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Rubik's Cube

2007 Schools Wikipedia Selection. Related subjects: Games

   Variations of Rubik's Cubes (from left to right: Rubik's Revenge,
   Rubik's Cube, Professor's Cube, & Pocket Cube)
   Enlarge
   Variations of Rubik's Cubes (from left to right: Rubik's Revenge,
   Rubik's Cube, Professor's Cube, & Pocket Cube)

   Rubik's Cube or (informally) Rubix Cube is a mechanical puzzle invented
   in 1974 by the Hungarian sculptor and professor of architecture Ernő
   Rubik. The plastic cube comes in four widely available versions: the
   2×2×2 (" Pocket Cube"), the 3×3×3 standard cube, the 4×4×4 (" Rubik's
   Revenge"), 5×5×5 (" Professor's Cube"). 6×6×6 and 7×7×7 cubes are
   currently being produced. The 3×3×3 version, which is the version
   usually meant by the term "Rubik's Cube," has nine square faces on each
   side, for a total area of fifty-four faces, and occupies the volume of
   twenty-six unit cubes (not counting the invisible cube in the centre).
   Typically, the faces of the Cube are covered by stickers in six solid
   colors, one for each side of the Cube. When the puzzle is solved, each
   side of the Cube is a solid colour. The original 3×3×3 version
   celebrated its twenty-fifth anniversary in 2005, when a special edition
   Cube in a presentation box was released, featuring a sticker in the
   centre of the white face (which was replaced with a reflective surface)
   with a "Rubik's Cube 1980-2005" logo.

   Originally called the Magic Cube by its inventor, it was renamed
   Rubik's Cube in 1980 and released worldwide in May of that year,
   winning a Spiel des Jahres special award for Best Puzzle. It is said to
   be the world's best-selling toy, with some 300,000,000 Rubik's Cubes
   and imitations sold worldwide.

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 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 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 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 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.

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 Rubik's Professor,
   respectively) and puzzles in other shapes, such as the Pyraminx, a
   tetrahedron.

   In May 2005, the Greek Panagiotis Verdes constructed a 6×6×6 Rubik's
   Cube. and 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 2
   minutes. 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 succesfully constructed the 7x7x7 cube, and on October 27 2006,
   a video of Frank Morris testing the cube was released. Videos of these
   tests can be viewed at http://www.olympicube.com

   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 both The Times and
   the New York Times bestseller lists 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.

   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.

   Financially, the Cube was so successful that Rubik became the first
   self-made elite in a communist country.

   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).

Workings

   Rubik's Cube partially disassembled
   Enlarge
   Rubik's Cube partially disassembled

   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 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 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 white and yellow sides, 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°, 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 colour 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, 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 Normal (3x3x3) Rubik's Cube can have (8! × 3^8−1) × (12! × 2^12−1)/2
   = 43,252,003,274,489,856,000 different positions, also referred to by
   the mathematical term permutations. This number can also be written as
   (~4.3 × 10^19), about 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-nine or fewer
   moves (see Optimal solutions for Rubik's Cube).

   In fact, there are (8! × 3^8) × (12! × 2^12) =
   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 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" 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 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 colored 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 4^6/2 = 2,048 possible configurations of
   the centre squares in the otherwise unscrambled position, increasing
   the total number of Cube permutation from 43,252,003,274,489,856,000 to
   88,580,102,706,155,225,088,000.

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.

   Solutions typically consist of a sequence of processes. A process, or
   algorithm or operator as it is sometimes called, is a series of 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 place. These sequences are performed in the appropriate
   order, as dictated by the current configuration of the puzzle, 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. 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 notation

   Rubik's Cube in a scrambled state
   Enlarge
   Rubik's Cube in a scrambled state
   Rubik's Cube being solved
   Enlarge
   Rubik's Cube being solved
   Rubik's Cube in solved state
   Enlarge
   Rubik's Cube in solved state

   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 colors 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 an apostrophe follows a letter, it means to turn the face
   counter-clockwise a quarter-turn, while a letter without an apostrophe
   means to turn it a quarter-turn clockwise. Such an apostrophe mark is
   pronounced prime. A letter followed by a 2 (occasionally superscript)
   means to turn the face a half-turn (the direction does not matter).

