![Rubik's cube](https://upload.wikimedia.org/wikipedia/commons/a/a6/Rubik%27s_cube.svg)
The Rubik's Cube is a
3-D combination puzzle
A combination puzzle, also known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations. Many such puzzles are mechanical puzzles of polyhedral s ...
originally invented in 1974
by
Hungarian sculptor and professor of architecture
Ernő Rubik
Ernő Rubik (; born 13 July 1944) commonly known by his nickname, "Little Man", is a Hungarian inventor, architect and professor of architecture. He is best known for the invention of mechanical puzzles including the Rubik's Cube (1974), Rubi ...
. Originally called the Magic Cube,
the puzzle was licensed by Rubik to be sold by
Pentangle Puzzles in the UK in 1978, and then by
Ideal Toy Corp in 1980
via businessman Tibor Laczi and Seven Towns founder
Tom Kremer. The cube was released internationally in 1980 and became one of the most recognized icons in popular culture. It won the 1980
German Game of the Year special award for Best Puzzle. , 350 million cubes had been sold worldwide, making it the world's bestselling puzzle game and bestselling toy. The Rubik's Cube was inducted into the US National Toy Hall of Fame in 2014.
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. Some later versions of the cube have been updated to use coloured plastic panels instead, which prevents peeling and fading.
Since 1988, the arrangement of colours has been standardised with white opposite yellow, blue opposite green, and orange opposite red, and the red, white, and blue arranged clockwise in that order.
On early cubes, the position of the colours varied from cube to cube. An internal pivot mechanism enables each face to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must be returned to have only one colour. Similar puzzles have now been produced with various numbers of sides, dimensions, and stickers, not all of them by Rubik.
Although the Rubik's Cube reached its height of mainstream popularity in the 1980s, it is still widely known and used. Many
speedcubers continue to practise it and similar puzzles, and compete for the fastest times in various categories. Since 2003, the
World Cube Association
The World Cube Association (WCA) is the worldwide non-profit organization that regulates and holds competitions for mechanical puzzles that are operated by twisting groups of pieces, commonly known as '' twisty puzzles'' (a subcategory of combina ...
, the international governing body of the Rubik's Cube, has organised competitions worldwide and recognises world records.
History
Precursors
![Patent US3655201](https://upload.wikimedia.org/wikipedia/commons/8/86/Patent_US3655201.png)
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 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
A sliding puzzle, sliding block puzzle, or sliding tile puzzle is a combination puzzle that challenges a player to slide (frequently flat) pieces along certain routes (usually on a board) to establish a certain end-configuration. The pieces to ...
on a spherical surface with "at least two 3×3 arrays" intended to be used for the game of
noughts and crosses
Tic-tac-toe (American English), noughts and crosses (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with ''X'' or ''O''. T ...
. He received his UK patent (1344259) on 16 January 1974.
Rubik's invention
![1980-Rubik's-Cube](https://upload.wikimedia.org/wikipedia/commons/f/fa/1980-Rubik%27s-Cube.jpg)
In the mid-1970s, Ernő Rubik worked at the Department of Interior Design at the
Academy of Applied Arts and Crafts in Budapest.
Although it is widely reported that the Cube was built as a teaching tool to help his students understand 3D objects, his actual purpose was solving the structural problem of moving the parts independently without the entire mechanism falling apart. He did not realise that he had created a puzzle until the first time he scrambled his new Cube and then tried to restore it. Rubik applied for a
patent
A patent is a type of intellectual property that gives its owner the legal right to exclude others from making, using, or selling an invention for a limited period of time in exchange for publishing an enabling disclosure of the invention."A p ...
in Hungary for his "Magic Cube" ( hu, Bűvös kocka) on 30 January 1975,
and HU170062 was granted later that year.
The first test batches of the Magic Cube were produced in late 1977 and released in
Budapest
Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...
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
Nuremberg ( ; german: link=no, Nürnberg ; in the local East Franconian dialect: ''Nämberch'' ) is the second-largest city of the German state of Bavaria after its capital Munich, and its 518,370 (2019) inhabitants make it the 14th-largest ...
Toy Fair in February 1979 in an attempt to popularise it.
It was noticed by Seven Towns founder Tom Kremer, and they signed a deal with Ideal Toys in September 1979 to release the Magic Cube worldwide.
Ideal wanted at least a recognisable name to trademark; that arrangement put Rubik in the spotlight because the Magic Cube was renamed after its inventor in 1980. The puzzle made its international debut at the toy fairs of London, Paris, Nuremberg, and New York in January and February 1980.
