspaper advertisements.^[21] At the end of 1980, Rubik'southward Cube won a German Game of the Twelvemonth special award^[22] and won similar awards for best toy in the Britain, France, and the Usa.^[23] By 1981, Rubik's Cube had become a craze, and information technology is estimated that in the menses from 1980 to 1983 around 200 one thousand thousand Rubik's Cubes were sold worldwide.^[24] In March 1981, a speedcubing title organised by the Guinness Book of Globe Records was held in Munich,^[22] and a Rubik'south Cube was depicted on the front cover of Scientific American that same month.^[25] In June 1981, The Washington Post reported that Rubik'due south 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 seven to 70 all over the world this summer."^[27]

As most people could solve simply one or ii sides, numerous books were published including David Singmaster'due south Notes on Rubik's "Magic Cube" (1980) and Patrick Bossert's You Can Practice the Cube (1981).^[22] At ane stage in 1981, three of the top x best selling books in the U.s.a. were books on solving Rubik's Cube,^[28] and the acknowledged book of 1981 was James Thou. Nourse's The Simple Solution to Rubik's Cube which sold over half-dozen million copies.^[29] In 1981, the Museum of Modern Art in New York exhibited a Rubik'south Cube, and at the 1982 World'southward Off-white in Knoxville, Tennessee a six-foot Cube was put on display.^[22] ABC Boob tube even adult a cartoon show called Rubik, the Amazing Cube.^[30] In June 1982, the Offset Rubik's Cube Earth Championship took place in Budapest and would become the just contest recognized every bit 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 Mainland china and the USSR, the craze had started afterwards and need was still loftier because of a shortage of Cubes.^{[33] [34]}

21st-century revival

Rubik'due south Cubes connected to exist marketed and sold throughout the 1980s and 1990s,^[22] simply it was not until the early on 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 "condign cool to ain a Cube once more".^[36] The 2003 World Rubik's Games Title was the outset speedcubing tournament since 1982.^[35] Information technology was held in Toronto and was attended by 83 participants.^[35] The tournament led to the germination of the Globe 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 equally YouTube, which allowed fans to share their solving strategies.^[37] Following the expiration of Rubik's patent in 2000, other brands of cubes appeared, particularly from Chinese companies.^[38] Many of these Chinese branded cubes have been engineered for speed and are favoured past speedcubers.^[38] On 27 October 2020, Spin Master said it will pay $50 million to buy the Rubik'due south Cube make.^[one]

Imitations

Taking advantage of an initial shortage of cubes, many imitations and variations appeared, many of which may accept violated one or more patents. In year 2000 the patents expired and since many Chinese companies produce copies of—and in most all cases, improvements upon—the Rubik and V-Cube designs.^[38]

Patent history

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×two Pocket Cube infringed Nichols'due south patent, but overturned the judgment on Rubik'south 3×three×iii Cube.^[39]

Even while Rubik's patent awarding was beingness candy, Terutoshi Ishigi, a self-taught engineer and ironworks owner nigh 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 part granted Japanese patents for non-disclosed applied science within Japan without requiring worldwide novelty.^{[forty] [41]} Hence, Ishigi's patent is more often than not accepted as an contained reinvention at that time.^{[42] [43] [44]} Rubik applied for more patents in 1980, including another Hungarian patent on 28 October. In the U.s.a., Rubik was granted U.S. Patent 4,378,116 on 29 March 1983, for the Cube. This patent expired in 2000.

Trademarks

Rubik'south Brand Ltd. also holds the registered trademarks for the give-and-take "Rubik" and "Rubik's" and for the 2D and 3D visualisations of the puzzle. The trademarks have been upheld past a ruling of the General Court of the European Wedlock on 25 November 2022 in a successful defense force confronting a German toy manufacturer seeking to invalidate them. Withal, European toy manufacturers are allowed to create differently shaped puzzles that accept a similar rotating or twisting functionality of component parts such every bit for example Skewb, Pyraminx or Impossiball.^[45]

On 10 November 2016, Rubik's Cube lost a ten-twelvemonth boxing over a fundamental trademark event. The Eu's highest court, the Court of Justice, ruled that the puzzle'due south shape was not sufficient to grant it trademark protection.^[46]

