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The Rubik's Revenge (also known as the 4×4×4 Rubik's Cube) is a 4×4×4 version of the Rubik's Cube. It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the Sebestény Cube until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube. Unlike the original puzzle (and other puzzles with an odd number of layers like the 5×5×5 cube), it has no fixed faces: the center faces (four per face) are free to move to different positions. Methods for solving the 3×3×3 cube work for the edges and corners of the 4×4×4 cube, as long as one has correctly identified the relative positions of the colours—since the center faces can no longer be used for identification.


Mechanics

The puzzle consists of 56 unique miniature cubes ("cubies") on the surface. These consist of 24 centres which show one colour each, 24 edges which show two colours each, and 8 corners which show three colours each. The original Rubik's Revenge can be taken apart without much difficulty, typically by turning one side through a 30° angle and prying an edge upward until it dislodges. The original mechanism designed by Sebestény uses a grooved ball to hold the centre pieces in place. The edge pieces are held in place by the centres and the corners are held in place by the edges, much like the original cube. There are three mutually perpendicular grooves for the centre pieces to slide through. Each groove is only wide enough to allow one row of centre pieces to slide through it. The ball is shaped to prevent the centre pieces of the other row from sliding, ensuring that the ball remains aligned with the outside of the cube. Turning one of the centre layers moves either just that layer or the ball as well.United States Patent 4421311
/ref> The Eastsheen version of the cube, which is slightly smaller at 6cm to an edge, has a completely different mechanism. Its mechanism is very similar to Eastsheen's version of the Professor's cube, instead of the ball-core mechanism. There are 42 pieces (36 movable and six fixed) completely hidden within the cube, corresponding to the centre rows on the Professor's Cube. This design is more durable than the original and also allows for screws to be used to tighten or loosen the cube. The central spindle is specially shaped to prevent it from becoming misaligned with the exterior of the cube.
/ref> Nearly all manufacturers of 4×4×4 use similar mechanisms. There are 24 edge pieces which show two coloured sides each, and eight corner pieces which show three colours. Each corner piece or pair of edge pieces shows a unique colour combination, but not all combinations are present (for example, there is no piece with both red and orange sides, if red and orange are on opposite sides of the solved Cube). The location of these cubes relative to one another can be altered by twisting the layers of the cube, 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. Edge pairs are often referred to as "," from double edges. For most recent cubes, the colours of the stickers are red opposite orange, yellow opposite white, and green opposite blue. However, there also exist cubes with alternative colour arrangements (yellow opposite green, blue opposite white and red opposite orange). The Eastsheen version has purple (opposite red) instead of orange.


Permutations

There are 8 corners, 24 edges and 24 centres. Any permutation of the corners is possible, including odd permutations. Seven of the corners can be independently rotated, and the orientation of the eighth depends on the other seven, giving 8!×37 combinations. There are 24 centres, which can be arranged in 24! different ways. Assuming that the four centres of each colour are indistinguishable, the number of permutations is reduced to 24!/(246) arrangements. The reducing factor comes about because there are 24 (4!) ways to arrange the four pieces of a given colour. This is raised to the sixth power because there are six colours. An odd permutation of the corners implies an odd permutation of the centres and vice versa; however, even and odd permutations of the centres are indistinguishable due to the identical appearance of the pieces.Cubic Circular Issue 7 & 8
David Singmaster David Breyer Singmaster (14 December 1938 – 13 February 2023) was an American-British mathematician who was emeritus professor of mathematics at London South Bank University, England. He had a huge personal collection of mechanical puzzles and ...
, 1985
There are several ways to make the centre pieces distinguishable, which would make an odd centre permutation visible. The 24 edges cannot be flipped, due to the internal shape of the pieces. Corresponding edges are distinguishable, since they are mirror images of each other. Any permutation of the edges is possible, including odd permutations, giving 24! arrangements, independently of the corners or centres. Assuming the cube does not have a fixed orientation in space, and that the permutations resulting from rotating the cube without twisting it are considered identical, the number of permutations is reduced by a factor of 24. This is because all 24 possible positions and orientations of the first corner are equivalent because of the lack of fixed centres. This factor does not appear when calculating the permutations of N×N×N cubes where N is odd, since those puzzles have fixed centres which identify the cube's spatial orientation. This gives a total number of permutations of :\frac \approx 7.40 \times 10^. The full number is possible permutationsCubic Circular Issues 3 & 4
David Singmaster David Breyer Singmaster (14 December 1938 – 13 February 2023) was an American-British mathematician who was emeritus professor of mathematics at London South Bank University, England. He had a huge personal collection of mechanical puzzles and ...
, 1982
(about septillion, 7.4 septilliard on the
long scale The long and short scales are two powers of ten number naming systems that are consistent with each other for smaller numbers, but are contradictory for larger numbers. Other numbering systems, particularly in East Asia and South Asia, ha ...
or 7.4 quattuordecillion on the short scale). Some versions of the cube have one of the centre pieces marked with a logo, distinguishing it from the other three of the same colour. Since there are four distinguishable positions for this piece, the number of permutations is quadrupled, yielding 2.96×1046 possibilities. Any of the four possible positions for this piece could be regarded as correct.


