General Information
The Rubik's Cube is a mechanical puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the "Magic Cube" by its inventor, this puzzle was renamed "Rubik's Cube" by Ideal Toys in 1980 and won the German Game of the Year special award for Best Puzzle that year. It is said to be the world's best-selling toy, with over 300,000,000 Rubik's Cubes and imitations sold worldwide.[2]
In a classic Rubik's Cube, each of the six faces is covered by 9 stickers, among six solid colours (traditionally being white, yellow, orange, red, blue, and green). A pivot mechanism enables each face to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must be a solid colour.
The Cube celebrated its twenty-fifth anniversary in 2005, when a special edition was released, featuring a sticker in the centre of the reflective face (which replaced the white face) with a "Rubik's Cube 1980-2005" logo, and different packaging. There exist four widely available variations: the 2×2×2 (Pocket Cube, also Mini Cube, Junior Cube, or Ice Cube), the standard 3×3×3 cube, the 4×4×4 (Rubik's Revenge, or Master Cube), and the 5×5×5 (Professor's Cube). Recently, larger sizes are also on the market (V-Cube 6 and V-Cube 7). All of these items belong to a broad category of puzzles commonly referred to as "twisty puzzles".
For readability, 3x3x3 is frequently abbreviated 3×3 (and similarly for the other sizes) when there is no ambiguity. Common misspellings include "rubix cube", "rubics cube", "rubick's cube", and "rubiks cube".
Conception and development
In March 1970, Larry 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 with magnets. Nichols was granted Template:US patent on April 11, 1972, two years before Rubik invented his improved cube.
On April 9, 1970, Frank Fox applied to patent his "Spherical 3×3×3". He received his UK patent (1344259) on January 16, 1974.
Rubik invented his "Magic Cube" in 1974 and 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. Magic Cube was held together with interlocking plastic pieces that were less expensive to produce than the magnets in Nichols's design. In September 1979, a deal was signed with Ideal Toys to bring the Magic Cube to the Western world, and 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 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.
Nichols assigned his patent to his employer Moleculon Research Corp., which sued Ideal Toy Company in 1982. In 1984, Ideal lost the patent infringement suit and appealed. In 1986, the appeals court affirmed the judgment that Rubik's 2×2×2 Pocket Cube infringed Nichols's patent, but overturned the judgment on Rubik's 3×3×3 Cube.<ref>Moleculon Research Corporation v. CBS, Inc.</ref>
Even while Rubik's patent application was being processed, Terutoshi Ishigi, a self-taught engineer and ironworks owner near Tokyo, filed for a Japanese patent for a nearly identical mechanism and was granted patent JP55‒8192 (1976); Ishigi's is generally accepted as an independent reinvention.<ref> Template:Cite bookHofstadter gives the name as "Ishige".</ref><ref>http://cubeman.org/cchrono.txt</ref><ref>The History of Rubik's Cube - Erno Rubik</ref>
Rubik applied for another Hungarian patent on October 28, 1980, and applied for other patents. In the United States, Rubik was granted Template:US patent on March 29, 1983, for the Cube.
Greek inventor Panagiotis Verdes patented a method of creating cubes beyond the 5×5×5, up to 11×11×11. His designs, which include improved mechanisms for the 3×3×3, 4×4×4, and 5×5×5, are suitable for speedcubing, whereas existing designs for cubes larger than 5×5×5 are prone to break. As of June 19, 2008, 5x5x5, 6x6x6, and 7x7x7 models are available.
Workings
A standard cube measures approximately 2¼ inches (5.7 cm) on each side. The puzzle consists of the twenty-six unique miniature cubes on the surface. However, the centre cube of each face is merely a single square façade; all are affixed to the core mechanisms. These provide structure for the other pieces to fit into and rotate around. So there are twenty-one pieces: a single core piece consisting of three intersecting axes holding the six centre squares in place but letting them rotate, and twenty smaller plastic pieces which fit into it to form the assembled puzzle. The Cube can be taken apart without much difficulty, typically by turning one side through a 45° angle and prying an edge cube away from a centre cube until it dislodges. However, as prying loose a corner cube is a good way to break off a centre cube — thus ruining the Cube — it is far safer to lever a centre cube out using a screwdriver. It is a very simple process to solve a Cube by taking it apart and reassembling it in a solved state. There are twelve edge pieces which show two coloured sides each, and eight corner pieces which show three colours. 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 90°, 180° or 270°, 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, Cubes with alternative colour arrangements also exist; for example, they might have the yellow face opposite the green, and the blue face opposite the white (with red and orange opposite faces remaining unchanged).
Douglas R. Hofstader, in the July 1982 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 been produced commercially.Template:Cn
Permutations
A normal (3×3×3) Rubik's Cube has eight corners and twelve edges. There are 8! ways to arrange the corner cubies. Seven can be oriented independently, and the orientation of the eighth depends on the preceding seven, giving 37 possibilities. There are 12!/2 ways to arrange the edges, since an odd permutation of the corners implies an odd permutation of the edges as well. Eleven edges can be flipped independently, with the flip of the twelfth depending on the preceding ones, giving 211 possibilities.<ref>Martin Schönert "Analyzing Rubik's Cube with GAP": the permutation group of Rubik's Cube is examined with GAP computer algebra system</ref>
- <math> {8! \cdot 3^7 \cdot 12! \cdot 2^{10}} \approx 4.33 \cdot 10^{19}</math>
There are exactly 43,252,003,274,489,856,000 possibilities. In other words, there are forty-three quintillion (short scale) or forty-three trillion (long scale). The puzzle is often advertised as having only "billions" of positions, as the larger numbers could be regarded as incomprehensible to many. To put this into perspective, if every permutation of a 57-millimeter Rubik's Cube were lined up end to end, it would stretch out approximately 261 light years.
The preceding figure is limited to permutations that can be reached solely by turning the sides of the cube. If one considers permuations reached through disassembly of the cube, the number becomes twelve times as large:
- <math> {8! \cdot 3^8 \cdot 12! \cdot 2^{12}} \approx 5.19 \cdot 10^{20}</math>
The full number is 519,024,039,293,878,272,000 or 519 quintillion (on the short scale) possible arrangements of the pieces that make up the Cube, but only one in twelve of these are actually solveable. 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 twelve possible sets of reachable configurations, sometimes called "universes" or "orbits", into which the Cube can be placed by dismantling and reassembling it.
Despite the vast number of positions, all Cubes can be solved in twenty-five or fewer moves (see Optimal solutions for Rubik's Cube). <ref name=D.Kunkle> Template:Cite conference </ref> <ref> Template:Cite conference </ref> The large number of permutations is often given as a measure of the Rubik's cube's complexity. However, the puzzle's difficulty does not necessarily follow from the large number of permutations. The problem of putting the 26 letters of the alphabet in alphabetical order has a larger complexity (26! = 4.03 × 1026 possible orderings), but is less difficult.
Centre faces
The original (official) Rubik's Cube has 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, if one has a marker pen, one 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 face. 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. Thus one can scramble and then unscramble the Cube yet have the markings on the centers rotated, and it becomes an additional test to "solve" the centers as well. This is known as "supercubing"Template:Fact.
Putting markings on the Rubik's Cube increases the difficulty mainly 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 = 2,048 possible configurations of the centre squares in the otherwise unscrambled position, increasing 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).