Mechanics

Rubik'south Cube partially disassembled

Rubik'southward Cube fully disassembled

Rubik'due south Cube in scrambled state

A standard Rubik'southward Cube measures v.6 centimetres (2+ 1⁄4  in) on each side.^[47] The puzzle consists of 26 unique miniature cubes, likewise known as "cubies" or "cubelets". Each of these includes a curtained inward extension that interlocks with the other cubes while permitting them to motility to different locations. However, the centre cube of each of the 6 faces is merely a single foursquare façade; all vi are affixed to the core mechanism. These provide structure for the other pieces to fit into and rotate around. Hence, there are 21 pieces: a single core slice consisting of three intersecting axes holding the six eye squares in place simply letting them rotate, and 20 smaller plastic pieces that fit into it to form the assembled puzzle.^[48]

Each of the six center pieces pivots on a screw (fastener) held by the eye piece, a "3D cross". A spring between each screw head and its corresponding slice tensions the slice inward, so that collectively, the whole assembly remains compact but tin still be easily manipulated. The screw can be tightened or loosened to change the "experience" of the Cube. Newer official Rubik's brand cubes have rivets instead of screws and cannot be adjusted. However, Old Cubes made by the Rubik's Brand Ltd. and from dollar stores do not have screws or springs, all they take is a plastic clip to keep the centre piece in identify and freely rotate.

The Cube can be taken apart without much difficulty, typically past rotating the top layer by 45° and then prying ane of its edge cubes away from the other two layers. Consequently, it is a unproblematic process to "solve" a Cube by taking it apart and reassembling information technology in a solved country.

There are six fundamental pieces that prove 1 coloured face, twelve border pieces that show 2 coloured faces, and eight corner pieces that prove three coloured faces. Each piece shows a unique colour combination, only not all combinations are nowadays (for example, if red and orangish 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 tin be altered by twisting an outer 3rd of the Cube by increments of xc degrees, but the location of the coloured sides relative to one some other in the completed state of the puzzle cannot be altered; it is stock-still by the relative positions of the center squares. Nonetheless, Cubes with alternative colour arrangements also exist; for case, with the xanthous face opposite the greenish, the bluish face opposite the white, and ruby and orange remaining opposite each other.

Douglas Hofstadter, in the July 1982 upshot of Scientific American, pointed out that Cubes could be coloured in such a manner 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 pop.^[42]

Mathematics

The puzzle was originally advertised as having "over three,000,000,000 (three billion) combinations merely only one solution".^[49] Depending on how combinations are counted, the actual number is significantly higher.

Permutations

The current colour scheme of a Rubik's Cube

The original (3×3×three) Rubik'south Cube has eight corners and twelve edges. There are 8! (40,320) ways to conform the corner cubes. Each corner has three possible orientations, although only seven (of eight) can be oriented independently; the orientation of the 8th (terminal) corner depends on the preceding seven, giving iii⁷ (2,187) possibilities. There are 12!/ii (239,500,800) ways to adapt the edges, restricted from 12! because edges must exist in an fifty-fifty permutation exactly when the corners are. (When arrangements of centres are also permitted, every bit described below, the dominion is that the combined arrangement of corners, edges, and centres must be an even permutation.) Eleven edges tin can exist flipped independently, with the flip of the twelfth depending on the preceding ones, giving two¹¹ (2,048) possibilities.^[l]

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

which is approximately 43 quintillion.^[51] To put this into perspective, if 1 had one standard-sized Rubik's Cube for each permutation, one could comprehend the Earth'south surface 275 times, or stack them in a tower 261 lite-years high.

The preceding figure is express to permutations that tin can exist 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:

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

which is approximately 519 quintillion^[51] possible arrangements of the pieces that make up the cube, but only ane in twelve of these are really solvable. This is because at that place is no sequence of moves that will bandy a single pair of pieces or rotate a single corner or edge cube. Thus, at that place are 12 possible sets of reachable configurations, sometimes chosen "universes" or "orbits", into which the cube can be placed by dismantling and reassembling information technology.

The preceding numbers assume the centre faces are in a fixed position. If one considers turning the whole cube to exist a dissimilar permutation, then each of the preceding numbers should be multiplied by 24. A chosen colour can be on ane 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.