Solutions

There are several methods that can be used to solve the puzzle. One such method is the reduction method, so called because it effectively reduces the 4×4×4 to a 3×3×3. Cubers first group the centre pieces of common colours together, then pair edges that show the same two colours. Once this is done, turning only the outer layers of the cube allows it to be solved like a 3×3×3 cube. Another method is the Yau method, named after Robert Yau. The Yau method is similar to the reduction method, and it is the most common method used by speedcubers. The Yau methods starts by solving two centers on opposite sides. Three cross are then solved. Next, the four remaining centers are solved. Afterwards, any remaining are solved. This reduces down to a 3x3x3 cube. A method similar to the Yau method is called Hoya. It was invented by Jong-Ho Jeong. It involves the same steps as Yau, but in a different order. It starts with all centers being solved except for 2 adjacent centers. Then form a cross on the bottom, then solve the last two centers. After this, it is identical to Yau, finishing the edges, and solving the cube as a 3x3.


Parity errors

When reducing the 4×4×4 to a 3×3×3, certain positions that cannot be solved on a standard 3×3×3 cube may be reached. There are two possible problems not found on the 3×3×3. The first is two edge pieces reversed on one edge, resulting in the colours of that edge not matching the rest of the cubies on either face (OLL parity): Notice that these two edge pieces are swapped. The second is two edge pairs being swapped with each other (PLL parity), may be two corners swapped instead depending on situation and/or method: These situations are known as parity errors. These positions are still solvable; however, special algorithms must be applied to fix the errors. Some methods are designed to avoid the parity errors described above. For instance, solving the corners and edges first and the centres last would avoid such parity errors. Once the rest of the cube is solved, any permutation of the centre pieces can be solved. Note that it is possible to apparently exchange a pair of face centres by cycling 3 face centres, two of which are visually identical. Direct solving of a 4×4×4 is uncommon, but possible, with methods such as K4. Doing so mixes a variety of techniques and is heavily reliant on commutators for the final steps.


World records

The world record fastest solve is 15.71 seconds, set by
Max Park Max Park (born November 28, 2001) is an American speedcuber. Widely regarded as one of the greatest speedcubers of all time, he is one of only two speedcubers ever to win the World Cube Association (WCA) World Championship twice (the other b ...
of the
United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...
on June 8th 2024 at CMT Evergreen 2024 in
Evergreen, Colorado Evergreen is an Unincorporated area, unincorporated town, a post office, and a Census-designated place, census-designated place (CDP) located in and governed by Jefferson County, Colorado, Jefferson County, Colorado, U.S. The CDP is a part of th ...
. The world record for fastest average of five solves (excluding fastest and slowest solves) is 19.17 seconds, set by
Tymon Kolasiński Tymon Kolasiński is a Polish speedcuber widely regarded as one of the fastest and most consistent NxNxN solvers. He currently holds the fourth-best average of five 3x3x3 solves (by WCA standards) at 4.67 seconds, behind Yiheng Wang, Xuanyi Gen ...
of
Poland Poland, officially the Republic of Poland, is a country in Central Europe. It extends from the Baltic Sea in the north to the Sudetes and Carpathian Mountains in the south, bordered by Lithuania and Russia to the northeast, Belarus and Ukrai ...
on 8-9th February 2025 at Hvidovre NxN 2025 in Hvidovre, Denmark, with the times of (22.21), 19.55, 18.95, (17.84), and 19.01 seconds. The world record for fastest blindfolded solve is 51.96 seconds (including inspection), set by Stanley Chapel of the
United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...
on 28th January 2023 at 4BLD in a Madison Hall 2023, in
Wisconsin, United States Wisconsin ( ) is a U.S. state, state in the Great Lakes region, Great Lakes region of the Upper Midwest of the United States. It borders Minnesota to the west, Iowa to the southwest, Illinois to the south, Lake Michigan to the east, Michig ...
. The record for mean of three blindfolded solves is 59.39 seconds (including inspection), also set by Stanley Chapel of the
USA The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 states and a federal capital district, Washington, D.C. The 48 contiguous ...
on 13-15th June, 2025 at New York Multimate PBQ II 2025, in
Elmsford, New York Elmsford is a village in Westchester County, New York, United States. It is part of the New York metropolitan area. Roughly one square mile, the village is fully contained within the borders of the town of Greenburgh. As of the 2010 census, th ...
with the times of 57.83. 1:04.79, and 55.54 seconds.


