Rubik's Cube

The Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer. Rubik's Cube won the 1980 German Game of the Year special award for Best Puzzle. As of January 2009, 350 million cubes had been sold worldwide, making it the world's bestselling puzzle game and bestselling toy.

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. In models as of 1988, white is opposite yellow, blue is opposite green, and orange is opposite red, and the red, white, and blue are arranged in that order in a clockwise arrangement. On early cubes, the position of the colours varied from cube to cube. An internal pivot mechanism enables each face to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must be returned to have only one colour. Similar puzzles have now been produced with various numbers of sides, dimensions, and stickers, not all of them by Rubik.

Although the Rubik's Cube reached its height of mainstream popularity in the 1980s, it is still widely known and used. Many speedcubers continue to practice it and similar puzzles; they also compete for the fastest times in various categories. Since 2003, the World Cube Association, the international governing body of the Rubik's Cube, has organised competitions worldwide and recognises world records.

Precursors

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

In March 1970, Larry D. Nichols invented a 2×2×2 "Puzzle with Pieces Rotatable in Groups" and filed a Canadian patent application for it. Nichols's cube was held together by magnets. Nichols was granted U.S. Patent 3,655,201 on 11 April 1972, two years before Rubik invented his Cube.

On 9 April 1970, Frank Fox applied to patent an "amusement device", a type of sliding puzzle on a spherical surface with "at least two 3×3 arrays" intended to be used for the game of noughts and crosses. He received his UK patent on 16 January 1974.

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

In the mid-1970s, Ernő Rubik worked at the Department of Interior Design at the Academy of Applied Arts and Crafts in Budapest. 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 in Hungary for his "Magic Cube" (Bűvös kocka in Hungarian) 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 toy shops. Magic Cube was held together with interlocking plastic pieces that prevented the puzzle being easily pulled apart, unlike the magnets in Nichols's design. With Ernő Rubik's permission, businessman Tibor Laczi took a Cube to Germany's Nuremberg Toy Fair in February 1979 in an attempt to popularise it. It was noticed by Seven Towns founder Tom Kremer, and they signed a deal with Ideal Toys in September 1979 to release the Magic Cube worldwide.[18] Ideal wanted at least a recognisable name to trademark; that arrangement put Rubik in the spotlight because the Magic Cube was renamed after its inventor in 1980. The puzzle made its international debut at the toy fairs of London, Paris, Nuremberg, and New York in January and February 1980.

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

See also: Rubik's Cube in popular culture

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 championship organised by the Guinness Book of World Records was held in Munich, and a Rubik's Cube was depicted on the front cover of Scientific American that same month. In June 1981, The Washington Post reported that Rubik's Cube is "a puzzle that's moving like fast food right now ... this year's Hoola Hoop or Bongo Board", and by September 1981, New Scientist noted that the cube had "captivated the attention of children of ages from 7 to 70 all over the world this summer."

As most people could solve only one or two sides, numerous books were published including David Singmaster's Notes on Rubik's "Magic Cube" (1980) and Patrick Bossert's You Can Do the Cube (1981).At one stage in 1981, three of the top ten best selling books in the US were books on solving Rubik's Cube,[28] and the best-selling book of 1981 was James G. Nourse's The Simple Solution to Rubik's Cube which sold over 6 million copies. In 1981, the Museum of Modern Art in New York exhibited a Rubik's Cube, and at the 1982 World's Fair in Knoxville, Tennessee a six-foot Cube was put on display. ABC Television even developed a cartoon show called Rubik, the Amazing Cube. In June 1982, the First Rubik's Cube World Championship took place in Budapest and would become the only competition recognized as official until the championship was revived in 2003.

In October 1982, The New York Times reported that sales had fallen and that "the craze has died", and by 1983 it was clear that sales had plummeted. However, in some Communist countries, such as China and the USSR, the craze had started later and demand was still high because of a shortage of Cubes.

Rubik's Cubes continued to be sold throughout the 1980s and 1990s, but it wasn't until the early 2000s that interest in the cube began to grow again. In the US, sales doubled between 2001 and 2003, with The Boston Globe noting that it "became cool to own a Cube again". The 2003 Rubik's World Championship was the first speedcubing tournament since 1982. It was held in Toronto and was attended by 83 participants[35]. The tournament led to the creation of the World Cube Association in 2004. In 2008, the annual sales of Rubik's Cubes worldwide are reported to have reached 15 million pieces. Part of the new appeal has been attributed to the emergence of video sites on the Internet such as YouTube, which allowed fans to share their solving strategies. After the Rubik's patent expired in 2000, other brands of cubes appeared, especially from Chinese companies.[38] Many of these Chinese branded cubes were designed for speed and are popular with speedcubers. On October 27, 2020, Spin Master stated that it would pay $50 million to purchase the Rubik's Cube brand.

