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Rubik's Cube

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Rubik's Cube in scrambled state.
Rubik's Cube in solved 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 which comes in four different versions, the 2X2 ("Pocket Cube"), the 3X3, the 4X4 ("Rubik's Revenge"), and the 5X5 ("Professor's Cube"). The 3X3 version has 9 square faces on each side, for a total area of 54 faces, and occupies the volume of 27 unit cubes. Typically the faces of the cube are covered by stickers in 6 colours, one for each side of the cube. When the puzzle is 'solved,' each side of the cube is a solid colour.

Originally known as the Magic Cube, it was remanufactured and renamed Rubik's Cube in 1980 and released in the May of that year. It is said to be the world's biggest selling toy, with some 300 million Rubik's Cubes and imitations sold worldwide. [1]

History

Conception and development

The Magic 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.

The progress of the Cube towards the toy shop shelves of the West was then briefly halted so that it could be remanufactured to Western World safety and packaging specifications. A lighter Cube was produced, and Ideal Toys 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.

Taking advantage of an initial shortage of Cubes, many cheap imitations appeared. In 1984, Ideal Toys lost a patent infringement suit by Larry Nichols for his patent US3655201. 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. [2] [3]

File:Rubiks cube newsletter.jpg
Ideal Toys published the Rubik's Cube Newsletter from 1982 to 1983.

Popularity

Over 100 million cubes were sold in the period from 1980 to 1982. [4] 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 England, 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 that year.

At the height of the puzzle's popularity, separate sheets of coloured 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. [5], although some sociologists disagree.

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 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 turning one side through a 45° angle and prying an "edge cubie" away from a "centre 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 coloured 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 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 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. For most recent Cubes, the colours of the stickers are red opposite orange, yellow opposite white, and green opposite blue. However, there also exist Cubes with alternative colour 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).

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 29 moves or fewer (see Optimal solutions for Rubik's Cube).

In fact, there are (8! × 38) × (12! × 212) = 519,024,039,293,878,272,000 (about 519 quintillion) possible arrangements of the pieces that make up the cube, but only one in 12 of these is actually reachable. This is because there is no sequence of moves that will swap a single pair or rotate a single corner or edge cubie. Thus there are twelve possible sets of reachable configurations, sometimes called "universes", into which the cube can be placed by dismantling and reassembling it.

Centre faces

The original and still official Rubik's Cube has no markings on the centre faces. This obscures the fact that the centre faces can rotate independently. If you have a marker pen, you could, for example, mark the central squares of an unshuffled cube with four coloured marks on each edge, each corresponding to the colour 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. Thus one can scramble and then unscramble the cube but still leave the markings on the centres 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. Thus there are 46/2 = 2048 possible configurations of the centre squares in the otherwise unscrambled position, increasing the total number of cube positions from 43,252,003,274,489,856,000 to 88,580,102,706,155,225,088,000.

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.

Move Notation

Most solution guides use the same system to communicate sequences of moves. This is generally referred to as cube notation. It is all relative to the side of the cube at which one is currently looking.

  • F: Front. The side at which one is currently looking.
  • B: Back. The side opposite the front.
  • U: Up. The side above or on top of the front side.
  • D: Down. The side opposite up.
  • L: Left. The side directly to the left of the front.
  • R: Right. The side directly to the right of the front.
  • X: Move the X side 90 degrees clockwise.
  • X': Move the X side 90 degrees counter-clockwise.
  • X2: Move the X side 180 degrees.

An example would be F2U'R'LF2RL'U'F2, which would mean to turn the front face 180 degrees, then the up face 90 degrees counterclockwise, et cetera. This makes for a much simpler and more efficient method of describing algorithms than longhand.

Competitions

Many speed cubing 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.

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.

On January 14, 2006, Leyan Lo, a 20-year-old California Institute of Technology student, set a new world record of 11.13 seconds for solving the cube. Though he was lucky in that he skipped a step of his solution, this still counts as the official world record. Lo belongs to Caltech's Rubik's Cube Club, which hosted a competition at the Exploratorium museum in San Francisco (Associated Press). The official world record based on an average of the best 3 out of 5 cubes is 14.52 seconds, 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 a 14-year-old 8th-grade student at the time, participating in the Caltech 2004 Fall Tournament. He also once held the official world record for the fastest single solve with a time of 12.11 seconds.

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.

Rubik's Cube in philosophy of science

Philosopher, scientist, mathematician and scholar Dr. Peter von Kraus has expanded the work of Anthony E. Durham and has argued that the basic structure of the universe is comparable to that of a Rubik's cube, showing that quantum events may be described by twists of the cube. Typically, the universe twists randomly without respect to human intervention, permuting endlessly towards a state of entropic dissarray. However, Von Kraus has shown that a select number of people are capable of actively performing commutations, opening up the possiblity of mankind intervening and bringing the state of the universe to a pure and solved state. His writings have inspired a group of followers, known as "The Cubists" to study the art of commutation, in an effort to complete this great task.

From 1983 to 1984, a Ruby-Spears produced Saturday morning cartoon based upon the toy, Rubik, the Amazing Cube, aired on ABC as part of a package program, The Pac-Man/Rubik, The Amazing Cube Hour.

See also

Variations of Rubik's Cubes. From left to right: Rubik's Revenge, Rubik's Cube, Professor's Cube, Pocket Cube.

References

  1. ^ Marshall, Ray. Squaring up to the Rubik challenge. icNewcastle. Retrieved August 15, 2005.
  2. Handbook of Cubik Math by Alexander H. Frey, Jr. and David Singmaster
  3. Notes on Rubik's 'Magic Cube' ISBN 0-89490-043-9 by David Singmaster
  4. 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.
  5. Four-Axis Puzzles by Anthony E. Durham.
  6. Mathematics of the Rubik's Cube Design ISBN 0-80593-919-9 by Hana M. Bizek
The Wikibook [[wikibooks:|]] has a page on the topic of: How to solve the Rubik's Cube

Rubik's Cube and its variants:

Software simulations:

Automated solvers:

Solution guides:

Speedcubing records:

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