After its international debut, the progress of the Cube towards the toy shop shelves of the West was briefly halted so that it could be manufactured to 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.
1980s Cube craze
![Expo 82 Rubik's Cube](https://upload.wikimedia.org/wikipedia/commons/c/c2/Expo_82_Rubik%27s_Cube.jpg)
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 advertisements. At the end of 1980, Rubik's Cube won a German Game of the Year special award
and won similar awards for best toy in the UK, France, and the US.
By 1981, Rubik's Cube had become a craze, and it is estimated that in the period from 1980 to 1983 around 200 million Rubik's Cubes were sold worldwide. In March 1981, a
speedcubing
Speedcubing (also known as speedsolving, or cubing) is a competitive sport involving solving a variety of combination puzzles, the most famous being the 3x3x3 puzzle or Rubik's Cube, as quickly as possible. An individual who practices solving tw ...
championship organised by the
Guinness Book of World Records
''Guinness World Records'', known from its inception in 1955 until 1999 as ''The Guinness Book of Records'' and in previous United States editions as ''The Guinness Book of World Records'', is a reference book published annually, listing world ...
was held in
Munich
Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the States of Germany, German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the List of cities in Germany by popu ...
,
and a Rubik's Cube was depicted on the front cover of ''
Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...
'' that same month.
In June 1981, ''
The Washington Post
''The Washington Post'' (also known as the ''Post'' and, informally, ''WaPo'') is an American daily newspaper published in Washington, D.C. It is the most widely circulated newspaper within the Washington metropolitan area and has a large nati ...
'' reported that Rubik's Cube is "a puzzle that's moving like fast food right now ... this year's
Hoola Hoop or
Bongo Board",
and by September 1981, ''
New Scientist
''New Scientist'' is a magazine covering all aspects of science and technology. Based in London, it publishes weekly English-language editions in the United Kingdom, the United States and Australia. An editorially separate organisation publishe ...
'' noted that the cube had "captivated the attention of children of ages from 7 to 70 all over the world this summer."
As most people could solve only one or two sides, numerous books were published including
David Singmaster
David Breyer Singmaster (born 1938) is an emeritus professor of mathematics at London South Bank University, England. A self-described metagrobologist, he has a huge personal collection of mechanical puzzles and books of brain teasers. He is mos ...
's ''Notes on Rubik's "Magic Cube"'' (1980) and Patrick Bossert's ''You Can Do the Cube'' (1981).
At one stage in 1981, three of the top ten best selling books in the US were books on solving Rubik's Cube, 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. In 1981, the
Museum of Modern Art
The Museum of Modern Art (MoMA) is an art museum located in Midtown Manhattan, New York City, on 53rd Street between Fifth and Sixth Avenues.
It plays a major role in developing and collecting modern art, and is often identified as one of ...
in New York exhibited a Rubik's Cube, and at the
1982 World's Fair
The 1982 World's Fair, officially known as the Knoxville International Energy Exposition (KIEE) and simply as Energy Expo '82 and Expo '82, was an international exposition held in Knoxville, Tennessee, United States. Focused on energy and ele ...
in
Knoxville
Knoxville is a city in and the county seat of Knox County in the U.S. state of Tennessee. As of the 2020 United States census, Knoxville's population was 190,740, making it the largest city in the East Tennessee Grand Division and the state's ...
, Tennessee a six-foot Cube was put on display.
ABC Television ABC Television most commonly refers to:
*ABC Television Network of the American Broadcasting Company, United States, or
*ABC Television (Australian TV network), a division of the Australian Broadcasting Corporation, Australia
ABC Television or ABC ...
even developed a cartoon show called ''
Rubik, the Amazing Cube
''Rubik, the Amazing Cube'' is a 1983 half-hour Saturday morning animated series based on the puzzle created by Ernő Rubik, produced by Ruby-Spears Enterprises and broadcast as part of '' The Pac-Man/Rubik, the Amazing Cube Hour'' block on AB ...
''. In June 1982, the
First Rubik's Cube World Championship took place in
Budapest
Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...
and would become the only competition recognized as official until the championship was revived in 2003.
In October 1982, ''
The New York Times
''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid ...
'' reported that sales had fallen and that "the craze has died",
and by 1983 it was clear that sales had plummeted.
However, in some countries such as China and the USSR, the craze had started later and demand was still high because of a shortage of Cubes.
