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Encyclopedia > Rubik's cube
Variations of Rubik's Cubes (from left to right: Rubik's Revenge, the original design of Rubik's Cube, Professor's Cube, & Pocket Cube, also known as "Mini-Cube").
Variations of Rubik's Cubes (from left to right: Rubik's Revenge, the original design of Rubik's Cube, Professor's Cube, & Pocket Cube, also known as "Mini-Cube").

Rubik's Cube is a mechanical puzzle invented in 1974[1] 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[1] and also won the 1980 German Game of the Year (Spiel des Jahres) special award for Best Puzzle. It is said to be the world's best-selling toy, with over 300,000,000 Rubik's Cubes and imitations sold worldwide.[2] Image File history File links Rubik's_cube_variations. ... Image File history File links Rubik's_cube_variations. ... A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces. ... Sculptor redirects here. ... The meaning of the word professor (Latin: [1]) varies. ... This article is about building architecture. ... ErnÅ‘ Rubik ErnÅ‘ Rubik (born July 13, 1944) is a Hungarian inventor, sculptor and professor of architecture. ... Ideal Toy Company was founded as Ideal Novelty and Toy Company in New York in 1907 by Morris and Rose Michtom after they had invented the teddy bear in 1903. ... The Spiel des Jahres (German for Game of the Year) is a prestigious award for board and card games. ...


In a typical Cube, each face is covered by nine stickers of one of six solid colours. When the puzzle is solved, each face of the Cube is a solid colour. The Cube 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 reflective face (which replaced the white face) with a "Rubik's Cube 1980-2005" logo.


The puzzle comes in four widely available versions: the 2×2×2 (Pocket Cube, also Mini Cube, Junior Cube, or Ice Cube), the 3×3×3 standard cube, the 4×4×4 (Rubik's Revenge), and the 5×5×5 (Professor's Cube). Larger sizes of the cubes, 6x6x6 and 7x7x7, are also available. Solved Pocket Cube Scrambled Pocket Cube Pocket Cube with one side tilted The Pocket Cube is the 2×2×2 equivalent of a Rubiks cube. ... Rubiks Revenge in solved state The Rubiks Revenge is the 4×4×4 version of Rubiks Cube. ... The Professors Cube (also known as Rubiks Professor) is a mechanical puzzle invented by Udo Krell. ...

Contents

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 U.S. Patent 3,655,201  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. For other uses, see Budapest (disambiguation). ... The Nuremberg International Toy Fair (Nürnberger Spielwarenmesse) is a international toy and game trade show which takes place annually in Nuremberg, Germany. ...


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. Occident redirects here. ... Alexander cuts the Gordian Knot, by Jean-Simon Berthélemy (1743–1811) The Gordian Knot is a legend associated with Alexander the Great. ...


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.[3]


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.[4][5][6]


Rubik applied for another Hungarian patent on October 28, 1980, and applied for other patents. In the United States, Rubik was granted U.S. Patent 4,378,116  on March 29, 1983, for the Cube. is the 301st day of the year (302nd in leap years) in the Gregorian calendar. ... Year 1980 (MCMLXXX) was a leap year starting on Tuesday (link displays the 1980 Gregorian calendar). ... is the 88th day of the year (89th in leap years) in the Gregorian calendar. ... For the Jimi Hendrix song, see 1983. ...


Recently, 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. Rubiks Cube being speedsolved. ... is the 170th day of the year (171st in leap years) in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Common Era (or Anno Domini), in accordance with the Gregorian calendar. ...


Workings

Rubik's Cube partially disassembled.
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 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 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 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. Image File history File links Download high-resolution version (1024x768, 95 KB) Other versions Originally from en. ... Image File history File links Download high-resolution version (1024x768, 95 KB) Other versions Originally from en. ...


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).


