Rubik's Cube

History

Conception and development

In March 1970, Larry D. Nichols invented a 2x2x2 "Puzzle with Pieces Rotatable in Groups" and filed a U.S. patent application for it. Nichols' cube was held together with magnets. Nichols was granted U.S. Patent 3,655,201 on April 11, 1972, two years before Rubik invented his improved cube.

In April 9, 1970, Frank Fox invented and applied to patent "Spherical 3x3x3", he finally received his UK patent (1344259) on January 16th 1974, but still before Erno Rubik received his.

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. Rubik's Cube was held together with interlocking plastic pieces that were less expensive to produce than the magnets in Nichols' design. Rubik's Cube was distributed in the U.S. by Ideal Toy Company.

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 2x2x2 Pocket Cube infringed Nichols' patent, but overturned the judgment on Rubik's 3x3x3 Cube. So Nichols and Moleculon lost. Terutoshi Ishigi acquired Japanese patent JP55‒8192 for a nearly identical mechanism while Rubik's patent application was being processed, but Ishigi is generally credited with an independent reinvention.

Rubik applied for another Hungarian patent on October 28, 1980 and applied for other patents in the U.S. Rubik was granted U.S. Patent 4,378,116 on March 29, 1983 for the Cube. Rubik also invented and patented several other puzzles which were not as popular as Rubik's Cube.

Popularity

Over one hundred million cubes were sold in the period from 1980 to 1982. 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 Professor's Cube, respectively) and puzzles in other shapes, such as the Pyraminx, a tetrahedron.

In May 2005, the Greek inventor Panagiotis Verdes constructed a 6×6×6 Rubik's Cube; on May 23, 2006, Frank Morris, a world champion Rubik's Cube solver, tested this version. He had previously solved the 3×3×3 in 15 seconds, the 4×4×4 in 1 minute and 10 seconds, and the 5×5×5 in 1 minute and 46.1 seconds. The 6×6×6 took him 5 minutes and 37 seconds to solve. Morris himself thanked the inventor for making it and purportedly stated that the bigger the Cube is, the greater the pleasure. In July 2006, Mr. Verdes successfully constructed the 7×7×7 cube; on October 27, 2006, a video of Morris testing the cube was released. He solved this cube in 6 minutes and 29.31 seconds. Videos of these tests can be viewed at http://www.olympicube.com.

In 1994, Melinda Green, Don Hatch, and Jay Berkenilt created a model of a 3×3×3×3 four-dimensional analogue of a Rubik's Cube called the MagicCube4D. Having more possible states than there are atoms in the known universe, only 55 people have solved it as of January 2007. In 2006, Roice Nelson and Charlie Nevill created a 3×3×3×3×3 five-dimensional model. As of January 2007, it has been solved by only 7 people.

In 1981, Patrick Bossert, a twelve-year-old schoolboy from England, published his own solution in a book called You Can Do the Cube (ISBN 0-14-031483-0). The book sold over 1.5 million copies worldwide in seventeen editions and became the number one book on The Times. He didn't reach the New York Times Best Seller list for that year.

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

The name "Rubik's Cube" is common in many languages except Hebrew and in Hungarian. In the former language, it is known as the "Hungarian Cube", whilst in the latter, its name is "Magic Cube" (Buvos kocka).
 

Workings

A standard Cube measures approximately 2¼ inches (5.7 cm) on each side. The puzzle consists of the twenty-six unique miniature cubes ("cubies") on the surface. However, the centre 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 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 cubie" away from a "centre cubie" until it dislodges (however, prying loose a corner cubie is a good way to break off a centre cubie - thus ruining the cube). It is a simple process to solve a Cube by taking it apart and reassembling it in a solved state; however, this is not the challenge.

There are twelve edge pieces which show two colored sides each, and eight corner pieces which show three colors. Each piece shows a unique color combination, but not all combinations are present (for example, there is no edge piece with both red and orange sides, if red and orange 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°, 180° or 270°, 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 centre 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, cubes with alternative color arrangements also exist, for example they might have yellow face opposite the green, and the blue face opposite the white (with red and orange opposite faces remaining unchanged).

Permutations

A normal (3×3×3) Rubik's Cube can have (8! × 38−1) × (12! × 212−1)/2 = 43,252,003,274,489,856,000 different positions (permutations), or about 4.3 × 1019, forty-three quintillion (short scale) or forty-three trillion (long scale), but the puzzle is advertised as having only "billions" of positions, due to the general incomprehensibility of such a large number to laymen. Despite the vast number of positions, all Cubes can be solved in twenty-six or fewer moves (see Optimal solutions for Rubik's Cube).

To put this into perspective, if every permutation of a Rubik's Cube was lined up end to end, it would stretch out approximately 261 light years. If they were laid side by side, it would cover the Earth approximately 256 times.

In fact, there are (8! × 38) × (12! × 212) = 519,024,039,293,878,272,000 (about 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 reachable. This is because there is no sequence of moves that will swap a single pair 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.

Centre faces

The original and still official Rubik's Cube has no orientation markings on the centre faces, and therefore solving it does not require any attention to correctly orienting those faces. If you have a marker pen, you could, for example, mark the central squares of an un-shuffled Cube with four colored marks on each edge, each corresponding to the color 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 challenge to "solve" the centers as well. This is known as "super cubing".

Putting markings on the Rubik's Cube increases the challenge 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 = 2,048 possible configurations of the centre squares in the otherwise unscrambled position, increasing the total number of 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).
 

Solutions

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 layer, designated the top, is solved first, followed by the middle layer, and then the final and bottom layer. 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. The first layer corners and second layer are done simultaneously, with each corner paired up with a second-layer edge piece. Another well-known method was developed by Lars Petrus. In this method, a 2×2×2 section is solved first, followed by a 2x2x3, and then the incorrect edges are solved using a 3 move algorithm, which eliminates the need for a 32 move algorithm later. One of the advantages of this method is that it tends to give solutions in fewer moves. For this reason the method is also popular for fewest move competitions.

Solutions typically follow a series of steps, and include a set of algorithms for solving each step. An algorithm, also known as a process or an operator, is a series of twists that accomplishes a particular goal. For instance, one algorithm might switch the locations of three corner pieces, while leaving the rest of the pieces in place. Basic solutions require learning as few as 4 or 5 algorithms but are generally inefficient, needing around 100 twists on average to solve an entire cube. In comparison, Fridrich's advanced solution requires learning 53+ algorithms, but allows the cube to be solved in only 55 moves on average. A different kind of solution developed by Ryan Heise uses no algorithms but rather teaches a set of underlying principles that can be used to solve in fewer than 40 moves. A number of complete solutions can also be found in any of the books listed in the bibliography, and most can be used to solve any Cube in under five minutes. These solutions typically are intended to be easy to learn, but much effort has gone into finding even faster solutions to Rubik's Cube.