21st-century revival
Rubik's Cubes continued to be marketed and sold throughout the 1980s and 1990s,
but it was not until the early 2000s that interest in the Cube began increasing again.
In the US, sales doubled between 2001 and 2003, and ''
The Boston Globe
''The Boston Globe'' is an American daily newspaper founded and based in Boston, Massachusetts. The newspaper has won a total of 27 Pulitzer Prizes, and has a total circulation of close to 300,000 print and digital subscribers. ''The Boston Glob ...
'' remarked that it was "becoming cool to own a Cube again".
The 2003 World Rubik's Games Championship was the first speedcubing tournament since 1982.
It was held in
Toronto
Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the ancho ...
and was attended by 83 participants.
The tournament led to the formation of the World Cube Association in 2004.
Annual sales of Rubik branded cubes were said to have reached 15 million worldwide in 2008.
Part of the new appeal was ascribed to the advent of Internet video sites, such as YouTube, which allowed fans to share their solving strategies.
Following the expiration of Rubik's patent in 2000, other brands of cubes appeared, especially from Chinese companies.
Many of these Chinese branded cubes have been engineered for speed and are favoured by speedcubers.
On 27 October 2020,
Spin Master
Spin Master is a Canadian multinational toy and entertainment company that markets consumer products for children. Its brands include '' Bakugan'', Gund, Etch A Sketch, Meccano/ Erector, Air Hogs, ''PAW Patrol'', Aquadoodle, Tech Deck, Hatch ...
said it will pay $50 million to buy the Rubik's Cube brand.
Imitations
Taking advantage of an initial shortage of cubes, many imitations and variations appeared, many of which may have violated one or more patents. In 2000 the patents expired, and since then, many Chinese companies have produced copies of, modifications and improvements upon the Rubik and
V-Cube designs.
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 2×2×2 Pocket Cube infringed Nichols's patent, but overturned the judgment on Rubik's 3×3×3 Cube.
Even while Rubik's patent application was being processed, Terutoshi Ishigi, a self-taught engineer and ironworks owner near Tokyo, filed for a Japanese patent for a nearly identical mechanism, which was granted in 1976 (Japanese patent publication JP55-008192). Until 1999, when an amended
Japanese patent law
Japanese patent law is based on the first-to-file principle and is mainly given force by the of Japan. Article 2 defines an invention as "the highly advanced creation of technical ideas utilizing the law of nature".
English translation
The de ...
was enforced, Japan's patent office granted Japanese patents for non-disclosed technology within Japan without requiring worldwide
novelty
Novelty (derived from Latin word ''novus'' for "new") is the quality of being new, or following from that, of being striking, original or unusual. Novelty may be the shared experience of a new cultural phenomenon or the subjective perception of an ...
. Hence, Ishigi's patent is generally accepted as an independent reinvention at that time.
Rubik applied for more patents in 1980, including another Hungarian patent on 28 October. In the United States, Rubik was granted on 29 March 1983, for the Cube. This patent expired in 2000.
Trademarks
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
The Skewb () is a combination puzzle and a mechanical puzzle in the style of the Rubik's Cube. It was invented by Tony Durham and marketed by Uwe Mèffert. Although it is cubical in shape, it differs from Rubik's construction in that its axes of ...
,
Pyraminx
The 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 Ernő Rubik, and introduced by Tomy Toys of Japan (then the 3rd largest toy comp ...
or
Impossiball.
On 10 November 2016, Rubik's Cube lost a ten-year battle over a key trademark issue. The
European Union
The European Union (EU) is a supranational political and economic union of member states that are located primarily in Europe. The union has a total area of and an estimated total population of about 447million. The EU has often been des ...
's highest court, the
Court of Justice, ruled that the puzzle's shape was not sufficient to grant it trademark protection.
Mechanics
![Scrumbled Rubik's Cube](https://upload.wikimedia.org/wikipedia/commons/b/b0/Scrumbled_Rubik%27s_Cube.jpg)
A standard Rubik's Cube measures on each side. The puzzle consists of 26 unique miniature cubes, also known as "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. Hence, there are 21 pieces: a single core piece consisting of three intersecting axes holding the six centre squares in place but letting them rotate, and 20 smaller plastic pieces that 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. However, Old Cubes made by the Rubik's Brand Ltd. and from dollar stores do not have screws or springs, all they have is a plastic clip to keep the centre piece in place and freely rotate.