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),[7] or about 4.3 × 1019, 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. This article is about permutation, a mathematical concept. ... Main article: Names of large numbers A quintillion is a number written as either: a 1 followed by 18 zeros (10 to the 18th power, as used in the short scale system of numeration. ... Long scale is the English translation of the French term échelle longue, which designates a system of numeric names in which the word billion means a million millions. ... Long scale is the English translation of the French term échelle longue, which designates a system of numeric names in which the word billion means a million millions. ... One thousand million (1,000,000,000) is the natural number following 999,999,999 and preceding 1,000,000,001. ...


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. A millimetre (American spelling: millimeter), symbol mm is an SI unit of length that is equal to one thousandth of a metre. ... A light year, abbreviated ly, is the distance light travels in one year: roughly 9. ...


In fact, there are (8! × 38) × (12! × 212) = 519,024,039,293,878,272,000 (about 5.2 × 1020 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 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. Main article: Names of large numbers A quintillion is a number written as either: a 1 followed by 18 zeros (10 to the 18th power, as used in the short scale system of numeration. ... Long scale is the English translation of the French term échelle longue, which designates a system of numeric names in which the word billion means a million millions. ... In mathematics, groups are often used to describe symmetries of objects. ...


Despite the vast number of positions, all Cubes can be solved in twenty-five or fewer moves (see Optimal solutions for Rubik's Cube). [8] [9] 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 a jumbled set of encyclopedias (26 volumes) in alphabetical order has a larger complexity (26! = 4.03 × 1026), but is less difficult. Wikibooks has a book on the topic of How to solve the Rubiks Cube There are many algorithms to solve scrambled Rubiks Cubes. ...


Center faces

The original (official) Rubik's Cube has no orientation markings on the center 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"[citation needed]. Modern representation of the Lo Shu square as a magic square. ... In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. ... Set of 78 French style playing cards with twenty two atouts, typically used to play French Tarot Set of 52 French style playing cards with two jokers Set of 52 Anglo-American style playing cards Some typical Anglo-American playing cards from the Bicycle brand Paul Cézanne - The Card... “Trump card” redirects here. ...


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).


Solutions

Wikibooks
Wikibooks has a book on the topic of

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 1981. 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. After practice, solving the Cube layer by layer can be done in under one minute. Other general solutions include "corners first" methods or combinations of several other methods. Most tutorials teach the layer by layer method, as it gives an easy-to-understand step-by-step guide on how to solve it. Image File history File links Wikibooks-logo-en. ... Wikibooks logo Wikibooks, previously called Wikimedia Free Textbook Project and Wikimedia-Textbooks, is a wiki for the creation of books. ... David Singmaster is a professor of Mathematics at Londons South Bank University. ...


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 2×2×3, and then the incorrect edges are solved using a three-move algorithm, which eliminates the need for a possible 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. Jessica Fridrich (born Jiri Fridrich) is the inventor of the most commonly used method for speed-solving the Rubiks Cube, better known as speedcubing. ... Flowcharts are often used to graphically represent algorithms. ... Lars Petrus (born in 1960) made his name as an internationally accomplished speed cuber in 1982 when he became the national champion of Sweden, and went on to finish fourth overall at the first official Rubiks Cube World Championships held in Budapest, Hungary. ...


Solutions 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 four or five algorithms but are generally inefficient, needing around 100 twists on average to solve an entire Cube. In comparison, Fridrich's advanced solution requires learning roughly 120 algorithms but allows the Cube to be solved in only 55 moves on average. A different kind of solution developed by Ryan Heise[10] 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. Jessica Fridrich is the inventor of the most commonly used method for speed-solving the Rubiks Cube, better known as speedcubing. ...


The search for optimal solutions

The manual solution methods described above are intended to be easy to learn, but much effort has gone into finding even faster solutions to the Rubik's Cube. Wikibooks has a book on the topic of How to solve the Rubiks Cube There are many algorithms to solve scrambled Rubiks Cubes. ...


