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 Algorithms 5.4 Relevance and application of mathematical group theory 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
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,
Packaging of Rubik's Cube, Toy of the year 1980–Ideal Toy Corp., made in Hungary In the mid-1970s,
A standard
The current colour scheme of a Rubik's Cube The original (3×3×3)
8 ! × 3 7 × ( 12 ! / 2 ) × 2 11 = 43 , 252 , 003 , 274 , 489 , 856 , 000 displaystyle 8!times 3^ 7 times (12!/2)times 2^ 11 =43,252,003,274,489,856,000 which is approximately 43 quintillion.[46] The puzzle was originally advertised as having "over 3,000,000,000 (three billion) combinations but only one solution".[47] 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[46] 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
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.[51] 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.[52] 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,[53] 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
Blindfolded solving[74] Multiple blindfolded solving, or "multi-blind", in which the contestant solves any number of cubes blindfolded in a row[75] Solving the Cube using a single hand[76] Solving the Cube with one's feet[77] Solving the Cube in the fewest possible moves [78] 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 memorizing 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, held jointly by
Average time: The world record average of the middle three of five
solve times (which excludes the fastest and slowest) is 5.80 seconds,
set by
One-handed solving: The world record fastest one-handed solve is 6.88
seconds, set by
Feet solving: The world record fastest
Blindfold solving: The world record fastest
Multiple blindfold solving: The world record for multiple Rubik's Cube
solving blindfolded is 43 out of 44 cubes, set by Mark Boyanowski of
the
Fewest moves solving: The world record of fewest moves to solve a
cube, given one hour to determine one's solution, is 19. This has been
achieved by Tim Wong of the
Non-human solving: The fastest non-human
Highest order physical n×n×n cube solving: Kenneth Brandon solved a 17×17×17 cube in a total of 7.5 hours.[91] Top 5 solvers by single solve Name Fastest solve Competition SeungBeom Cho (조승범) 4.59s ChicaGhosts 2017 Feliks Zemdegs 4.59s Hobart Summer 2018 Patrick Ponce 4.69s Ralley In The Valley 2017 Mats Valk 4.74s Jawa Timur Open 2016 Drew Brads 4.76s Bluegrass Spring 2017 Top 5 solvers by average of 5 solves Name Fastest average Competition Feliks Zemdegs 5.80s Malaysia Cube Open 2017 Max Park 6.18s Reno Fall 2017 Seung Hyuk Nahm (남승혁) 6.43s China Championship 2017 Kai-Wen Wang (王楷文) 6.51s Kaohsiung Autumn Open 2017 Patrick Ponce 6.53s Maryland 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.[94] Variations Variations of Rubik's Cubes. Top row: V-Cube 7, Professor's Cube, V-Cube 6. Bottom row: Rubik's Revenge, original Rubik's Cube, Pocket Cube. Clicking on a cube in the picture will redirect to the respective cube's page. An 11×11×11 cube There are different variations of Rubik's Cubes with up to thirty-three 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) was until December 2017 the largest (and most expensive, costing more than two thousand dollars) commercially sold cube. A working design for a 22×22×22 cube exists and was demonstrated in January 2016,[95] and a 33x33 in December 2017.[96] Chinese manufacturer ShengShou has been producing cubes in all sizes from 2×2×2 to 10×10×10 (as of late 2013),[97] and have also come out with an 11x11x11. 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[98] 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
All five platonic solid versions of Rubik's cube 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 Kepler-Poinsot
polyhedra, such as
Novelty keychain Puzzles have been built resembling the
Chrome Cube Lab
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. Archived from the original on January 20, 2013. 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). "
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 Wikimedia Commons Textbooks from Wikibooks Learning resources from Wikiversity Official website
Safecracker Method: Solving
v t e Rubik's Cube Puzzle inventors Ernő Rubik Uwe Mèffert Tony Fisher Panagiotis Verdes Oskar van Deventer Rubik's Cubes Overview 2×2×2 (Pocket Cube) 3×3×3 (Rubik's Cube) 4×4×4 (Rubik's Revenge) 5×5×5 (Professor's Cube) 6×6×6 (V-Cube 6) 7×7×7 (V-Cube 7) 8×8×8 (V-Cube 8) Cubic variations Helicopter Cube Skewb Square 1 Sudoku Cube Nine-Colour Cube Void Cube Non-cubic variations Tetrahedron Pyraminx
Octahedron
Dodecahedron
Icosahedron Impossiball Dogic Great dodecahedron Alexander's Star Truncated icosahedron Tuttminx Cuboid
Virtual variations (>3D) MagicCube4D
MagicCube5D
MagicCube7D
Derivatives Missing Link Rubik's 360 Rubik's Clock Rubik's Magic Master Edition Rubik's Revolution Rubik's Snake Rubik's Triamid Rubik's Cheese Renowned solvers Erik Akkersdijk Yu Nakajima Bob Burton, Jr. Jessica Fridrich Chris Hardwick Rowe Hessler Leyan Lo Shotaro Makisumi Toby Mao Tyson Mao Frank Morris Lars Petrus Gilles Roux David Singmaster Ron van Bruchem Eric Limeback Anthony Michael Brooks Mats Valk Feliks Zemdegs Collin Burns Lucas Etter Solutions Speedsolving Speedcubing Methods Layer by Layer CFOP Method Roux Method Corners First Optimal Mathematics God's algorithm
Superflip
Thistlethwaite's algorithm
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