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 that show one coloured face, twelve edge pieces that show two coloured faces, and eight corner pieces that 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 by increments of 90 degrees, 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
Douglas Richard Hofstadter (born February 15, 1945) is an American scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, an ...
, 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.
Mathematics
The puzzle was originally advertised as having "over 3,000,000,000 (three
billion
Billion is a word for a large number, and it has two distinct definitions:
*1,000,000,000, i.e. one thousand million, or (ten to the ninth power), as defined on the short scale. This is its only current meaning in English.
* 1,000,000,000,000, i.e ...
) combinations but only one solution". Depending on how combinations are counted, the actual number is significantly higher.
Permutations
![Rubik's cube colors](https://upload.wikimedia.org/wikipedia/commons/9/9d/Rubik%27s_cube_colors.svg)
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
In mathematics, when ''X'' is a finite set with at least two elements, the permutations of ''X'' (i.e. the bijective functions from ''X'' to ''X'') fall into two classes of equal size: the even permutations and the odd permutations. If any total or ...
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.
:
which is approximately 43
quintillion
Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-Eng ...
.
[Counting the Permutations of the Rubik's Cube](_blank)
Scott Vaughen. Professor of Mathematics. Miami Dade College. To put this into perspective, if one had one standard-sized Rubik's Cube for each
permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...
, one could cover the Earth's surface 275 times, or stack them in a tower 261
light-year
A light-year, alternatively spelled light year, is a large unit of length used to express astronomical distances and is equivalent to about 9.46 trillion kilometers (), or 5.88 trillion miles ().One trillion here is taken to be 1012 ...
s 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
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
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
", 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.
Centre faces
The original Rubik's Cube had no orientation markings on the centre faces (although some carried the words "Rubik's Cube" on the centre square of the white 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
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...
or
playing card
A playing card is a piece of specially prepared card stock, heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic that is marked with distinguishing motifs. Often the front (face) and back of each card has a fi ...
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 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).
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).
Algorithms
In Rubik's cubers' parlance, a memorised sequence of moves that has a desired effect on the cube is called an "algorithm". This terminology is derived from the mathematical use of ''
algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...
'', 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. Towards the end of the solution, the more specific (and usually 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
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory.
Group theory
The commutator of two elements, a ...
'' structure, namely ''XYX''
−1''Y''
−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".
In addition, the fact that there are well-defined
subgroup
In group theory, a branch of mathematics, given a group ''G'' under a binary operation ∗, a subset ''H'' of ''G'' is called a subgroup of ''G'' if ''H'' also forms a group under the operation ∗. More precisely, ''H'' is a subgroup ...
s 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 that 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.
Solutions
Move notation
Many 3×3×3 Rubik's Cube enthusiasts use a notation developed by
David Singmaster
David Breyer Singmaster (born 1938) is an emeritus professor of mathematics at London South Bank University, England. A self-described metagrobologist, he has a huge personal collection of mechanical puzzles and books of brain teasers. He is mos ...
to denote a sequence of moves, referred to as "Singmaster notation".
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
* ''f'' (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
The prime symbol , double prime symbol , triple prime symbol , and quadruple prime symbol are used to designate units and for other purposes in mathematics, science, linguistics and music.
Although the characters differ little in appearance fr ...
( ′ ) 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'' is primed, it is an indication that the cube must be rotated in the opposite direction. When ''x'', ''y'', or ''z'' is squared, the cube must be rotated 180 degrees.
The most common deviation from Singmaster notation, and in fact the current official standard, is to use "w", for "wide", instead of lowercase letters to represent moves of two layers; thus, a move of ''Rw'' is equivalent to one of ''r''.
For methods using middle-layer turns (particularly corners-first methods), there is a generally accepted "MES" extension to the notation where letters ''M'', ''E'', and ''S'' denote middle layer turns. It was used e.g. in Marc Waterman's Algorithm.
* ''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'')
' ''l''2 ''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, 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′ U L′ U′ R U2 in Singmaster notation). The 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 the 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.
Period of move sequences
The repetition of any given move sequence on a cube which is initially in solved state will eventually return the cube back to its solved state: the smallest number of iterations required is the period of the sequence. For example, the 180-degree turn of any side has period 2 (e.g. ''
2''); the 90-degree turn of any side has period 4 (e.g. ''
4''). The maximum period for a move sequence is 1260:
for example, allowing for full rotations, ''
1260'' or ''
1260'' or ''
1260''; not allowing for rotations, ''
1260'', or ''
1260'', or ''
1260''; only allowing for clockwise quarter turns, ''
1260'', or ''
1260'', or ''
1260''; only allowing for lateral clockwise quarter turns, ''
1260'', or ''
1260'', or ''
1260''.