Rubik's Brand Ltd. also holds the registered trademarks for the word "Rubik" and "Rubik's" and for the 2D and 3D visualisations of the puzzle. The trademarks have been upheld by a ruling of the General Court of the European Union on 25 November 2014 in a successful defence against a German toy manufacturer seeking to invalidate them. However, European toy manufacturers are allowed to create differently shaped puzzles that have a similar rotating or twisting functionality of component parts such as for example Skewb, Pyraminx or Impossiball.

On 10 November 2016, Rubik's Cube lost a ten-year battle over a key trademark issue. The European Union's highest court, the Court of Justice, ruled that the puzzle's shape was not sufficient to grant it trademark protection.

A standard Rubik's Cube measures 5.6 centimetres (2+1⁄4 in) 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.[48]

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, 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.

The original (3×3×3) Rubik's Cube has eight corners and twelve edges. There are 8! (40,320) ways to arrange the corner cubes. Each corner has three possible orientations, although only seven (of eight) can be oriented independently; the orientation of the eighth (final) corner depends on the preceding seven, giving 37 (2,187) possibilities. There are 12!/2 (239,500,800) ways to arrange the edges, restricted from 12! because edges must be in an even permutation exactly when the corners are. (When arrangements of centres are also permitted, as described below, the rule is that the combined arrangement of corners, edges, and centres must be an even permutation.) Eleven edges can be flipped independently, with the flip of the twelfth depending on the preceding ones, giving 211 (2,048) possibilities.[50]

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

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

The preceding figure is limited to permutations that can be reached solely by turning the sides of the cube. If one considers permutations reached through disassembly of the cube, the number becomes twelve times larger:

{\displaystyle {8!\times 3^{8}\times 12!\times 2^{12}}=519{,}024{,}039{,}293{,}878{,}272{,}000}{\displaystyle {8!\times 3^{8}\times 12!\times 2^{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 one in twelve of these are actually solvable. This is because there is no sequence of moves that will swap a single pair of pieces or rotate a single corner or edge cube. Thus, there are 12 possible sets of reachable configurations, sometimes called "universes" or "orbits", into which the cube can be placed by dismantling and reassembling it.

The preceding numbers assume the centre faces are in a fixed position. If one considers turning the whole cube to be a different permutation, then each of the preceding numbers should be multiplied by 24. A chosen colour can be on one of six sides, and then one of the adjacent colours can be in one of four positions; this determines the positions of all remaining colours.

The original Rubik's Cube had no orientation markings on the centre faces (although some carried the words "Rubik's Cube" on the centre square of the white face), and therefore solving it does not require any attention to orienting those faces correctly. However, with marker pens, one could, for example, mark the central squares of an unscrambled Cube with four coloured marks on each edge, each corresponding to the colour of the adjacent face; a cube marked in this way is referred to as a "supercube". Some Cubes have also been produced commercially with markings on all of the squares, such as the Lo Shu magic square or playing card suits. Cubes have also been produced where the nine stickers on a face are used to make a single larger picture, and centre orientation matters on these as well. Thus one can nominally solve a Cube yet have the markings on the centres rotated; it then becomes an additional test to solve the centres as well.

Marking Rubik's Cube's centres increases its difficulty, because this expands the set of distinguishable possible configurations. There are 46/2 (2,048) ways to orient the centres since an even permutation of the corners implies an even number of quarter turns of centres as well. In particular, when the Cube is unscrambled apart from the orientations of the central squares, there will always be an even number of centre squares requiring a quarter turn. Thus orientations of centres increases the total number of possible Cube permutations from 43,252,003,274,489,856,000 (4.3×1019) to 88,580,102,706,155,225,088,000 (8.9×1022).[52]

When turning a cube over is considered to be a change in permutation then we must also count arrangements of the centre faces. Nominally there are 6! ways to arrange the six centre faces of the cube, but only 24 of these are achievable without disassembly of the cube. When the orientations of centres are also counted, as above, this increases the total number of possible Cube permutations from 88,580,102,706,155,225,088,000 (8.9×1022) to 2,125,922,464,947,725,402,112,000 (2.1×1024).

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

Many algorithms are designed to transform only a small part of the cube without interfering with other parts that have already been solved so that they can be applied repeatedly to different parts of the cube until the whole is solved. For example, there are well-known algorithms for cycling three corners without changing the rest of the puzzle or flipping the orientation of a pair of edges while leaving the others intact.

Some algorithms do have a certain desired effect on the cube (for example, swapping two corners) but may also have the side-effect of changing other parts of the cube (such as permuting some edges). Such algorithms are often simpler than the ones without side effects and are employed early on in the solution when most of the puzzle has not yet been solved and the side effects are not important. Most are long and difficult to memorise. Towards the end of the solution, the more specific (and usually more complicated) algorithms are used instead.