Center faces

The original Rubik's Cube had no orientation markings on the centre faces (although some carried the words "Rubik'south Cube" on the centre foursquare of the white face), and therefore solving it does not require any attending to orienting those faces correctly. Yet, with marker pens, ane could, for example, marker the central squares of an unscrambled Cube with iv coloured marks on each edge, each corresponding to the colour of the adjacent confront; 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 foursquare or playing bill of fare suits. Cubes take also been produced where the nine stickers on a face are used to make a unmarried larger picture, and heart orientation matters on these every bit well. Thus ane tin can nominally solve a Cube even so accept the markings on the centres rotated; it then becomes an additional test to solve the centres besides.

Mark Rubik's Cube'south centres increases its difficulty, because this expands the set of distinguishable possible configurations. There are 4^vi/2 (2,048) means to orient the centres since an even permutation of the corners implies an even number of quarter turns of centres likewise. In particular, when the Cube is unscrambled apart from the orientations of the central squares, there will always be an even number of eye 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 (iv.3×10^xix) to 88,580,102,706,155,225,088,000 (8.9×x²²).^[52]

When turning a cube over is considered to exist a alter in permutation then nosotros must also count arrangements of the centre faces. Nominally there are six! ways to arrange the 6 center faces of the cube, merely merely 24 of these are achievable without disassembly of the cube. When the orientations of centres are besides counted, equally in a higher place, this increases the total number of possible Cube permutations from 88,580,102,706,155,225,088,000 (viii.ix×10²²) to 2,125,922,464,947,725,402,112,000 (ii.1×x²⁴).

Algorithms

In Rubik'due south cubers' parlance, a memorised sequence of moves that has a desired result on the cube is called an algorithm. This terminology is derived from the mathematical utilise of algorithm, meaning a listing of well-defined instructions for performing a task from a given initial country, through well-defined successive states, to a desired finish-state. Each method of solving the Cube employs its own set of algorithms, together with descriptions of what effect the algorithm has, and when information technology can be used to bring the cube closer to being solved.

Many algorithms are designed to transform only a small function of the cube without interfering with other parts that have already been solved so that they can exist practical repeatedly to different parts of the cube until the whole is solved. For example, in that location 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 practise have a sure desired effect on the cube (for example, swapping two corners) but may also take the side-effect of changing other parts of the cube (such every bit permuting some edges). Such algorithms are ofttimes simpler than the ones without side effects and are employed early on in the solution when near of the puzzle has not yet been solved and the side effects are not important. Well-nigh are long and difficult to memorise. Towards the end of the solution, the more specific (and unremarkably more complicated) algorithms are used instead.

Relevance and application of mathematical group theory

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 construction, namely XYX ^−one Y ⁻¹ (where X and Y are specific moves or move-sequences and Ten ⁻¹ and Y ^−one are their respective inverses), or a conjugate construction, namely XYX ^−one, often referred to by speedcubers colloquially every bit a "setup motility".^[53] 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 cocky-independent "levels of difficulty". For example, one such "level" could involve solving cubes that accept been scrambled using just 180-degree turns. These subgroups are the principle underlying the computer cubing methods past Thistlethwaite and Kociemba, which solve the cube by further reducing information technology to another subgroup.

Solutions

Move annotation

Many 3×iii×3 Rubik's Cube enthusiasts use a notation adult by David Singmaster to announce a sequence of moves, referred to as "Singmaster annotation".^[54] 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 (Upward): the side above or on elevation of the front side
• D (Downward): the side opposite the top, underneath the Cube
• L (Left): the side direct to the left of the front end
• R (Right): the side directly to the right of the front
• f (Front two layers): the side facing the solver and the corresponding middle layer
• b (Back 2 layers): the side opposite the front and the corresponding heart layer
• u (Up 2 layers): the acme side and the corresponding center layer
• d (Down two layers): the bottom layer and the corresponding middle layer
• 50 (Left two layers): the side to the left of the forepart and the corresponding heart layer
• r (Correct ii layers): the side to the right of the front and the respective 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 number symbol ( ′ ) follows a letter, it denotes an anticlockwise face plow; while a letter without a prime number symbol denotes a clockwise plow. These directions are as one is looking at the specified face up. A letter followed by a ii (occasionally a superscript²) denotes ii turns, or a 180-degree turn. R is right side clockwise, merely R′ is right side anticlockwise. The letters x, y, and z are used to bespeak that the unabridged Cube should exist turned almost one of its axes, corresponding to R, U, and F turns respectively. When ten, y, or z is primed, information technology is an indication that the cube must be rotated in the opposite management. When x, y, or z is squared, the cube must exist rotated 180 degrees.