Optimal solutions
![1982 expedition to Tartu Ülikool 350 (23)](https://upload.wikimedia.org/wikipedia/commons/9/97/1982_expedition_to_Tartu_%C3%9Clikool_350_%2823%29.jpg)
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
David Breyer Singmaster (born 1938) is an emeritus professor of mathematics at London South Bank University, England. A self-described metagrobologist, he has a huge personal collection of mechanical puzzles and books of brain teasers. He is mos ...
first published his solution in the book ''Notes on Rubik's "Magic Cube"'' in 1981.
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". In 2007, Daniel Kunkle and Gene Cooperman used computer search methods to demonstrate that any 3×3×3 Rubik's Cube configuration can be solved in 26 moves or fewer.
In 2008, Tomas Rokicki lowered that number to 22 moves, and in July 2010, a team of researchers including Rokicki, working with Google, proved that the so-called "
God's number
God'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 fe ...
" for Rubik's Cube is 20.
This means that all initial configurations can be solved in 20 moves or less, and some (in fact millions) require 20.
[ 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.
]
Speedcubing methods
A solution commonly used by speedcubers was developed by Jessica Fridrich
Jessica Fridrich is a professor at Binghamton University, who specializes in data hiding applications in digital imagery. She is also known for documenting and popularizing the CFOP method (sometimes referred to as the "Fridrich method"), one o ...
. 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
Lars Erik Petrus (born 4 November 1960 in Luleå in Sweden) is an accomplished speedcuber.
In 1982, he became the national champion of Sweden, and went on to finish fourth overall at the first official Rubik's Cube World Championships held in Buda ...
. 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.
The Roux Method, developed by Gilles Roux
Gilles Roux (born 20 January 1971) is a French speedcuber primarily known for inventing a 3x3x3 Rubik's Cube method, the Roux Method, and achieving fast times with it.
WCA
Gilles was a member of the World Cube Association Board from October 2 ...
, 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.
Beginners' methods
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.
In 1981, thirteen-year-old Patrick Bossert developed a solution for solving the cube, along with a graphical notation, designed to be easily understood by novices. It was subsequently published as ''You Can Do The Cube'' and became a best-seller.
In 1997, Denny Dedmore published a solution described using diagrammatic icons representing the moves to be made, instead of the usual notation.
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.
Rubik's Cube solver program
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.
Competitions and records
Speedcubing competitions
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
Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the States of Germany, German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the List of cities in Germany by popu ...
on 13 March 1981. The contest used standardised scrambling and fixed inspection times, and the winners were Ronald Brinkmann and Jury Fröschl with times of 38.0 seconds. The first world championship was the 1982 World Rubik's Cube Championship
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 Ameri ...
held in Budapest
Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...
on 5 June 1982, which was won by Minh Thai
Minh Thai (born 1965 as Thái Minh) is a Vietnamese-American speedcuber. He was a sixteen-year-old Eagles Rock High School student from Los Angeles when he won the first world championship on June 5, 1982 in Budapest by solving a Rubik's Cube
...
, a Vietnamese student from Los Angeles, with a time of 22.95 seconds.
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.
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:
* Blindfolded solving
* Multiple Blindfolded solving, or "multi-blind", in which the contestant solves any number of cubes blindfolded in a row
* Solving the cube using a single hand, or one handed solving
* Solving the cube in the fewest possible moves
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.
Records
Competition records
* 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.
* Average time: The world record average of the middle three of five solve times (which excludes the fastest and slowest) is 4.86 seconds, set by Tymon Kolasiński
Tymon is a surname and male given name. Notable people with this name include:
Surname
* Angelle Tymon (born 1983), American broadcast journalist and game show host
* Josh Tymon (born 1999), English football player
Given name
* Tymon Dogg, Engl ...
of Poland on 30 July 2022 at Cube4Fun In Warsaw 2022
* One-handed solving: The world record fastest one-handed solve is 6.82 seconds, set by Max Park
Max Park is an American Rubik's Cube speedsolver who is currently tied with Tymon Kolasiński of Poland for the world record average of five 3×3×3 solves (by WCA standards), 4.86 seconds, set on 24 September 2022. Park first held this record ...
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 8.65 seconds, set by Patrick Ponce of the United States on 1 May 2022 at Stevenage Spring 2022 .
