RUBIK\'S CUBE is a 3-D combination puzzle invented in 1974 by
Hungarian sculptor and professor of architecture
On a classic Rubik's Cube, each of the six faces is covered by nine stickers, each of one of six solid colours: white, red, blue, orange, green, and yellow. In currently sold models, white is opposite yellow, blue is opposite green, and orange is opposite red, and the red, white and blue are arranged in that order in a clockwise arrangement. On early cubes, the position of the colours varied from cube to cube. An internal pivot mechanism enables each face to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must be returned to have only one colour. Similar puzzles have now been produced with various numbers of sides, dimensions, and stickers, not all of them by Rubik. Although the
CONTENTS * 1 Conception and development * 1.1 Prior attempts * 1.2 Rubik\'s invention * 2 Subsequent history * 2.1 1980s Cube craze * 2.2 21st-century revival * 3 Imitations * 3.1
* 4 Mechanics * 5 Mathematics * 5.1 Permutations
* 5.2 Centre faces
* 5.3
* 6 Solutions * 6.1 Move notation
* 6.2 Optimal solutions
* 6.3
* 7 Competitions and records * 7.1
* 8 Variations * 8.1 Custom-built puzzles * 8.2 Rubik\'s Cube software * 8.3 Chrome Cube Lab * 9 Popular culture * 10 See also * 11 References * 12 Further reading * 13 External links CONCEPTION AND DEVELOPMENT PRIOR ATTEMPTS Diagram from Nichols' patent showing a cube held together with magnets In March 1970,
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\'S INVENTION Packaging of Rubik's Cube, Toy of the year 1980–Ideal Toy
Corp., made in Hungary Current colour scheme of a
In the mid-1970s,
The first test batches of the
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 decided to rename it. "The
SUBSEQUENT HISTORY See also: Rubik\'s Cube in popular culture 1980S CUBE CRAZE After the first batches of Rubik's Cubes were released in May 1980,
initial sales were modest, but Ideal began a television advertising
campaign in the middle of the year which it supplemented with
newspaper adverts. At the end of 1980
As most people could only solve one or two sides, numerous books were
published including
In October 1982
21ST-CENTURY REVIVAL Rubik's Cubes continued to be marketed and sold throughout the 1980s
and 90s, but it was not until the early 2000s that interest in the
Cube began increasing again. In the US sales doubled between 2001 and
2003, and
IMITATIONS Taking advantage of an initial shortage of Cubes, many imitations and variations appeared, many of which may have violated one or more patents. Today, the patents have expired and many Chinese companies produce copies of, and in some cases improvements upon, the Rubik and V-Cube designs. PATENT HISTORY Nichols assigned his patent to his employer Moleculon Research Corp.,
which sued Ideal 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
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, which was
granted in 1976 (Japanese patent publication JP55-008192). Until 1999,
when an amended
Greek inventor
TRADEMARKS Rubik's Brand Ltd. also holds the registered trademarks for the word
Rubik and Rubik's and for the 2D and 3D visualisations of the puzzle.
The trademarks have been upheld by a ruling of the General Court of
the
On 10 November 2016,
MECHANICS
A standard
Each of the six centre pieces pivots on a screw (fastener) held by the centre piece, a "3D cross". A spring between each screw head and its corresponding piece tensions the piece inward, so that collectively, the whole assembly remains compact, but can still be easily manipulated. The screw can be tightened or loosened to change the "feel" of the Cube. Newer official Rubik's brand cubes have rivets instead of screws and cannot be adjusted. The Cube can be taken apart without much difficulty, typically by rotating the top layer by 45° and then prying one of its edge cubes away from the other two layers. Consequently, it is a simple process to "solve" a Cube by taking it apart and reassembling it in a solved state. There are six central pieces which show one coloured face, twelve edge pieces which show two coloured faces, and eight corner pieces which show three coloured faces. 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. However, Cubes with alternative colour arrangements also exist; for example, with the yellow face opposite the green, the blue face opposite the white, and red and orange remaining opposite each other.