The almost common divergence from Singmaster notation, and in fact the current official standard, is to use "westward", for "wide", instead of lowercase letters to correspond moves of two layers; thus, a move of Rw is equivalent to i of r.^[55]

For methods using middle-layer turns (especially corners-first methods), there is a generally accepted "MES" extension to the notation where letters M, Eastward, and Southward denote eye layer turns. Information technology was used e.g. in Marc Waterman'southward Algorithm.^[56]

• M (Centre): the layer between Fifty and R, turn direction as L (top-downwardly)
• Eastward (Equator): the layer between U and D, plough management as D (left-right)
• Southward (Standing): the layer betwixt F and B, turn direction as F

The 4×four×iv and larger cubes utilise an extended notation to refer to the boosted middle layers. Generally speaking, capital 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 (50*), a number in front of information technology (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)'502f' 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 half dozen×6×6 and larger, moves of three layers are notated by the number 3, for example, 3L.

An alternative notation, Wolstenholme notation,^[57] is designed to make memorising sequences of moves easier for novices. This annotation uses the same letters for faces except it replaces U with T (top), then that all are consonants. The central difference is the utilise 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′ U 50′ U′ R U2 in Singmaster notation). The addition of a C implies rotation of the unabridged cube, so ROC is the clockwise rotation of the cube around its correct face up. Middle layer moves are denoted by adding an Grand to the corresponding face motion, so RIM means a 180-degree plough of the middle layer side by side to the R face.

Another notation appeared in the 1981 book The Simple Solution to Rubik's Cube. Singmaster notation was non widely known at the fourth dimension of publication. The faces were named Top (T), Lesser (B), Left (L), Correct (R), Front end (F), and Posterior (P), with + for clockwise, – for anticlockwise, and ii for 180-degree turns.

Another note appeared in the 1982 "The Ideal Solution" book for Rubik's Revenge. Horizontal planes were noted as tables, with tabular array 1 or T1 starting at the top. Vertical front to dorsum planes were noted every bit books, with book one or B1 starting from the left. Vertical left to right planes were noted equally windows, with window 1 or W1 starting at the forepart. Using the front face as a reference view, table moves were left or right, book moves were up or downwards, and window moves were clockwise or anticlockwise.

Period of move sequences

The repetition of whatever given move sequence on a cube which is initially in solved state will eventually return the cube dorsum to its solved land: the smallest number of iterations required is the catamenia of the sequence. For case, the 180-caste turn of whatsoever side has period 2 (e.g. {U^two}^two ); the 90-degree turn of any side has period 4 (e.m. {R}^iv ). The maximum menstruum for a motility sequence is 1260:^[54] for example, allowing for total rotations, {F 10}¹²⁶⁰ or {R y}¹²⁶⁰ or {U z}¹²⁶⁰ ; not allowing for rotations, {D R' Uⁱⁱ M}¹²⁶⁰ , or {B E Fifty' F²}¹²⁶⁰ , or {Due south' U' B D²}¹²⁶⁰ ; only allowing for clockwise quarter turns, {U R Due south U L}¹²⁶⁰ , or {F L E B 50}¹²⁶⁰ , or {R U R D S}¹²⁶⁰ ; just allowing for lateral clockwise quarter turns, {F B L F B R F U}¹²⁶⁰ , or {U D R U D L U F}¹²⁶⁰ , or {R L D R L U R F}¹²⁶⁰ .