   (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 (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) F2U'R'LF2RL'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).

Competitions

   Many speedcubing competitions have been held to determine who can solve
   the Rubik's Cube in the shortest time.

   Ideal Toys held the first UK competition in 1981 less than a year after
   the cube was launched (sponsored by the Daily Mirror). The following
   times were recorded in the regional championships;

   Edinburgh heat - Alex McNair from Edinburgh in 48.85 secs, Manchester
   heat - Edgar Whitley from Colwyn Bay in 39.98 secs, York heat - Brian
   Storey from Sunderland in 41.76 secs, Midlands heat Nicolas Hammond
   from Nottingham in 35.38 secs, Bristol heat - Julian Bush from Bristol
   in 52.09 secs, Great Yarmouth heat - Julian Chilvers from Great
   Yarmouth in 38.67 secs, Southampton heat - Christopher Lennon from
   Portsmouth in 55.35 secs, London heat - Ben Jones from St
   Nicholas-at-Wade in 46.12 secs.

   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 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.

   Toby Mao set the current world record of 10.48 seconds at the 2006 US
   Nationals competition on August 6, 2006. The official world record
   based on an average of the middle three out of five Cubes is 13.22
   seconds, set on March 20, 2006 in Norrköping, Sweden by Anssi Vanhala,
   a Finn. This record is recognized by the World Cube Association, the
   official governing body which regulates events and records.

Alternative Competitions

   In addition, informal alternative competitions have been held,
   challenging participants to solve the cube under unusual situations.
   These include:
     * Blindfolded solving
     * Solving a cube in a room with colored lights intended to confuse
       participants in the colors of the tiles
     * Solving the cube underwater in a single breath
     * Solving the cube using a single hand

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 (+⅔ and −⅓) and antiquarks (−⅔ and +⅓). Feasible combinations of
   corner twists are paralleled by allowable combinations of quarks and
   antiquarks—both corner twist and the quark/antiquark charge must total
   to an integer. Combinations of two or three twisted corners may be
   compared to various hadrons, though this analogy is not always
   workable.

Rubik's Cube in popular culture

     * 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."
     * Saturday Night Live has had two commercial parodies for Rubik's
       cube-esque products: Rubik's Teeth (a pair of dentures that are
       multicolored 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)
     * The Rubik's Cube makes several appearances in The Simpsons, most
       notably when Homer is distracted by a Rubik's Cube when learning
       the power plant controls in " Homer Defined", when Marge attempts
       to solve the Cube while the rest of the family shouts hints at her
       in " Hurricane Neddy", and when Homer speedcubes a basket full of
       Cubes after becoming a person with average intelligence (with the
       IQ of 105 points) in " HOMЯ".
     * A Rubik's Cube serves as the MacGuffin in Dude, Where's My Car?
     * It won a Spiel des Jahres Best Puzzle prize in 1980.
     * The Australian sketch comedy show The Ronnie Johns Half Hour
       features a fictional Rubik's cube world champion named Sergei
       Haminov.
     * Rubik's Cubes are used as a NASA testing method for Harry Stamper's
       team in the movie Armageddon
     * In a recent commercial for the Playstation 3, demonstrating the
       game console's "advanced intelligence," it is presented in a
       colorless cubic room with the puzzle in front of it. It then
       telekinetically grasps the cube, levitating it to the centre of the
       room and speedsolving it in mid-air. The cube then violently
       explodes and fills each corresponding wall of the room with the
       respective colour of the Rubik's Cube sides.
     * It is seen in the Family Guy episode "Saving Private Brian" when
       Brian solves a Rubik's Cube in order to pass basic training.
     * In an episode of The Fresh Prince of Bel Air, The Alma Matter, Will
       Smith solves a rubik's cube in a few seconds during an interview
       for Princeton and is then recommended to attend the school.
     * Speedcubing champions Tyson Mao and Toby Mao were hired as
       consultants in the 2006 Sony Picture's movie The Pursuit of
       Happyness, to teach Will Smith's character how to solve a Rubik's
       Cube. There is a scene in the movie where a man tells him how
       impossible it is to solve the Rubik's cube, yet Smith solves it in
       mere seconds.

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