MATHEMATICS PERMUTATIONS The original (3×3×3)
which is approximately 43 quintillion . The puzzle was originally advertised as having "over 3,000,000,000 (three billion ) combinations but only one solution". To put this into perspective, if one had as many standard sized Rubik's Cubes as there are permutations , one could cover the Earth's surface 275 times. The preceding figure is limited to permutations that can be reached solely by turning the sides of the cube. If one considers permutations reached through disassembly of the cube, the number becomes twelve times as large: 8 ! 3 8 12 ! 2 12 = 519 , 024 , 039 , 293 , 878 , 272 , 000. {displaystyle {8!times 3^{8}times 12!times 2^{12}}=519,024,039,293,878,272,000.} which is approximately 519 quintillion possible arrangements of the pieces that make up the Cube, but only one in twelve of these are actually solvable. 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. CENTRE FACES The original
Marking the Rubik's Cube's centres increases its difficulty because this expands the set of distinguishable possible configurations. There are 46/2 (2,048) ways to orient the centres, since an even permutation of the corners implies an even number of quarter turns of centres as well. In particular, when the Cube is unscrambled apart from the orientations of the central squares, there will always be an even number of centre squares requiring a quarter turn. Thus orientations of centres increases 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). When turning a cube over is considered to be a change in permutation then we must also count arrangements of the centre faces. Nominally there are 6! ways to arrange the six centre faces of the cube, but only 24 of these are achievable without disassembly of the cube. When the orientations of centres are also counted, as above, this increases the total number of possible Cube permutations from 88,580,102,706,155,225,088,000 (8.9×1022) to 2,125,922,464,947,725,402,112,000 (2.1×1024). ALGORITHMS In Rubik's cubers' parlance, a memorised sequence of moves that has a
desired effect on the cube is called an algorithm. This terminology is
derived from the mathematical use of algorithm , meaning a list of
well-defined instructions for performing a task from a given initial
state, through well-defined successive states, to a desired end-state.
Each method of solving the
Many algorithms are designed to transform only a small part of the cube without interfering with other parts that have already been solved, so that they can be applied repeatedly to different parts of the cube until the whole is solved. For example, there are well-known algorithms for cycling three corners without changing the rest of the puzzle, or flipping the orientation of a pair of edges while leaving the others intact. Some algorithms do have a certain desired effect on the cube (for example, swapping two corners) but may also have the side-effect of changing other parts of the cube (such as permuting some edges). Such algorithms are often simpler than the ones without side-effects, and are employed early on in the solution when most of the puzzle has not yet been solved and the side-effects are not important. Most are long and difficult to memorise. Towards the end of the solution, the more specific (and usually more complicated) algorithms are used instead. RELEVANCE AND APPLICATION OF MATHEMATICAL GROUP THEORY
SOLUTIONS MOVE NOTATION Many 3×3×3
* F (Front): the side currently facing the solver * B (Back): the side opposite the front * U (Up): the side above or on top of the front side * D (Down): the side opposite the top, underneath the Cube * L (Left): the side directly to the left of the front * R (Right): the side directly to the right of the front * ƒ (Front two layers): the side facing the solver and the corresponding middle layer * b (Back two layers): the side opposite the front and the corresponding middle layer * u (Up two layers) : the top side and the corresponding middle layer * d (Down two layers) : the bottom layer and the corresponding middle layer * l (Left two layers) : the side to the left of the front and the corresponding middle layer * r (Right two layers) : the side to the right of the front and the corresponding middle layer * x (rotate): rotate the entire Cube on R * y (rotate): rotate the entire Cube on U * z (rotate): rotate the entire Cube on F When a prime symbol ( ′ ) follows a letter, it denotes a face turn counter-clockwise, while a letter without a prime symbol denotes a clockwise turn. A letter followed by a 2 (occasionally a superscript 2) denotes two turns, or a 180-degree turn. R is right side clockwise, but R' is right side counter-clockwise. The letters x, y, and z are used to indicate that the entire Cube should be turned about one of its axes, corresponding to R, U, and F turns respectively. When x, y or z are primed, it is an indication that the cube must be rotated in the opposite direction. When they are squared, the cube must be rotated 180 degrees. The most common deviation from Singmaster notation, and in fact the current official standard, is to use "w", for "wide", instead of lowercase letters to represent moves of two layers; thus, a move of Rw is equivalent to one of r. For methods using middle-layer turns (particularly corners-first methods) there is a generally accepted "MES" extension to the notation where letters M, E, and S denote middle layer turns. It was used e.g. in Marc Waterman's Algorithm. * M (Middle): the layer between L and R, turn direction as L (top-down) * E (Equator): the layer between U and D, turn direction as D (left-right) * S (Standing): the layer between F and B, turn direction as F The 4×4×4 and larger cubes use an extended notation to refer