In 1982, David Singmaster and Alexander Frey hypothesized that the number of moves needed to solve the Rubik's Cube, given an ideal algorithm, might be in "the low twenties". In 2007, Daniel Kunkle and Gene Cooperman used computer search methods to demonstrate that any 3×3×3 Rubik's Cube configuration can be solved in a maximum of 26 moves. [8] [11] In 2008, Tomas Rokicki lowered the maximum to 23 moves. [12] [13] Work continues to try to reduce the upper bound on optimal solutions. The arrangement known as the super-flip, where every edge is in its correct position but flipped, requires 20 moves to be solved (Using the notations explained below, these are: U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2.). No arrangement of the Rubik's Cube has been discovered so far that requires more than 20 moves to solve.


Move notation

Rubik's Cube in a tilted state.
Rubik's Cube in a tilted state.
Rubik's Cube in solved state.
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), or sometimes (but rarely) it is called "direction inferred notation" or "DIN". 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. Image File history File links Rubik's_cube. ... Image File history File links Rubik's_cube. ... Image File history File links This page meets Wikipedias criteria for speedy deletion. ... Image File history File links This page meets Wikipedias criteria for speedy deletion. ... Flowcharts are often used to represent algorithms. ...

  • 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 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
  • f (Front two layers): the side facing you 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 Cube up
  • y (rotate): rotate the Cube to the left
  • z (rotate): rotate the Cube on its side to the right

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 a superscript ²) means to turn the face a half-turn (the direction does not matter). So R is right side clockwise, but R' is right side counter-clockwise. When x, y or z are primed, simply rotate the cube in the opposite direction. When they are squared, rotate it twice. For 'z', you should still be viewing the same front face when rotating.


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 '-' counter-clockwise, 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.)


However there is another (less common) system of move notation. It is very similar to cube notation, but has a key difference that makes it less daunting to new cube solvers. It is called "direction displayed notation" or "DDN". Each move is represented by two letters. The first indicates which side is to be moved, the second indicates which direction that side is turned. from the F point of view.

  • F (Front): The side facing you. "R" means turn it right or clockwise. "L" means turn it left or counter-clockwise.
  • U (Up): The side on top. "R" means turn it right (from the F perspective). "L" means turn it left (from the F perspective).
  • D (Down): The side on the bottom. "R" means turn it right (from the F perspective). "L" means turn it left (from the F perspective).
  • R (Right): The side to right. "D" means turn it downward (from the F perspective). "U" means turn it upward (from the F perspective).
  • L (Left): "D" means turn it downward (from the F perspective). "U" means turn it upward (from the F perspective).
  • B (Back): The side opposite from the side facing you. This side is hardly ever used in algorithms of any notation let alone direction displayed notation. However if you need to know, first turn the entire cube so that the B side faces you then rotate it as if you were rotating the F side. "R" means turn it right or clockwise. "L" means turn it left or counter-clockwise.

To indicate a half move just put a 2 at the end of the first letter. To indicate rotation of the cube as a whole, use the same notation for direction displayed notation as one would for Singmaster notation. (x y z)


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) 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: Flowcharts are often used to graphically represent algorithms. ...

  1. Turn the Front face 180 degrees.
  2. Turn the Up face 90 degrees counter-clockwise.
  3. Turn the Right face 90 degrees counter-clockwise.
  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 counter-clockwise.
  8. Turn the Up face 90 degrees counter-clockwise.
  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. Flowcharts are often used to graphically represent algorithms. ...


4×4×4 and larger cubes use slightly different notation to incorporate the 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). 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 and record times

Many speedcubing competitions have been held to determine who can solve the Rubik's Cube in the shortest time. The number of contests is going up every year; there were 72 official competitions from 2003 to 2006; 33 were in 2006 alone. Rubiks Cube being speedsolved. ...