* 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. Since 1 January 2020, 3x3x3 With Feet is no longer an event recognized by the WCA, and no results are being accepted.
* Blindfold solving: The world record fastest Rubik's Cube solve blindfolded is 14.61 seconds (including memorization), set by Tommy Cherry of the United States on 13 March 2022 at Florida Big & Blind & Time 2022. The world record mean of three for blindfold solving is 15.24 seconds, also set by Tommy Cherry on 12 December 2021 at Florida Fall 2021.
* Multiple blindfold solving: The world record for multiple Rubik's Cube solving blindfolded is 62 out of 65 cubes in 57 minutes and 47 seconds, set by Graham Siggins of the United States on 26 June 2022 at Blind Is Back LA 2022. Siggins inspected 60 cubes, donned a blindfold, and solved successfully 59 of them, all under the time limit of one hour.
* 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 21.00, set by Cale Schoon of the United States on 19 January 2020 at North Star Cubing Challenge 2020.
Other records
* 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.
* Highest order physical ''n×n×n'' cube solving: Jeremy Smith solved a 17x17x17 in 45 minutes and 59.40 seconds.
* 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.
* Group solving (30 minutes): On 21 November 2012, at the O2 Arena O2 Arena may refer to:
*The O2 Arena (London)
*O2 Arena (Prague)
*The 3Arena
The 3Arena (originally The O2) is an indoor amphitheatre located at North Wall Quay in the Dublin Docklands in Dublin, Ireland. The venue opened as The O2 on 16 Decemb ...
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.
:On 4 November 2012, 3248 people, mainly students of the College of Engineering Pune
COEP Technological University, is A Unitary Public University of Government of Maharashtra, situated in Pune, Maharashtra, India. Established in 1854, it is the 2nd oldest engineering college in India, after IIT Roorkee (1847). The students and ...
, successfully solved Rubik's cube in 30 minutes on college ground. The successful attempt is recorded in the Limca Book of Records
The ''Limca Book of Records'' is an annual reference book published in India documenting world records held by Indians. The records are further categorized into education, literature, agriculture, medical science, business, sports, nature, advent ...
. The college will submit the relevant data, witness statements and video of the event to Guinness authorities.
Top 10 solvers by single solve
Top 10 solvers by average of 5 solves
Variations
File:Rubik's Cube variants.jpg, 250px, alt=Rubik's Cube Variants, Variations of Rubik's Cubes. Top row: V-Cube 7
The V-Cube 7 is a combination puzzle in the form of a 7×7×7 cube. The first mass-produced 7×7×7 was invented by Panagiotis Verdes and is produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a n ...
, Professor's Cube
The 5x5 Rubik's Cube (also known as the Professor's Cube) is a 5×5×5 version of the original Rubik's Cube. It has qualities in common with both the 3×3×3 Rubik's Cube and the 4×4×4 4x4 Rubik's Cube, and solution strategies for both can be a ...
, V-Cube 6
The V-Cube 6 is a 6×6×6 version of the original Rubik's Cube. The first mass-produced 6×6×6 was invented by Panagiotis Verdes and is produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a numbe ...
. Bottom row: Rubik's Revenge
The 4x4 Rubik's Cube (also known as the Rubik's Revenge) is a 4×4×4 version of the Rubik's Cube. It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the Sebestény Cube until a somewhat last-minute decision change ...
, original Rubik's Cube, Pocket Cube
The 2x2 Rubik's Cube (also known as the Pocket Cube or Mini Cube) is a 2×2×2 version of the Rubik's Cube. The cube consists of 8 pieces, all corners.
History
In March 1970, Larry D. Nichols invented a 2×2×2 "Puzzle with Pieces Rotatable in ...
. Clicking on a cube in the picture will redirect to the respective cube's page. (Note:scrambled states)
default none
poly 964 370 1082 448 1065 545 970 622 865 545 875 445 Pocket Cube
The 2x2 Rubik's Cube (also known as the Pocket Cube or Mini Cube) is a 2×2×2 version of the Rubik's Cube. The cube consists of 8 pieces, all corners.