to the additional middle layers. Generally speaking, uppercase letters (F B U D L R) refer to the outermost portions of the cube (called faces). Lowercase letters (f b u d l r) refer to the inner portions of the cube (called slices). An asterisk (L*), a number in front of it (2L), or two layers in parentheses (Ll), means to turn the two layers at the same time (both the inner and the outer left faces) For example: (Rr)' l2 f' means to turn the two rightmost layers anticlockwise, then the left inner layer twice, and then the inner front layer anticlockwise. By extension, for cubes of 6x6 and larger, moves of three layers are notated by the number 3, for example 3L. An alternative notation, Wolstenholme notation, is designed to make memorising sequences of moves easier for novices. This notation uses the same letters for faces except it replaces U with T (top), so that all are consonants. The key difference is the use of the vowels O, A and I for clockwise, anticlockwise and 180-degree turns, which results in word-like sequences such as LOTA RATO LATA ROTI (equivalent to LU′R′UL′U′RU2 in Singmaster notation). Addition of a C implies rotation of the entire cube, so ROC is the clockwise rotation of the cube around its right face. Middle layer moves are denoted by adding an M to corresponding face move, so RIM means a 180-degree turn of the middle layer adjacent to the R face. Another notation appeared in the 1981 book The Simple Solution to Rubik\'s Cube . Singmaster notation was not widely known at the time of publication. The faces were named Top (T), Bottom (B), Left (L), Right (R), Front (F) and Posterior (P), with + for clockwise, - for anticlockwise and 2 for 180-degree turns. Another notation appeared in the 1982 "The Ideal Solution" book for Rubik's Revenge. Horizontal planes were noted as tables, with table 1 or T1 starting at the top. Vertical front to back planes were noted as book, with book 1 or B1 starting from the left. Vertical left to right planes were noted as windows, with window 1 or W1 starting at the front. Using the front face as a reference view, table moves were left or right, book moves were up or down, and window moves were clockwise or counter-clockwise. OPTIMAL SOLUTIONS Main article: Optimal solutions for Rubik\'s Cube Mountaineer
solving
Although there are a significant number of possible permutations for the Rubik's Cube, a number of solutions have been developed which allow solving the cube in well under 100 moves. Many general solutions for the
SPEEDCUBING METHODS In 1981, thirteen-year-old Patrick Bossert developed a solution for solving the cube, along with a graphical notation, designed to be easily understood by novices. It was subsequently published as You Can Do The Cube and became a best-seller. A solution commonly used by speed cubers was developed by Jessica Fridrich . It is similar to the layer-by-layer method but employs the use of a large number of algorithms, especially for orienting and permuting the last layer. The cross is done first, followed by first layer corners and second layer edges simultaneously, with each corner paired up with a second-layer edge piece, thus completing the first two layers (F2L). This is then followed by orienting the last layer, then permuting the last layer (OLL and PLL respectively). Fridrich\'s solution requires learning roughly 120 algorithms but allows the Cube to be solved in only 55 moves on average. Philip Marshall's The Ultimate Solution to
A now well-known method was developed by
The Roux Method, developed by
In 1997, Denny Dedmore published a solution described using diagrammatic icons representing the moves to be made, instead of the usual notation. BEGINNER\'S METHOD Most beginner solution methods involve solving the cube one layer at a time, using algorithms that preserve what has already been solved. The easiest layer by layer methods require only 3-8 algorithms. RUBIK\'S CUBE SOLVER PROGRAM The most move optimal online
COMPETITIONS AND RECORDS SPEEDCUBING COMPETITIONS Main article:
The first world championship organised by the Guinness Book of World
Records was held in
Since 2003, the winner of a competition is determined by taking the
average time of the middle three of five attempts. However, the single
best time of all tries is also recorded. The World Cube Association
maintains a history of world records. In 2004, the WCA made it
mandatory to use a special timing device called a
In addition to the main 3x3x3 event, the WCA also holds events where the cube is solved in different ways: * Blindfolded solving * Multiple blindfolded solving, or "multi-blind", in which the contestant solves any number of cubes blindfolded in a row * Solving the Cube using a single hand * Solving the Cube with one's feet * Solving the Cube in the fewest possible moves In blindfolded solving, the contestant first studies the scrambled cube (i.e., looking at it normally with no blindfold), and is then blindfolded before beginning to turn the cube's faces. Their recorded time for this event includes both the time spent examining the cube and the time spent manipulating it. In multiple blindfolded, all of the cubes are memorised, and then all of the cubes are solved once blindfolded; thus, the main challenge is memorising many - often ten or more - separate cubes. The event is scored not by time but by the number of solved cubes minus the number of unsolved cubes after one hour has elapsed. In fewest moves solving, the contestant is given one hour to find his or her solution, and must write it down. RECORDS * Single time: The world record time for solving a 3×3×3 Rubik's
Cube is 4.59 seconds, set by Seung Beom Cho (16 year old boy) of South
Korea on 28 October 2017 at the ChicaGhosts 2017 competition.
