The Rubik's Revenge Cube scrambled.
Early Rubik's Revenge cube, with white opposite blue, and green opposite yellow.
An Eastsheen cube is on the left, and an official Rubik's Revenge is on the right.
A disassembled Rubik's Revenge, showing all the pieces and central ball.
A disassembled Eastsheen 4×4×4.
The Rubik's Revenge, also known as the 4x4x4, is the sequel cube to the Rubik's Cube. The idea of the Rubik's Revenge is that it has more combinations and ways to solve, which also makes it harder. It has 16 pieces on each side.
The Unicode character U+25A6 (▦) resembles this cube.
History[]
The Rubik's Revenge was patented by Péter Sebestény on December 20th 1981. It was originally going to be named the Péter Sebestény Cube, until a last minute change was made to attract fans of the original Rubik's Cube.
Design[]
Since the Rubik's Revenge has 16 cubies on one side, it is built differently than the 3x3x3. Unlike a 3x3x3 Cube, the RR has 4 center cubies on each side, and 12 edge cubies. The 3x3x3 is built on a cross-like object, with the center pieces fixed into place and the edges interlocking with each other, but the RR is built on a spherical body. The sphere that the RR is built on has 8 pieces lifted approximately 0.25" off of the sphere. The 8 pieces can be loosened or tightened with a screwdriver. The center cubies are snapped in where 4 pieces make one point. The edge cubies then interlock with the center pieces from 2 sides. The corner cubies fit between 2 sets of edge cubies. This design makes it harder to speedcube. To speedcube the RR, people make their own custom built Rubik's Cubes or buy higher quality 4x4x4's.
Permutations[]
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!/(4!6) arrangements. The reducing factor comes about because there are 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.[3] There are several ways to make the centre pieces distinguishable, which would make an odd centre permutation visible.
The 24 edges cannot be flipped, because the internal shape of the pieces is asymmetrical. 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.
The full number is 7 401 196 841 564 901 869 874 093 974 498 574 336 000 000 000 possible permutations[4] (about 7,401 septillion or 7.4 septilliard on the long scale or 7.4 quattuordecillion on the short scale).
Solving the Rubik's Revenge[]
Reduction Method[]
The Rubik's Revenge can be solved with formulas very similar to the 3x3x3 cube. Unlike the 3x3x3 cube, this cube has the center cubie is split into 4 smaller cubies, and 12 edge pieces split into 2 smaller cubies each. To solve the cube, you must solve the center cubies, by making a 2x2 square on the center of each side of the cube, each representing the color of that side in its solved state. You must then solve the edge pairs by placing each color pair on one edge of the cube together. After solving those, you can solve the cube with any method used on the 3X3X3 cube. The final step is to fix what is called a parity. The 4x4x4 can have two possible problems not found on the 3x3x3. The first is two edge pieces reversed on one edge, resulting in the colors for that edge not matching the rest of the cubies on either face. The second is two edge pairs, known as dedges, being flipped with each other. Two more algorithms are required to fix these parities.
Yau Method[]
A more advanced method where some centers and edges are solved early on, reducing the number of moves needed later in the solve.
World Records[]
The world record for fastest solve is 15.71 seconds, set by Max Park of the United States on 8 June 2024 at CMT Evergreen 2024. The world record for fastest average of five solves (excluding fastest and slowest solves) is 19.17 seconds, set by Tymon Kolasiński of Poland on 9 February 2025 at Hvidovre NxN 2025. The world record for fastest blindfolded solve (including inspection time) is 51.96 seconds, set by Stanley Chapel of the United States on 29 January 2023 at 4BLD in a Madison Hall 2023. The average 4x4 blind world record is 59.39 seconds, also set by Chapel on 15 June 2025 at New York Multimate PBQ II 2025.
Trivia[]
- An early design of a Rubik's Revenge shows the Japanese Color Scheme, showing blue opposite with white, and yellow opposite with green. It is currently now blue opposite green, and yellow opposite white.