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Rubiks-cube

A standard 3x3 rubik's cube.

Conception and developmentEdit

The Magic Cube was invented in 1974 by Erno Rubik, a Hungarian sculptor and professor of architecture with an interest in geometry and the study of three-dimensional 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 progress of the Cube towards the toy shop shelves of the West was then 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. In 1984, Ideal lost a patent infringement suit by Larry Nichols for his US patent #3655201. 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.[1][2]

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PopularityEdit

Over one hundred million cubes were sold in the period from 1980 to 1982.[3] 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 in Java, 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. [1] In 2006, Roice Nelson and Charlie Nevill created a 3×3×3×3×3 Fifth dimension|five-dimensional model. As of January 2007, it has been solved by only 7 people. [2]

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 [3].

At the height of the puzzle's popularity, separate sheets of coloured stickers were sold so that frustrated or impatient Cube owners could restore their puzzle to its original appearance.[4]

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

Recently, Greek inventor Panagiotis Verdes patented a method of creating cubes beyond the 5×5×5, up to 11×11×11 level. His designs, which include improved mechanisms for the 3×3×3, 4×4×4, and 5×5×5, are suitable for speed cubing,[5] whereas existing designs for cubes larger than 3×3×3 are prone to breaking.[6] As of April 2007, these designs are still being tested and are not widely available yet, although videos of actual, working prototypes for the 6×6×6 and 7×7×7 have been released.


EDITPLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Edit

WorkingsEdit

A standard Cube measures approximately 2¼ inches (57 mm) 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 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 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 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, 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 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 yellow face opposite the green, and the blue face opposite the white (with red and orange opposite faces remaining unchanged).

PermutationsEdit

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 "<a href="tel:1000000000">1000000000</a> (number)|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 or fewer moves.

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 facesEdit

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 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 centres rotated, and it becomes an additional challenge to "solve" the centres as well.

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), an increase of more than 2000 times.

SolutionsEdit

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.

Speedcubing solutions have been developed for solving the Rubik's Cube as quickly as possible. The most common speedcubing 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.


EDITPLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Edit

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 (see Optimal solutions for Rubik's Cube).

Move notationEdit

Rubik's cube notation

This is the notation of a rubik's cube. The asrrows indicate how you would rotate the face clockwise.

Most 3×3×3 Rubik's Cube solution guides use the same notation, originated by David Singmaster, to communicate sequences of moves. This is generally referred to as "Cube notation" or in some literature "Singmaster notation" (or variations thereof). Its relative nature allows algorithms to be written in such a way that they can be applied regardless of which side is designated the top or how the colours are organized on a particular Cube.

  • F (Front): the side currently facing you
  • 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 or on bottom
  • L (Left): the side directly to the left of the front
  • R (Right): the side directly to the right of the front

When a prime symbol ['] follows a letter, it means to turn the face counter-clockwise a quarter-turn, while a letter without a prime symbol means to turn it a quarter-turn clockwise. Such a symbol is pronounced prime. A letter followed by a 2 (occasionally superscript) means to turn the face a half-turn (the direction does not matter).

This notation can also be used on the Pocket Cube, the Revenge, and the Professor, with additional notation. They not only have the F, B, L, R, U, D notation but also f, b, l, r, u, d. For example: (Rr)' l2 f'

(Some solution guides, including Ideal's official publication, The Ideal Solution, use slightly different conventions. Top and Bottom are used rather than Up and Down for the top and bottom faces, with Back being replaced by Posterior. + indicates clockwise rotation and - counterclockwise, with ++ representing a half-turn. However, alternative notations failed to catch on, and today the Singmaster scheme is used universally by those interested in the puzzle.)

Less often used moves include rotating the entire Cube or two-thirds of it. The letters x, y, and z are used to indicate that the entire Cube should be turned about one of its axes. The X-axis is the line that passes through the left and right faces, the Y-axis is the line that passes through the up and down faces, and the Z-axis is the line that passes through the front and back faces. (This type of move is used infrequently in most solutions, to the extent that some solutions simply say "stop and turn the whole Cube upside-down" or something similar at the appropriate point.)

Lowercase letters f, b, u, d, l, and r signify to move the first two layers of that face while keeping the remaining layer in place. This is of course equivalent to rotating the whole Cube in that direction, then rotating the opposite face back the same amount in the opposite direction, but is useful notation to describe certain triggers for speedcubing. Furthermore, M, E, and S [middle, equatorial, and side] (and respectively their lowercase for larger sized cubes), are used for inner-slice movements. M signifies turning the layer that is between L and R downward (clockwise if looking from the left side). E signifies turning the layer between U and D towards the right (counter-clockwise if looking from the top). S signifies turning the layer between F and B clockwise.

For example, the algorithm (or operator, or sequence) F2 U' R' L F2 R L' U' F2, which cycles three edge cubes in the top layer without affecting any other part of the Cube, means:

  1. Turn the Front face 180 degrees
  2. Turn the Up face 90 degrees counterclockwise
  3. Turn the Right face 90 degrees counterclockwise
  4. Turn the Left face 90 degrees clockwise
  5. Turn the Front face 180 degrees
  6. Turn the Right face 90 degrees clockwise
  7. Turn the Left face 90 degrees counterclockwise
  8. Turn the Up face 90 degrees counterclockwise
  9. Finally, turn the front face 180 degrees.

For beginning students of the Cube, this notation can be daunting, and many solutions available online therefore incorporate animations that demonstrate the algorithms presented. For an example, see an animation of the above sequence.

