Rubik's Cube

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Rubik's Cube in solved state.

Rubik's Cube in scrambled state.

Rubik's Cube is a mechanical puzzle invented in 1974 by the Hungarian sculptor and professor of architecture Ernő Rubik. It is a plastic cube comprising 26 smaller cubes that rotate around a typically unseen kernel. Each of the nine visible facets on a side of the Rubik's Cube exhibits one of six colors. When the puzzle is solved, each side of the Rubik's Cube is a different color, but the rotation of each face allows the smaller cubes to be rearranged in many different ways. The challenge of the puzzle is to return the cube to its original state, in which each face of the cube consists of nine squares of a similar color.

The Rubik's Cube reached the height of its popularity in the early 1980s, and has since become a pop culture icon associated with the decade. It is said to be the world's biggest selling toy, with 300,000,000 Rubik's Cubes and imitations sold worldwide. ^[1]

1 History
- 1.1 Conception and development
- 1.2 Popularity
2 Workings
- 2.1 Permutations
- 2.2 Center faces
3 Solutions
4 Competitions
5 Rubik's Cube in mathematics and science
6 See also
7 References
8 External links

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History

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Conception and development

The Rubik's Cube was invented in 1974 by Ernő Rubik, a Hungarian sculptor and professor of architecture with an interest in geometry and the study of 3D forms. Ernő obtained Hungarian patent HU170062 for the "Magic Cube" in 1975, but did not take out international patents. The first test batches of the product were produced in late 1977 and released to Budapest toy shops.

The Cube slowly grew in popularity throughout Hungary as word of mouth spread. Western academics also showed interest in it. In September 1979, a deal was reached with Ideal Toys to release the Magic Cube internationally. It made its international debut at the toy fairs of London, New York, Nuremberg, and Paris in early 1980. Ideal Toys renamed it "Rubik's Cube", and the first batch was exported from Hungary in May 1980.

"Rubik's Cube" is a trademark of Seven Towns Limited. Ideal Toys was somewhat reluctant to produce the toy for that reason, and indeed clones appeared almost immediately. In 1984, Ideal Toys lost a patent infringement suit by Larry Nichols for his patent US3655201. [2] Terutoshi Ishigi acquired Japanese patent JP55‒8192 for a nearly identical mechanism while Rubik's patent was being processed, but Ishigi is generally credited with an independent reinvention. [3] [4]

Ideal Toys published the Rubik's Cube Newsletter from 1982 to 1983.

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Popularity

The Rubik's Cube reached its height of popularity during the early 1980s. Over 100 million cubes were sold in the period from 1980 to 1982. [5] It won the BATR Toy of the Year award in 1980, and again in 1981. Many similar puzzles were released shortly after the Rubik's Cube, both from Rubik himself and from other sources, including the Rubik's Revenge, a 4×4×4 version of the Rubik's Cube. There are also 2×2×2 and 5×5×5 cubes (known as the Pocket Cube and the Rubik's Professor, respectively), and puzzles in other shapes, such as the Pyraminx, a tetrahedron.

In 1981, Patrick Bossert, a 12-year-old schoolboy from Britain, published his own solution in a book called You Can Do the Cube (ISBN 0140314830). The book sold over 1.5 million copies worldwide in 17 editions and became the number one book on both The Times and the New York Times bestseller lists for 1981.

At the height of the puzzle's popularity, separate sheets of colored stickers were sold so that frustrated or impatient people could restore their cube to its original appearance.

From 1983 to 1984, Hanna-Barbera produced 12 episodes of Rubik, The Amazing Cube, a Saturday morning cartoon based upon the toy, which aired on ABC as part of "The Pac-Man/Rubik, Amazing Cube Hour".

It has been suggested that the international appeal and export achievement of the Cube became one of the contributing factors in the reform and liberalization of the Hungarian economy between 1981 and 1985, which finally led to the move from communism to capitalism. [6], although some sociologists disagree.

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Workings

A standard cube measures approximately 2 1/8 inches (5.4 cm) on each side. The puzzle consists of the 26 unique miniature cubes ("cubies") on the surface. However, the center cube of each face is merely a single square facade; all are affixed to the core mechanisms. These provide structure for the other pieces to fit into and rotate around. So there are 21 pieces: a single core piece consisting of three intersecting axes holding the six center squares in place but letting them rotate, and 20 smaller plastic pieces which fit into it to form a cube. The cube can be taken apart without much difficulty, typically by prying an "edge cubie" away from a "center cubie" until it dislodges. It is a simple process to "solve" a cube in this manner, by reassembling the cube in a solved state; however, this is not the challenge.

There are 12 edge pieces which show two colored sides each, and 8 corner pieces which show three colors. Each piece shows a unique color combination, but not all combinations are realized (For example, there is no edge piece showing both white and yellow, if white and yellow are on opposite sides of the solved cube). The location of these cubes relative to one another can be altered by twisting an outer third of the cube 90 degrees, 180 degrees or 270 degrees; but the location of the colored sides relative to one another in the completed state of the puzzle cannot be altered: it is fixed by the relative positions of the center squares and the distribution of color combinations on edge and corner pieces. For most recent Cubes, the colors of the stickers are red opposite orange, yellow opposite white, and green opposite blue. However, there also exist Cubes with alternative color arrangements. These alternative Cubes have the yellow face opposite the green, and the blue face opposite the white (with red and orange opposite faces remaining unchanged).