* Average time: The world record average of five solves (excluding
fastest and slowest) is 5.80 seconds, set by
TOP 5 SOLVERS BY SINGLE SOLVE NAME FASTEST SOLVE COMPETITION SeungBeom Cho 4.59s ChicaGhosts 2017 Patrick Ponce 4.69s Ralley In The Valley 2017
TOP 5 SOLVERS BY AVERAGE OF 5 SOLVES NAME FASTEST AVERAGE COMPETITION
Seung Hyuk Nahm (남승혁) 6.43s China Championship 2017
* Group solving (12 minutes): The record for most people solving a
On November 4, 2012, 3248 people, mainly students of College of Engineering Pune , successfully solved the Rubik's cube in 30 minutes on college ground. The successful attempt is recorded in the Limca Book of Records . The college will submit the relevant data, witness statements and video of the event to Guinness authorities. VARIATIONS Variations of Rubik's Cubes. Top row:
There are different variations of Rubik's Cubes with up to seventeen layers: the 2×2×2 (Pocket/Mini Cube ), the standard 3×3×3 cube, the 4×4×4 (Rubik\'s Revenge/Master Cube ), and the 5×5×5 (Professor\'s Cube ) being the most well known. The 17×17×17 "Over The Top" cube (available late 2011) is currently the largest (and most expensive, costing more than a thousand dollars) commercially sold cube. A working design for a 22×22×22 cube exists and was demonstrated in January 2016. Chinese manufacturer ShengShou has been producing cubes in all sizes from 2×2×2 to 10×10×10 (as of late 2013). Non-licensed physical cubes as large as 13×13×13 based on the V-Cube patents are commercially available to the mass-market circa 2015 in China; these represent about the limit of practicality for the purpose of "speed-solving" competitively (as the cubes become increasingly ungainly and solve-times increase quadratically). Rubik's TouchCube There are many variations of the original cube, some of which are
made by Rubik. The mechanical products include the Rubik's Magic, 360,
and Twist. Also, electronics like the
The Cube has inspired an entire category of similar puzzles, commonly
referred to as twisty puzzles , which includes the cubes of different
sizes mentioned above as well as various other geometric shapes. Some
such shapes include the tetrahedron (
In 2011,
Since 2015, with the mass production of the Icosaix, all five platonic solids analogous to Rubik's cube (face-turning with cuts one-third from each face, except the Pyraminx, which also has turnable tips) became available. Besides Rubik's cube, the tetrahedron is available as the Pyraminx, the octahedron as the Face Turning Octahedron, the dodecahedron as the Megaminx, and the icosahedron as the Icosaix. Some puzzles have also been created in the shape of the
CUSTOM-BUILT PUZZLES Novelty keychain Puzzles have been built resembling the
Some custom puzzles are not derived from any existing mechanism, such as the Gigaminx v1.5-v2, Bevel Cube, SuperX, Toru, Rua, and 1×2×3. These puzzles usually have a set of masters 3D printed, which then are copied using moulding and casting techniques to create the final puzzle. Other
RUBIK\'S CUBE SOFTWARE Puzzles like the
*
CHROME CUBE LAB
POPULAR CULTURE Main article: Rubik\'s Cube in popular culture SEE ALSO *
REFERENCES * ^ William Fotheringham (2007). Fotheringham's Sporting Pastimes.
Anova Books. p. 50. ISBN 1-86105-953-1 .
* ^ de Castella, Tom. "The people who are still addicted to the
Rubik\'s Cube". BBC News Magazine. BBC. Retrieved 28 April 2014.
* ^ \'Driven mad\' Rubik\'s nut weeps on solving cube... after 26
years of trying, Daily Mail Reporter, January 12, 2009.
* ^ Daintith, John (1994). A Biographical Encyclopedia of
Scientists. Bristol: Institute of Physics Pub. p. 771. ISBN
0-7503-0287-9 .
* ^ Michael Shanks (May 8, 2005). "History of the Cube". Stanford
University. Retrieved July 26, 2012.
* ^ William Lee Adams (2009-01-28). "The Rubik\'s Cube: A Puzzling
Success". TIME . Archived from the original on 2009-02-01. Retrieved
2009-02-05.
* ^ Alastair Jamieson (2009-01-31). "Rubik\'s Cube inventor is back
with Rubik\'s 360".
FURTHER READING * Frey, Alexander; Singmaster, David (1982). Handbook of Cubic Math.
Enslow. ISBN 0894900587 .
* Rubik, Ernő; Varga, Tamas; Keri, Gerson; Marx, Gyorgy; Vekerdy,
Tamas (1987). Singmaster, David, ed. Rubik's Cubic Compendium. Oxford
University Press. ISBN 0198532024 .
* Bizek, Hana M. (1997). Mathematics of the
EXTERNAL LINKS Find more aboutRUBIK\'S CUBEat's sister projects * Definitions from Wiktionary * Media from Commons * Textbooks from Wikibooks * Learning resources |