History
In March 1970, Larry D. Nichols invented a 2×2×2 "Puzzle with Pieces Rotatable in ...
poly 620 370 844 363 862 536 850 680 628 682 Rubik's Cube
The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik t ...
poly 455 280 570 440 580 605 355 705 255 530 220 363 Rubik's Revenge
The 4x4 Rubik's Cube (also known as the Rubik's Revenge) is a 4×4×4 version of the Rubik's Cube. It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the Sebestény Cube until a somewhat last-minute decision change ...
poly 540 75 780 90 780 225 760 360 620 365 605 420 560 420 505 340 500 235 Professor's Cube
The 5x5 Rubik's Cube (also known as the Professor's Cube) is a 5×5×5 version of the original Rubik's Cube. It has qualities in common with both the 3×3×3 Rubik's Cube and the 4×4×4 4x4 Rubik's Cube, and solution strategies for both can be a ...
poly 890 50 1125 90 1065 420 1040 420 965 365 930 390 850 380 845 365 830 360 840 205 V-Cube 6
The V-Cube 6 is a 6×6×6 version of the original Rubik's Cube. The first mass-produced 6×6×6 was invented by Panagiotis Verdes and is produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a numbe ...
poly 255 50 320 90 405 225 420 290 210 360 230 460 210 465 150 410 90 320 60 240 45 155 120 100 190 70 V-Cube 7
The V-Cube 7 is a combination puzzle in the form of a 7×7×7 cube. The first mass-produced 7×7×7 was invented by Panagiotis Verdes and is produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a n ...
There are many different variations of Rubik's Cubes. The most common class of variants changes the "order" of the cube, defined by the number of layers in each dimension or equivalently by the number of pieces along each edge (including corners). 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) are the most well known, as they are all available under the official Rubik's brand. The WCA WCA may refer to:
Schools
* Waterbury Career Academy, public high school in Waterbury, Connecticut
* Wake Christian Academy, private Christian school in Raleigh, North Carolina
* Washington Christian Academy, private Christian school in Silver Spr ...
sanctions speedsolving competitions for cube orders up to 7x7x7. These "big cubes" represent about the limit of practicality for the purpose of competitive speedsolving, as the cubes become increasingly ungainly and prone to mechanical failure (such as "popping", where one or more pieces become dislodged from the puzzle), and average solve times increase quadratically with each larger order, in proportion to the number of total "facelets" of the cube.
Even larger cubes based on the V-Cube patents are commercially available to the mass-market from non-licensed manufacturers, most of them Chinese firms who also produce popular cubes designed for speed-solving. The 17×17×17 "Over The Top" cube (available late 2011) was until December 2017 the largest commercially sold cube, and the most expensive, costing over US$2000. A mass-produced 17×17×17 was later introduced by the Chinese manufacturer YuXin. A working design for a 22×22×22 cube exists and was demonstrated in January 2016, and a 33×33×33 in December 2017, though designs this large are not currently mass-produced. Chinese manufacturer ShengShou has been producing cubes in all sizes from 2×2×2 to 15×15×15 (as of May 2020), and have also come out with a 17×17×17. The largest currently mass-produced cube is 21x21x21, made by MoYu beginning in 2021, and costing between $1100 and $1600.
There are many variations of the original cube, some of which are made by Rubik. The mechanical products include Rubik's Magic, 360, and Twist. Also, electronics like Rubik's Revolution and Slide, were also inspired by the original. One of the 3×3×3 Cube variants is Rubik's TouchCube. Sliding a finger across its faces causes its patterns of coloured lights to rotate the same way they would on a mechanical cube. The TouchCube also has buttons for hints and self-solving, and it includes a charging stand. The TouchCube was introduced at the American International Toy Fair
The North American International Toy Fair (formerly the American International Toy Fair and also known as Toy Fair New York) is an annual toy industry trade show held in mid-February in New York City's Jacob K. Javits Convention Center and at t ...
in New York on 15 February 2009.
The Cube has inspired an entire category of similar puzzles, commonly referred to as ''twisty puzzles
A combination puzzle, also known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations. Many such puzzles are mechanical puzzles of polyhedral ...
'', which includes the cubes of different sizes mentioned above, as well as various other geometric shapes. Some such shapes include the tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...
(Pyraminx
The 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 Ernő Rubik, and introduced by Tomy Toys of Japan (then the 3rd largest toy comp ...
), the octahedron
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
(Skewb Diamond
The Skewb Diamond is an octahedron-shaped combination puzzle similar to the Rubik's Cube. It has 14 movable pieces which can be rearranged in a total of 138,240 possible combinations. This puzzle is the dual polyhedron of the Skewb. It was inven ...
), the dodecahedron
In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon ...
(Megaminx
The Megaminx or Mégaminx (, ) is a dodecahedron-shaped 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.
History
The Megaminx, or Magic Dodecahedron, ...