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. The official winner, with a record of 38 seconds, was Jury Froeschl, born in Munich. For other uses, see Munich (disambiguation). ... is the 72nd day of the year (73rd in leap years) in the Gregorian calendar. ... AUGUST 25 1981 US Marine Sean Vance is Born on the 25th of August {ear nav|1981}} Year 1981 (MCMLXXXI) was a common year starting on Thursday (link displays the 1981 Gregorian calendar). ... White Petrolatum Petroleum jelly, vaseline, petrolatum or soft paraffin [2] is a semi-solid mixture of hydrocarbons (with carbon numbers mainly higher than 25),[3] originally promoted as a topical ointment for its healing properties. ...


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. For other uses, see Budapest (disambiguation). ... is the 156th day of the year (157th in leap years) in the Gregorian calendar. ... Year 1982 (MCMLXXXII) was a common year starting on Friday (link displays the 1982 Gregorian calendar). ... A sixteen-year-old Vietnamese high school student from Los Angeles, Minh Thai won the world championship in Budapest (June 1982) by unscrambling a Rubiks Cube ® in 22. ... Los Angeles and L.A. redirect here. ...


Since 2003, competitions are decided by the best average (middle three of five attempts); but the single best time of all tries is also recorded. The World Cube Association maintains a history of world records [14]. In 2004, the WCA made it mandatory to use a special timing device called a Stackmat timer. The World Cube Association is an association that holds Rubiks Cube competitions. ... Stackmat timers are the official timing device for speed stacking. ...


The current world records for both average and single times were set by Yu Nakajima in 2008, he set an average of 11.28 seconds and a best time of 8.72 on May 4, 2008 at Kashiwa Open 2008. is the 124th day of the year (125th in leap years) in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Common Era (or Anno Domini), in accordance with the Gregorian calendar. ...


Alternative competitions

In addition, informal alternative competitions have been held, inviting participants to solve the Cube under unusual situations. These include:

  • Blindfolded solving[15]
  • Solving the Cube with one person blindfolded and the other person saying what moves to do, known as "Team Blindfold"
  • Solving the Cube underwater in a single breath[16]
  • Solving the Cube using a single hand[17]
  • Solving the Cube with one's feet[18]

Of these informal competitions, the World Cube Association only sanctions blindfolded, one-handed, and feet solving as official competition events.[19]


Custom built puzzles

A lot of puzzles have been built in the past resembling the Rubik's Cube or just its working (as a permutation puzzle). For example, a Cuboid is a Rubik's Cube extended with one or more extra layers, which are glued or fused onto it. Since the extra layer is not functional, the cube will function like the original Cube, although in some cases the extra pieces do place additional constraints on the moves that can be used. People often make extended cubes thanks to the unique shapes they can form. The most common extended cube is the 3×3×5 (extended) cube.


Rubik's Cube software

Four-dimensional Rubik's Cube

Several computer programs have been written to perform various functions, such as, among other things, solving the Cube or animating it. In general, these programs can be considered to fall in one of several categories: Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ...

  • Timers
  • Solvers
  • Graphical programs
    • Animations
    • Image generators
  • Analyzers

Some of the software handles not only the 3×3×3 cube, but also other puzzle types. There is even software for virtual puzzles that do not have a real life counterpart. Examples are the four-dimensional cube, the five-dimensional cube and the gliding cube.


In addition these programs may also record player metrics, store and generate scrambled Cube positions or offer either animations or online competition. Solvers are usually given a scramble, after which a solution is generated automatically. Graphical programs can generate a static image or animate the Cube and its motions, e.g. using Java or Flash. Programs may also analyze sequences of moves and transform them to other notations or give player metrics. This article is about the Java island. ...


See also

  • List of Rubik's Cube software
  • N-dimensional sequential move puzzles

A very popular category of Rubiks cube software is the playable 3D Rubiks Cube (animated cube), often implemented as a Java applet, which has a long history. ...

References

  • 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 [ISBN 0-465-04566-9] by Douglas R. Hofstadter contains two insightful chapters regarding Rubik's Cube and similar puzzles, "Magic Cubology" and "On Crossing the Rubicon", 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

Douglas Richard Hofstadter (born February 15, 1945) is an American academic. ...

