Rubiks Cube

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Rubik's Cube™ is a mechanical puzzle invented by a 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. The challenge is to be able to return the cube to its original state with all sides consisting of stickers of the same colour, from any position.

A Rubik's Cube consists of 21 plastic pieces which fit together to form a cube. Standard cubes measure approximately 2 1/8 inches (5.4 cm) on each side. The cube can quite easily be taken apart, although this is not the challenge. The cube is divided into smaller cubes, called cubies. The pieces are assembled such that the entire cube appears to be a 3 x 3 x 3 block of cubies. The 6 pieces which are in the center of each face of the cube are connected by the unseen middle piece of the cube to provide a structure for the other pieces to fit into and turn around. There are 12 edge pieces which have two colored stickers, and 8 corner pieces which have three colored stickers. The colors of the stickers are traditionally red opposite orange, yellow opposite white, and green opposite blue. The location of the cubies relative to one another can be altered by twisting an outer third of the cube 90 degrees, 180 degrees or 270 degrees.

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

Countless general solutions for the Rubik's Cube have been discovered independently (see How to solve the Rubiks 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. A Rubik's Cube can have 43,252,003,274,489,856,000 different positions (~4.3 x 1019), 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. Many mathematicians are interested in the Rubik's Cube because it is a tangible representation of a mathematical group.

Competitions have been held to determine who can solve the Rubik's Cube in the shortest amount of time. The first such competition was won by Minh Thai of Vietnam, with a time of 22.95 seconds. However, many individuals have recorded faster 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 in North America. 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. "Rubik's Cube" is a trademark of Ideal Toy Corporation. Ernö Rubik holds patents related to the cube's mechanism.

References:

  • "Handbook of Cubik Math" by Alexander H. Frey, Jr. and David Singmaster
  • "Notes on Rubik's Magic Cube" by David Singmaster

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