Top 5 solvers by single solve


Top 5 solvers by average of 5 solves


Top 5 solvers by single solve blindfolded


Top 5 solvers by average of 3 solves blindfolded


In popular culture

In "Cube Wars", an episode from the animated series '' Whatever Happened to... Robot Jones?'', the students play a colored cube called the Wonder Cube which is similar to the Rubik's Revenge.


Reception

''
Games A game is a Structure, structured type of play (activity), play usually undertaken for entertainment or fun, and sometimes used as an Educational game, educational tool. Many games are also considered to be Work (human activity), work (such as p ...
'' included ''Rubik's Revenge'' in their "Top 100 Games of 1982", finding that it helped to solve the original Rubik's Cube that the center pieces did not move, but noted "That's not true of this Supercube, which has added an extra row of subcubes in all three dimensions."


See also

*
Pocket Cube The Pocket Cube (also known as the Mini Cube and Twizzle) is a 2×2×2 combination puzzle invented in 1970 by American puzzle designer Larry D. Nichols. The cube consists of 8 pieces, which are all corners. History In February 1970, Larry D. ...
(2×2×2) * Rubik's Cube (3×3×3) *
Professor's Cube The Professor's Cube (also known as the 5×5×5 Rubik's Cube and many other names, depending on manufacturer) is a 5×5×5 version of the original Rubik's Cube. It has qualities in common with both the 3×3×3 Rubik's Cube and the 4×4×4 Rubik's ...
(5×5×5) *
V-Cube 6 The V-Cube 6 is a 6×6×6 version of the original Rubik's Cube. The first mass-produced 6×6×6 was invented by Panagiotis Verdes and is produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a num ...
(6×6×6) *
V-Cube 7 The V-Cube 7 is a combination puzzle in the form of a 7×7×7 cube. The first mass-produced 7×7×7 was invented by Panagiotis Verdes and is produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a ...
(7×7×7) *
V-Cube 8 The V-Cube 8 is an 8×8×8 version of the Rubik's Cube. Unlike the original puzzle (but like the 4×4×4 and 6×6×6 cubes), it has no fixed centers: the center facets (36 per face) are free to move to different positions. The design was cove ...
(8×8×8) *
Combination puzzle In mathematics, a combination is a selection of items from a set (mathematics), set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a ...


References


Further reading

* ''Rubik's Revenge: The Simplest Solution'' by William L. Mason *''Speedsolving the Cube'' by Dan Harris, 'Rubik's Revenge' pages 100-120. *''The Winning Solution to Rubik's Revenge'' by
Minh Thai Minh Thai (born 1965 as Thái Minh) is a Vietnamese-American speedcuber. As a sixteen-year-old Eagle Rock High School student from Los Angeles, he won the first Rubik's Cube world championship on June 5, 1982 in Budapest by solving a Rubik's Cu ...
, with Herbert Taylor and M. Razid Black.


External links


Beginner/Intermediate solution to the Rubik's Revenge
by Chris Hardwick
'K4' Method
Advanced direct solving method.

A collection of pretty patterns for Rubik's Revenge
4x4x4 Parity Algorithms
at the Speedsolving Wiki
Program Rubik's Cube 3D Unlimited size
{{Rubik's Cube Rubik's Cube Novelty items Single-player games 1980s toys 1980s fads and trends Ideal Toy Company