Notes

  1. ^ a b Rubik's Official Online Site
  2. ^ Marshall, Ray. Squaring up to the Rubchallenge. icNewcastle. Retrieved August 15, 2005.
  3. ^ Moleculon Research Corporation v. CBS, Inc.
  4. ^ Hofstadter, Douglas R. (1985). Metamagical Themas. Basic Books. Hofstadter gives the name as "Ishige".
  5. ^ http://cubeman.org/cchrono.txt
  6. ^ The History of Rubik's Cube - Erno Rubik
  7. ^ Martin Schönert "Analyzing Rubik's Cube with GAP": the permutation group of Rubik's Cube is examined with GAP computer algebra system
  8. ^ a b Kunkle, D.; Cooperman, C. (2007). "Twenty-Six Moves Suffice for Rubik's Cube". Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC '07), ACM Press. 
  9. ^ KFC (2008). "Rubik’s cube proof cut to 25 moves".. 
  10. ^ Ryan Heise's method
  11. ^ Julie J. Rehmeyer. Cracking the Cube. MathTrek. Retrieved on 2007-08-09.
  12. ^ Tom Rokicki. Twenty-Five Moves Suffice for Rubik's Cube. Retrieved on 2008-03-24.
  13. ^ Rubik's Cube Algorithm Cut Again, Down to 23 Moves. Slashdot. Retrieved on 2008-06-05.
  14. ^ World Cube Association Official Results. World Cube Association. Retrieved on 2008-02-16.
  15. ^ Rubik's 3x3x3 Cube: Blindfolded records
  16. ^ Rubik's Cube 3x3x3: Underwater
  17. ^ Rubik's 3x3x3 Cube: One-handed
  18. ^ Rubik's 3x3x3 Cube: With feet
  19. ^ Competition Regulations, Article 9: Events. World Cube Association (2008-04-09). Retrieved on 2008-04-16.

This article is about the day of the year. ... Year 2005 (MMV) was a common year starting on Saturday (link displays full calendar) of the Gregorian calendar. ... In mathematics, a permutation group is a group G whose elements are permutations of a given set M, and whose operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself); the relationship is often written as (G,M). ... GAP (Groups, Algorithms and Programming) is a computer algebra system for computational discrete algebra similar to Mathematica with particular emphasis on, but not restricted to, computational group theory. ... Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 221st day of the year (222nd in leap years) in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Common Era (or Anno Domini), in accordance with the Gregorian calendar. ... is the 83rd day of the year (84th in leap years) in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Common Era (or Anno Domini), in accordance with the Gregorian calendar. ... is the 156th day of the year (157th in leap years) in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Common Era (or Anno Domini), in accordance with the Gregorian calendar. ... is the 47th day of the year in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Common Era (or Anno Domini), in accordance with the Gregorian calendar. ... is the 99th day of the year (100th in leap years) in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Common Era (or Anno Domini), in accordance with the Gregorian calendar. ... is the 106th day of the year (107th in leap years) in the Gregorian calendar. ...

