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Rubik's Cube

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Rubik's Cube™ is a mechanical puzzle invented by the Hungarian professor Ernö Rubik[?] in the mid 1970s. It has been estimated that over 100,000,000 Rubik's Cubes or imitations have been sold worldwide.

A Rubik's Cube is a cubic block with its surface subdivided so that each face consists of nine squares. Each face can be rotated, giving the appearance of an entire slice of the block rotating upon itself. This gives the impression that the cube is made up of 27 smaller cubes (3 x 3 x 3). In its original state 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 is to be able to return the Cube to its original state from any position.


Warning: Wikipedia contains spoilers. Some of the remarks below might make it easier for the reader to solve this puzzle.

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 centre cube of each face is merely a single square facade; all six are affixed to the core mechanisms. These provide structure for the other pieces to fit into and turn around. So there are 21 pieces: a single core, of three intersecting axes holding the six centre 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 a "edge cubie" away from an "center cubie" until it dislodges. This is not the challenge.

There are 12 edge pieces which show two colored sides each, and 8 corner pieces which show three colours. Each piece shows a unique colour 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 cubies 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 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 and the distribution of colour combinations on edge and corner pieces. The colors of the stickers are traditionally red opposite orange, yellow opposite white, and green opposite blue.

Figure 1: A Rubik's cube (Image in the PD)

Figure 2: A Rubik's cube (Photo taken for Wikipedia)

Countless general solutions for the Rubik's Cube have been discovered independently (see How to solve the Rubik's Cube for one such solution). Solutions typically consist of a sequence of processes. A process is a series of cube twists which accomplishes a well-defined 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.

Patrick Bossert[?] a 12 year-old schoolboy from Britain, published his own solution in a book called You Can do The Cube. The book sold over 1.5 million copies world-wide in 17 editions and became the number one book on both The Times and the New York Times bestseller lists for 1981.

A Rubik's Cube can have (8!*38-1)*(12!*212-1)/2 = 43,252,003,274,489,856,000 different positions (~4.3 x 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, it has not been proven that any given position is more than 18 moves away from being solved.
It has been proven that every position can be solved in 22 moves or fewer; however, no general method for finding every such solution has been discovered (See Constructive proof[?].)

Many mathematicians are interested in the Rubik's Cube because it is a tangible representation of a mathematical group. Indeed, 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 counterclockwise "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 cubie twists are paralleled by allowable combinations of quarks and antiquarks—both cubie twist and the quark/antiquark charge must total to an integer. Combinations of two or three twisted corners may be compared to various hadrons.

Many 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 on 5 June 1982 in Budapest and was won by Minh Thai of Vietnam, with a time of 22.95 seconds. However, many individuals have recorded shorter times. There is no current official record, due partly to the lack of agreed-upon standards for timing competitors.

The Rubik's Cube reached its height of popularity during the early 1980s. 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 x 4 x 4 version of the Rubik's Cube. There are also 2 x 2 x 2 and 5 x 5 x 5 cubes, and puzzles in other shapes, such as the Pyraminx[?]™, a tetrahedron.

"Rubik's Cube" is a trademark of Ideal Toy Corporation. Ernö Rubik holds patents related to the cube's mechanism.


  • 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.

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