Optimal solutions

Although there are a pregnant number of possible permutations for Rubik's Cube, a number of solutions have been developed which permit 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.^[53] This solution involves solving the Cube layer by layer, in which ane layer (designated the tiptop) is solved beginning, followed by the centre layer, and and so the final and bottom layer. After sufficient practise, solving the Cube layer past layer can exist done in nether 1 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 platonic algorithm, might be in "the low twenties".^[58] In 2007, Daniel Kunkle and Gene Cooperman used computer search methods to demonstrate that any 3×3×3 Rubik's Cube configuration tin can be solved in 26 moves or fewer.^{[59] [60] [61]} In 2008, Tomas Rokicki lowered that number to 22 moves,^{[62] [63] [64]} and in July 2010, a team of researchers including Rokicki, working with Google, proved the and so-called "God's number" to exist twenty.^{[65] [66]} This is optimal, since there exist some starting positions which require a minimum of 20 moves to solve. More than generally, it has been shown that an northward×due north×north Rubik's Cube can be solved optimally in Θ(n ^two / log(n)) moves.^[67]

Speedcubing methods

A solution unremarkably used by speedcubers was developed past Jessica Fridrich. This method is called CFOP standing for "cross, F2L, OLL, PLL". It is similar to the layer-by-layer method just employs the use of a big number of algorithms, especially for orienting and permuting the last layer. The cross is done kickoff, followed by first layer corners and second layer edges simultaneously, with each corner paired upwardly with a 2d-layer edge piece, thus completing the beginning two layers (F2L). This is then followed by orienting the last layer, so permuting the last layer (OLL and PLL respectively). Fridrich'south solution requires learning roughly 120 algorithms but allows the Cube to be solved in simply 55 moves on average.

A at present well-known method was developed by Lars Petrus. In this method, a 2×2×2 department is solved first, followed by a two×two×three, and then the incorrect edges are solved using a three-move algorithm, which eliminates the need for a possible 32-move algorithm subsequently. The principle backside this is that in layer-by-layer, one must constantly break and fix the completed layer(s); the 2×2×two and 2×2×3 sections let three or ii layers (respectively) to exist 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 as well popular for fewest motion competitions.^[68]

The Roux Method, adult by Gilles Roux, is like to the Petrus method in that information technology relies on block building rather than layers, but derives from corners-first methods. In Roux, a 3×2×1 cake is solved, followed by another 3×2×1 on the contrary side. Next, the corners of the top layer are solved. The cube tin can then be solved using just moves of the U layer and M slice.^[69]

Beginners' methods

Most beginner solution methods involve solving the cube ane layer at a fourth dimension, using algorithms that preserve what has already been solved. The easiest layer past layer methods crave but iii–eight algorithms.^{[70] [71]}

In 1981, thirteen-year-old Patrick Bossert developed a solution for solving the cube, along with a graphical notation, designed to exist easily understood by novices.^[72] It was later published as You Can Practice The Cube and became a all-time-seller.^[73]

In 1997, Denny Dedmore published a solution described using diagrammatic icons representing the moves to exist made, instead of the usual notation.^[74]

Philip Marshall'due south The Ultimate Solution to Rubik'southward Cube takes a different approach, averaging only 65 twists nonetheless requiring the memorisation of only 2 algorithms. The cross is solved start, followed by the remaining edges, then v corners, and finally the terminal three corners.^[75]

Rubik's Cube solver plan

The most move optimal online Rubik's Cube solver programs use Herbert Kociemba's Two-Stage Algorithm which can typically determine a solution of 20 moves or fewer. The user has to gear up the colour configuration of the scrambled cube, and the program returns the steps required to solve it.^[76]

Competitions and records

Speedcubing competitions

Speedcubing (or speedsolving) is the practice of trying to solve a Rubik'due south Cube in the shortest time possible. There are a number of speedcubing competitions that accept place around the world.

A speedcubing title organised past the Guinness Book of Earth Records was held in Munich on 13 March 1981.^[77] The contest used standardised scrambling and stock-still inspection times, and the winners were Ronald Brinkmann and Jury Fröschl with times of 38.0 seconds.^[77] The showtime 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.^[78]

Since 2003, the winner of a competition is determined past taking the average time of the centre three of five attempts. All the same, the single best time of all tries is also recorded. The Earth Cube Association maintains a history of world records.^[79] In 2004, the WCA made information technology mandatory to use a special timing device called a Stackmat timer.

In addition to the main 3x3x3 outcome, the WCA too holds events where the cube is solved in different ways:^[80]

• Blindfolded solving^[81]
• Multiple Blindfolded solving, or "multi-blind", in which the contestant solves any number of cubes blindfolded in a row^[82]
• Solving the cube using a single hand^[83]
• Solving the cube in the fewest possible moves^[84]

In Blindfolded Solving, the contestant first studies the scrambled cube (i.due east., looking at it commonly with no blindfold), and is then blindfolded earlier beginning to turn the cube's faces. Their recorded time for this event includes both the fourth dimension spent memorizing the cube and the time spent manipulating information technology.