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Rubik's cube

Ernő Rubik Ernő Rubik (born July 13, 1944) is a Hungarian inventor, sculptor and professor of architecture. ... Solved Pocket Cube Scrambled Pocket Cube Pocket Cube with one side tilted The Pocket Cube is the 2×2×2 equivalent of a Rubiks cube. ... Rubiks Revenge in solved state The Rubiks Revenge is the 4×4×4 version of Rubiks Cube. ... The Professors Cube (also known as Rubiks Professor) is a mechanical puzzle invented by Udo Krell. ... The Square One, also known as Back to Square One, is a puzzle similar to the Rubiks Cube, invented by Karel Hršel and Vojtěch Kopský around 1990. ... The Skewb in unscrambled state The Skewb is a magic polyhedron—that is, a mechanical puzzle in the style of Rubiks Cube—invented and marketed by Uwe Mèffert. ... A scrambled sudokube puzzle Sudokube is a variation on a Rubiks Cube in which each face resembles one-ninth of a Sudoku grid: the numbers from one to nine. ... The 6-color Megaminx The 12-color Megaminx, in a star-pattern arrangement The Megaminx is a dodecahedron-shaped puzzle similar to the Rubiks Cube. ... The Pyramorphix in its solved state. ... Pyraminx in its solved state The Pyraminx (aka Pyramix) is a tetrahedron-shaped puzzle similar to the Rubiks Cube. ... The Skewb Diamond The Skewb Diamond is an octahedron-shaped puzzle similar to the Rubiks Cube. ... Mefferts version of the 6-color Skewb Ultimate The Skewb Ultimate is a twelve-sided puzzle derivation of the Skewb. ... The 12-color Dogic The Dogic is an icosahedron-shaped puzzle like the Rubiks cube. ... Alexanders Star is a mechanical puzzle invented by Adam Alexander in 1982. ... Rubiks Magic Rubiks Magic, like Rubiks Cube, is a mechanical puzzle invented by the Hungarian sculptor and professor of architecture Ernő Rubik and first manufactured by Matchbox in the mid-1980s. ... Snake in a ball solution. ... Missing Link is a mechanical puzzle invented in 1981 by Steven P. Hanson and Jeffrey D. Breslow. ... Rubiks Revolution is based on a puzzle called Rubiks Cube and includes six electronic games. ... Rubiks Clock, like Rubiks Cube, is a mechanical puzzle invented by the Hungarian sculptor and professor of architecture Ernő Rubik. ... Jessica Fridrich (born Jiri Fridrich) is the inventor of the most commonly used method for speed-solving the Rubiks Cube, better known as speedcubing. ... Lars Petrus (born in 1960) made his name as an internationally accomplished speed cuber in 1982 when he became the national champion of Sweden, and went on to finish fourth overall at the first official Rubiks Cube World Championships held in Budapest, Hungary. ... Ron van Bruchem (born in the Netherlands) is a well known speedcuber. ... It is proposed that this article be deleted, because of the following concern: Absolutely no evidence of notability If you can address this concern by improving, copyediting, sourcing, renaming or merging the page, please edit this page and do so. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Tyson Francis Mao (Born on May 8, 1984 in San Francisco, California), is one of the worlds top competitive Rubiks Cube solvers. ... Leyan Andrew Lo (born November 24, 1985), held the world record of 11. ... This article or section may contain original research or unverified claims. ... Wikibooks has a book on the topic of How to solve the Rubiks Cube There are many algorithms to solve scrambled Rubiks Cubes. ... Rubiks Cube being speedsolved. ... A Rubiks Cube In mathematics, the Rubiks Cube is an interesting object because it provides a tangible representation of a mathematical group. ... A very popular category of Rubiks cube software is the playable 3D Rubiks Cube (animated cube), often implemented as a Java applet, which has a long history. ...


  Results from FactBites:
 
The Rubiks Cube Solution (3411 words)
After spending hours and days twisting and turning the vaunted cube in vain, many resorted to removing and replacing the multi-colored facelets of the cube in a dastardly attempt to cheat the seemingly infallible logic of the cube, while others simply tossed it to the side and dubbed it impossible.
The Rubik's cube, it seemed, had defeated all.
On our cube, we would need the bottom of the Red T cubie to be either Yellow (which when moved to the right would match up with the Red and Yellow centers) or the Red-White cubie (which on our cube could be moved left, matching up with the Red and White centers).
Rubik's Cube (Rubix cube, Rubick's cube) - history, solution and where to buy one (838 words)
The Rubik's cube is one of the most puzzling toys of all time.
Cheap imitations of Rubik's cube flooded the market and with the 'original' cube in short supply, pirates were having a field day.
Pirated cubes appeared in all shapes and sizes - from just one centimetre across and hanging off a chain (there was also a legal version of this too), to cylinders and shaved corners to give the appearance of 16 sides.
  More results at FactBites »

 
 

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