4×4×4 and larger Cubes use slightly different notation to incorporate the middle layers. Generally speaking, upper case letters (FBUDLR) refer to the outermost portions of the cube (called faces). Lower case letters (fbudlr) refer to the inner portions of the cube (called slices). Again Ideal breaks rank by describing their 4×4×4 solution in terms of layers (vertical slices that rotate about the Z-axis), tables (horizontal slices), and books (vertical slices that rotate about the X-axis). And Micheal Ferraglio solved it in 1 minute, on April 30th. LFSS

CompetitionsEdit

Many speedcubing competitions have been held to determine who can solve the Rubik's Cube in the shortest time. From 2003 - 2006 there have been 72 official competitions with 33 of them in 2006 alone.

The first world championship organized by the Guinness Book of World Records was held in Munich on March 13, 1981. All cubes were moved 40 times and rubbed with petroleum jelly. Official winner with a record of 38 seconds was Jury Froeschl, born in Munich.

The first international 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 recognized due to lack of compliance with agreed-upon standards for timing and competing. Only records set during official World Cube Association (WCA)-sanctioned tournaments are acknowledged.

In 2004, the WCA established a new set of standards, with a special timing device called a Stackmat timer.

Currently, the official world record is held by Feliks Zemdegs of Australia, at 5.66 seconds at the Melbourne Winter Open 2011. He also holds the offical world record average at 7.64 seconds, set at the same competition.



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Rubik's Cube in popular cultureEdit

  • In the My Name Is Earl episode Number One, Randy solves a Rubik's Cube while Earl was talking to Paul.
  • From 1983 to 1984, a Ruby-Spears produced Saturday morning cartoon based upon the toy Rubik, the Amazing Cube aired on the American Broadcasting Company as part of a package program, "The Pac-Man/Rubik, The Amazing Cube Hour".
  • Saturday Night Live has had two commercial parodies for Rubik's cube-esque products: Rubik's Teeth (a pair of dentures that are multicoloured like a Rubik's cube) and Rubik's Grenade (a live hand grenade with a Rubik's cube puzzle on the side that explodes if the puzzle isn't solved correctly)
  • It won a Spiel des Jahres Best Puzzle prize in 1980.
  • In the 2006 movie The Pursuit of Happyness starring Will Smith, Chris Gardner (Smith's character) successfully solves a Rubik's Cube to the astonishment of his future employer (who thinks that it is impossible to solve). Will Smith also solved the cube in an episode of The Fresh Prince of Bel Air during a school interview. Will Smith's actual ability to solve the puzzle is a topic of hot debate.
  • A commercial spot for the PlayStation 3 video game console places the machine against an unsolved Rubik's Cube in a bland room. The Rubik's Cube levitates, gets solved by an unseen force, then explodes, painting the sides of the bare room with the same colours as its solved faces.
  • A commercial spot for Hyundai features a blindfolded young man solving a Rubik's Cube. (Watch video)
  • In the movie UHF (starring "Weird Al" Yankovic), a blind man is shown solving a Rubik's cube and asking the person next to him, "Is this it?" after every turn.
  • In The Simpsons, the Rubik's Cube makes several appearances. In "Homer Defined", Homer Simpson blames a Rubik's Cube for distracting him during his nuclear power plant training. In another episode, Milhouse reads information on a giant mechanical Rubik's Cube in Hungary. Also, Marge tries solving a cube as the rest of the Simpsons holler suggestions to her frustration. Finally, in "HOMR", where Homer removes a crayon from his head and becomes a genius, he is seen solving a basket of cubes with ease. A variety of Simpsons-themed Rubik's Cubes have seen popularity as well, particularly one of Homer's head.[7]
  • In the US sitcom Seinfeld, George Louis Costanza played by Jason Alexander, solves the cube while abstaining from sex.
  • In the Australian sketch show The Ronnie John's Half Hour, Ronnie does several sketches playing a fake Russian Rubik's cube champion, Sergei Haminov, who endorses made up products.
  • In the movie, Dude, Where's My Car, the Continuum Transfunctioner is actually Jesse and Chester's Rubik's Cube.
  • In the old professional wrestling promotion ECW, Joel Gertner referred to the Rubik's Cube in one of his promos saying, "I'm just like Rubik's Cube, the more you play with it, the harder it gets."
  • Steve Buscemi's character solves one in Armageddon, commenting how easy it was.
  • In 30 Rock the episode Jack The Writer, a Rubik's cube can be seen on the table.
  • In the 2004 movie Hellboy, Abe Sapien shows an unsolved Rubik's Cube while commenting "Listen, I'm not much of a problem solver. Three decades... and I've only completed two sides."
  • In the 2008 movie Wall-E, Wall-E has a Rubik's cube in his collection of assorted junk. Later in the film, Wall-E gives the cube to Eve and turns away. When he turns back, he is suprised to see that Eve solved it.

NotesEdit

  1. http://cubeman.org/cchrono.txt
  2. http://inventors.about.com/library/weekly/aa040497.htm
  3. http://www.rubiks.com/lvl3/index_lvl3.cfm?lan=eng&lvl1=inform&lvl2=medrel&lvl3=cubfct
  4. Tim Walsh: "Timeless Toys: Classic Toys And the Playmakers Who Created Them" p233 ISBN 10: 0-7407-5571-4
  5. http://www.olympicube.com/
  6. https://secure.rubiks.com/lvl3/index_lvl3.cfm?lan=eng&lvl1=produc&lvl2=rubbrn&lvl3=clasic&lvl4=cubprf
  7. https://secure.rubiks.com/lvl3/index_lvl3.cfm?lan=eng&lvl1=produc&lvl2=rubbrn&lvl3=collec&lvl4=hdhomr

ReferencesEdit

  • 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.
  • Mathematics of the Rubik's Cube Design ISBN 0-8059-3919-9 by Hana M. Bizek

External linksEdit

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