In Multiple Blindfolded, all of the cubes are memorised, and then all of the cubes are solved once blindfolded; thus, the chief challenge is memorising many – oftentimes ten or more – divide cubes. The consequence is scored not by time only by the number of points achieved afterwards the one-hour fourth dimension limit has elapsed. The number of points achieved is equal to the number of cubes solved correctly, minus the number of cubes unsolved afterwards the cease of the endeavour, where a greater number of points is meliorate. If multiple competitors achieve the same number of points, rankings are assessed based on the total fourth dimension of the attempt, with a shorter time beingness improve.

In Fewest Moves solving, the contestant is given one hour to find a solution and must write it down.

Records

Contest records

• Single time: The world tape time for solving a iii×three×3 Rubik's Cube is 3.47 seconds, held by Du Yusheng (杜宇生) of China, on 24 November 2022 at Wuhu Open up 2018.^[85]
• Average time: The world record average of the middle iii of 5 solve times (which excludes the fastest and slowest) is 5.09 seconds, prepare by Tymon Kolasiński of Poland at Cubers Eve Lubartów 2021^[86]
• One-handed solving: The world record fastest one-handed solve is half-dozen.82 seconds, set by Max Park of the U.s. on 12 October 2022 at Bay Area Speedcubin' 20 2019. The world record fastest average of five i-handed solves is ix.42 seconds, also gear up past Max Park at Berkeley Summer 2018.^[87]
• Feet solving: The earth record fastest Rubik'southward Cube solve with one'south feet is fifteen.56 seconds, set past Mohammed Aiman Koli of India on 27 Dec 2022 at VJTI Mumbai Cube Open 2019. The world record average of 5 anxiety solves is xix.90 seconds, set by Lim Hung (林弘) of Malaysia on 21 December 2022 at Medan 10th Anniversary 2019.^[88] Since 1 January 2020, 3x3x3 With Feet is no longer an event recognized by the WCA, and no results are being accustomed.^[89]
• Blindfold solving: The world tape fastest Rubik's Cube solve blindfolded is 14.67 seconds (including memorization), set past Tommy Cherry-red of the United states on 12 December 2022 at Florida Fall 2021. The world record mean of three for blindfold solving is 15.24 seconds, besides set by Tommy Ruby at the same event.^[90]
• Multiple blindfold solving: The globe record for multiple Rubik's Cube solving blindfolded is 59 out of 60 cubes, set by Graham Siggins of the United States on nine November 2022 at OSU Blind Weekend 2019. Siggins inspected lx cubes, donned a blindfold, and solved successfully 59 of them, all nether the time limit of i hour.^[91]
• Fewest moves solving: The world record of fewest moves to solve a cube, given one hour to determine i'due south solution, is 16, which was achieved past Sebastiano Tronto of Italy on 15 June 2022 at FMC 2019. The globe record mean of three for the fewest moves challenge (with different scrambles) is 21.00, fix by Cale Schoon of the United States on nineteen January 2022 at Due north Star Cubing Challenge 2020.^[92]

Other records

• Non-man solving: The fastest not-human Rubik's Cube solve was performed by Rubik'southward Contraption, a robot fabricated past Ben Katz and Jared Di Carlo. A YouTube video shows a 0.38-second solving time using a Nucleo with the min2phase algorithm.^[93]
• Highest club physical n×northward×n cube solving: Jeremy Smith solved a 17x17x17 in 45 minutes and 59.40 seconds.^{[94] [95]}
• Grouping solving (12 minutes): The tape for most people solving a Rubik'southward 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.^[96]
• Group solving (xxx 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 Earth Record of 937. The outcome was hosted by Depaul UK.^[97]

On iv November 2012, 3248 people, mainly students of the Higher of Engineering science Pune, successfully solved Rubik's cube in 30 minutes on higher ground. The successful attempt is recorded in the Limca Volume of Records. The higher will submit the relevant data, witness statements and video of the outcome to Guinness regime.^[98]

Top ten solvers past single solve^[99]