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Permutations

A Rubik's Cube can have (8! × 3⁸⁻¹) × (12! × 2¹²⁻¹)/2 = 43,252,003,274,489,856,000 different positions (~4.3 × 10¹⁹), about 43 quintillion, but it is advertised only as having "billions" of positions, due to the general incomprehensibility of that number. Despite the vast number of positions, all cubes can be solved in 23 moves or fewer. [7]

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Center faces

Most Rubik's Cubes are sold without any markings on the center faces. This obscures the fact that the center faces can rotate independently. If you have a marker pen, you could, for example, mark the central squares of an unshuffled cube with four colored marks on each edge, each corresponding to the color of the adjacent square. Some cubes have also been commercially produced with markings on all of the squares, such as the Lo Shu magic square or playing card suits. You could scramble and then unscramble the cube but still leave the markings rotated.

Putting markings on the Rubik's cube increases the challenge of solving the cube, chiefly because it expands the set of distinguishable possible configurations. When the cube is unscrambled apart from the orientations of the central squares, there will always be an even number of squares requiring a quarter turn.

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Solutions

Rubik's Cube being solved.

Many general solutions for the Rubik's Cube have been discovered independently. The most popular method was developed by David Singmaster and published in the book Notes on Rubik's Magic Cube in 1980. This solution involves solving the cube layer by layer, in which one face is solved, followed by the middle row, and finally the last and bottom face. Other general solutions include "corners first" methods, or combinations of several other methods.

Speed cubing solutions have been developed for solving the Rubik's Cube as quickly as possible. The most common speed cubing solution was developed by Jessica Fridrich. It is a very efficient layer-by-layer method that requires a large number of algorithms, especially for orienting and permuting the last layer. Another well-known method was developed by Lars Petrus.

Solutions typically consist of a sequence of processes. A process, or algorithm as it's sometimes called, is a series of cube twists which accomplishes a particular goal. For instance, one process might switch the locations of three corner pieces, while leaving the rest of the pieces in their places. These sequences are performed in the appropriate order to solve the cube. Complete solutions can be found in any of the books listed in the bibliography, and most can be used to solve any cube in under five minutes. In addition, much research has been done on optimal solutions for Rubik's Cube.

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Competitions

Many speedcubing competitions have been held to determine who can solve the Rubik's Cube in the shortest amount of time. The first world championship was held in Budapest on June 5, 1982, and was won by Minh Thai, a Vietnamese student from Los Angeles with a time of 22.95 seconds. The official world record of 14.52 seconds (average of 5 cubes) was set on October 16, 2004 in Pasadena by Shotaro "Macky" Makisumi, a Japanese high school student living in California. This record is recognized by the World Cube Association, the official governing body which regulates events and records. Makisumi was an 8th-grade student at the time at the age of 14 participating in the Caltech 2004 Fall Tournament. He used to hold the official world record for fastest single solve, but his time of 12.11 seconds was defeated by the time of 11.75 seconds set by Jean Pons of France during the Dutch Open 2005.

Many individuals have recorded shorter times, but these records were not recognised due to lack of compliance with agreed-upon standards for timing and competing. Therefore only records set during official World Cube Association sanctioned tournaments are acknowledged.

In 2004, the World Cube Association established a new set of standards, with a special timing device called a Stackmat timer.

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Rubik's Cube in mathematics and science

The Rubik's Cube is of interest to many mathematicians, partly because it is a tangible representation of a mathematical group. Additionally, a parallel between Rubik's Cube and particle physics was noted by mathematician Solomon W. Golomb, and then extended and modified by Anthony E. Durham. Essentially, clockwise and counter-clockwise "twists" of corner cubies may be compared to the electric charges of quarks (+2/3 and −1/3) and antiquarks (−2/3 and +1/3). Feasible combinations of cube twists are paralleled by allowable combinations of quarks and antiquarks—both cube twist and the quark/antiquark charge must total to an integer. Combinations of two or three twisted corners may be compared to various hadrons. This, however, is not always feasible.

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References

^ Marshall, Ray. Squaring up to the Rubik challenge. icNewcastle. Retrieved August 15, 2005.
Handbook of Cubik Math by Alexander H. Frey, Jr. and David Singmaster
Notes on Rubik's 'Magic Cube' ISBN 0-89490-043-9 by David Singmaster
Metamagical Themas by Douglas R. Hofstadter contains two insightful chapters regarding Rubik's Cube and similar puzzles, originally published as articles in the March 1981 and July 1982 issues of Scientific American.
Four-Axis Puzzles by Anthony E. Durham.
Mathematics of the Rubik's Cube Design ISBN 0-80593-919-9 by Hana M. Bizek