), and the icosahedron
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
(Dogic
The Dogic () is an icosahedron-shaped puzzle like the Rubik's Cube. The 5 triangles meeting at its tips may be rotated, or 5 entire faces (including the triangles) around the tip may be rotated. It has a total of 80 movable pieces to rearrange, c ...
). There are also puzzles that change shape such as Rubik's Snake
A Rubik's Snake (also Rubik's Twist, Rubik's Transformable Snake, Rubik’s Snake Puzzle) is a toy with 24 wedges that are right isosceles triangular prisms. The wedges are connected by screw, spring bolts, so that they can be twisted, but ...
and the Square One
Square One may refer to:
Film and TV
* '' Square One: Michael Jackson'', a 2019 investigative documentary about the first allegations of child sexual abuse brought by the Chandler family
*''Square One Television'', a children's television series ...
.
In 2011, Guinness World Records awarded the "largest order Rubiks magic cube" to a 17×17×17 cube, made by Oskar van Deventer
Oskar van Deventer (born 1965) is a Dutch puzzle maker. He prototypes puzzles using 3D printing. His work combines mathematics, physics, and design, and he collaborates at academic institutions. Many of his combination puzzles are in mass produc ...
. 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. On 8 April 2018, Grégoire Pfennig announced another world record, the 2x2x50 cube. 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 Kepler–Poinsot polyhedra, such as Alexander's Star
Alexander's Star is a puzzle similar to the Rubik's Cube, in the shape of a great dodecahedron.
History
Alexander's Star was invented by Adam Alexander, an American mathematician, in 1982. It was patented on 26 March 1985, with US patent n ...
(a great dodecahedron
In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of . It is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces (six pairs of parallel pentagon ...
). Grégoire Pfennig has also created at least one puzzle in the shape of a small stellated dodecahedron
In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol . It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeti ...
.
Custom-built puzzles
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. 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 "shape mods", 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.
Rubik's Cube software
Puzzle
A puzzle is a game, Problem solving, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together (Disentanglement puzzle, or take them apart) in a logical way, in order to arrive at th ...
s, like Rubik's Cube, can be simulated by computer software
Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work.
At the lowest programming level, executable code consists ...
to provide very large puzzles that are impractical to build, as well as virtual puzzles that cannot be physically built, such as many higher dimensional analogues of the Rubik's Cube.
File:4-cube 2^4 highlighted.png, A 2×2×2×2 in MagicCube4D
File:4d cube.png, A 3×3×3×3 in MagicCube4D
File:4-cube 4^4.png, A 4×4×4×4 in MagicCube4D
File:5D Rubik's Cube.png, A 3×3×3×3×3 in MagicCube5D
Chrome Cube Lab
Google has released the Chrome Cube Lab in association with Ernő Rubik
Ernő Rubik (; born 13 July 1944) commonly known by his nickname, "Little Man", is a Hungarian inventor, architect and professor of architecture. He is best known for the invention of mechanical puzzles including the Rubik's Cube (1974), Rubi ...
. The site has various interactive objects based on Rubik's Cube. Customised versions of Rubik's Cube can be created and uploaded.
See also
* Mirror blocks
* n-dimensional sequential move puzzle
The Rubik's Cube is the original and best known of the three-dimensional sequential move puzzles. There have been many virtual implementations of this puzzle in software. It is a natural extension to create sequential move puzzles in more than ...
* Rubik's Domino
* Rubik's family cubes of all sizes
* Spatial ability
Spatial ability or visuo-spatial ability is the capacity to understand, reason, and remember the visual and spatial relations among objects or space.
Visual-spatial abilities are used for everyday use from navigation, understanding or fixing equi ...
* V-Cube 8
The V-Cube 8 is an 8×8×8 version of the Rubik's Cube. Unlike the original puzzle (but like the 4×4×4 and 6×6×6 cubes), it has no fixed facets: the center facets (36 per face) are free to move to different positions. The design was cover ...
(8×8×8)
References
Further reading
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External links
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Safecracker Method: Solving Rubik's Cube with just 10 Numbers
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World Cube Association
List of related puzzles and solutions
Complete disassembly of a 3^3 classic Rubik's cube
Speedsolving Wiki
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Educational toys
Logic puzzles
Mechanical puzzle cubes
Novelty items
Single-player games
1980s toys
1980s fads and trends
Hungarian inventions
Spiel des Jahres winners
Ideal Toy Company
Products introduced in 1977
1970s toys