Position	Proper noun	Result	Nationality	Competition
i	Yusheng Du (杜宇生)	three.47	Red china	Wuhu Open 2018
2	Ruihang Xu (许瑞航)	4.06	China	Wuhan Open 2021
3	Tymon Kolasiński	iv.eleven	Poland	SST Rzeszów 2021
four	Feliks Zemdegs	4.16	Australia	Auckland Summer 2020
v	Patrick Ponce	4.24	Us	CubingUSA Northeast Title 2019
6	Sebastian Weyer	4.32	Deutschland	Gesté Barrière Open 2021
vii	Matty Hiroto Inaba	4.34	United States	Utah Fall 2021
8	Nicolás Sánchez	4.38	United States	GA Cubers Feet Fest 2019
9	Max Park	4.40	United States	SacCubing V 2018
10	Lukas Shelley	4.42	Denmark	Hangzhou Open PM 2021

Top 10 solvers by average of five solves^[100]

Position	Proper noun	Average	Nationality	Competition	Solves
one	Tymon Kolasiński	five.09	Poland	Cubers Eve Lubartów 2021	4.73 / four.83 / 5.24 / 6.57 / v.20
2	Max Park	v.32	United states	United States	five.34 / 5.50 / 5.12 / 4.54 / 5.96
3	Ruihang Xu (许瑞航)	v.48	China	Wuhan Open 2021	5.48 / 5.52 / 5.45 / four.06 / vii.51
four	Feliks Zemdegs	5.53	Australia	Odd Twenty-four hour period in Sydney 2019	7.16 / five.04 / 4.67 / half-dozen.55 / four.99
v	Yezhen Han (韩业臻)	5.57	China	Guangdong Open up 2021	5.87 / 5.42 / v.30 / 7.53 / 5.42
vi	Matty Hiroto Inaba	v.68	United States	BCCC A 2021	6.01 / six.12 / 4.76 / 7.05 / 4.92
7	Patrick Ponce	5.83	United States	GA Cubers Return A 2021	5.92 / 5.26 / vii.23 / half dozen.14 / 5.43
eight	Sean Patrick Villanueva	5.98	Philippines	Marikina City Open up II 2019	seven.67 / v.72 / 5.99 / five.52 / 6.23
9	Luke Garrett	6.01	United States	Florida Returns 2021	five.94 / 5.20 / five.41 / 7.43 / vi.69
10	Philipp Weyer	vi.06	Frg	Swisscubing Cup Final 2018	4.81 / six.43 / 5.48 / 6.26 / 7.51

Variations

In that location are different variations of Rubik'southward Cubes with up to thirty-3 layers: the 2×2×2 (Pocket/Mini Cube), the standard 3×3×3 cube, the four×iv×4 (Rubik's Revenge/Master Cube), and the five×5×five (Professor's Cube) beingness the most well known. As of 1981, the official Rubik's Brand has licensed twisty puzzle cubes merely up to the five×v×v. The 17×17×17 "Over The Top" cube (available late 2011) was until December 2022 the largest (and nigh expensive, costing more than than 2 thou dollars) commercially sold cube. A mass-produced 17×17×17 was after introduced by the Chinese manufacturer YuXin. A working design for a 22×22×22 cube exists and was demonstrated in January 2016,^[101] and a 33×33×33 in December 2017.^[102] Chinese manufacturer ShengShou has been producing cubes in all sizes from 2×two×2 to fifteen×15×15 (every bit of May 2020), and have too come out with a 17×17×17.^[103]

Non-licensed physical cubes as big equally 17×17×17 based on the V-Cube patents^{[ commendation needed ]} are commercially bachelor to the mass-market place; these represent about the limit of practicality for the purpose of "speed-solving" competitively (as the cubes go increasingly ungainly and solve-times increase quadratically).

There are many variations^[104] of the original cube, some of which are fabricated by Rubik. The mechanical products include Rubik's Magic, 360, and Twist. Also, electronics similar Rubik'due south Revolution and Slide, were as well inspired by the original. I of the 3×3×3 Cube variants is Rubik'due south 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 likewise has buttons for hints and cocky-solving, and it includes a charging stand. The TouchCube was introduced at the American International Toy Fair in New York on 15 February 2009.^{[105] [106]}

The Cube has inspired an entire category of like puzzles, normally referred to as twisty puzzles, which includes the cubes of different sizes mentioned above, every bit well as various other geometric shapes. Some such shapes include the tetrahedron (Pyraminx), the octahedron (Skewb Diamond), the dodecahedron (Megaminx), and the icosahedron (Dogic). There are also puzzles that change shape such as Rubik'due south Snake and the Square 1.

In 2011, Guinness World Records awarded the "largest order Rubiks magic cube" to a 17×17×17 cube, made by Oskar van Deventer.^{[107] [108]} On 2 Dec 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.^[102] On 8 April 2018, Grégoire Pfennig announced another world record, the 2x2x50 cube.^[109] Whether this is a replacement for the 33x33x33 record, or an additional record, remains to be seen.

All v ideal solids represented past twisty puzzles

Some puzzles accept also been created in the shape of Kepler–Poinsot polyhedra, such as Alexander's Star (a great dodecahedron). Grégoire Pfennig has also created at to the lowest degree one puzzle in the shape of a modest stellated dodecahedron.

Custom-built puzzles

Puzzles have been congenital resembling Rubik's Cube, or based on its inner workings. For instance, a cuboid is a puzzle based on Rubik's Cube, but with different functional dimensions, such as two×2×four, 2×iii×4, and 3×iii×five.^[110] Many cuboids are based on 4×4×iv or five×five×v mechanisms, via edifice plastic extensions or by directly modifying the mechanism.

Some custom puzzles are not derived from whatever existing mechanism, such as the Gigaminx v1.five-v2, Bevel Cube, SuperX, Toru, Rua, and 1×2×3. These puzzles usually take a set of masters 3D printed, which and so are copied using moulding and casting techniques to create the terminal puzzle.^{[ citation needed ]}

Other Rubik'due south 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 tin can be built past truncating and extending portions of a regular 3×3×3. Most shape modifications can exist adjusted to higher-order cubes. In the case of Tony Fisher's Rhombic Dodecahedron, there are three×3×3, four×four×4, v×5×5, and 6×half dozen×6 versions of the puzzle.

Rubik'south Cube software

Puzzles, like Rubik's Cube, can be faux by computer software to provide very large puzzles that are impractical to build, too as virtual puzzles that cannot be physically congenital, such as many higher dimensional analogues of the Rubik's Cube.^{[111] [112]}

• 

  A 2×two×two×ii in MagicCube4D

• 

  A 3×3×3×3 in MagicCube4D

• 

  A 4×4×4×four in MagicCube4D

• 

  A 3×3×3×3×iii in MagicCube5D

Chrome Cube Lab

Google has released the Chrome Cube Lab in association with^[113] Ernő Rubik. The site has various interactive objects based on Rubik's Cube. Customised versions of Rubik's Cube can exist created and uploaded.^[114]

See as well

• Mirror blocks
• n-dimensional sequential move puzzle
• Rubik's Domino
• Rubik's family cubes of all sizes
• Spatial ability
• 5-Cube viii (viii×8×viii)

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Farther reading

• Frey, Alexander; Singmaster, David (1982). Handbook of Cubic Math . Enslow. ISBN0894900587.
• Rubik, Ernő; Varga, Tamas; Keri, Gerson; Marx, Gyorgy; Vekerdy, Tamas (1987). Singmaster, David (ed.). Rubik's Cubic Compendium. Oxford University Press. ISBN0198532024.
• Bizek, Hana M. (1997). Mathematics of the Rubik'south Cube Pattern. Pittsburgh, Pa: Dorrance Pub. Co. ISBN0805939199.
• Slocum, Jerry; Singmaster, David; Huang, Wei-Hwa; Gebhardt, Dieter; Hellings, Geert; Rubik, Ernő (2009). The Cube: The Ultimate Guide to the World's Bestselling Puzzle . Blackness Canis familiaris & Leventhal. ISBN978-1579128050.

External links

• Official website
• Safecracker Method: Solving Rubik'southward Cube with simply 10 Numbers
• Rubik's Cube at Curlie
• How to solve a Rubik'southward Cube on YouTube
• World Cube Association
• List of related puzzles and solutions
• Consummate disassembly of a iii^3 classic Rubik'south cube
• Speedsolving Wiki
• "Rubik's Cube". Google Putter. Retrieved 19 May 2014. (Working model)

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Source: https://en.wikipedia.org/wiki/Rubik%27s_Cube

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