# Difference between revisions of "Rubik's Cube Fact sheet"

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* The 4x4x4 has 7! * 3^6 * (24!)^2 / (4!)^6 positions. This is about 7.4 * 10^45. | * The 4x4x4 has 7! * 3^6 * (24!)^2 / (4!)^6 positions. This is about 7.4 * 10^45. | ||

* There are 56 pieces on this cube: 8 corner pieces, 24 edge pieces, and 24 center pieces. There are also some number of hidden internal pieces, depending on the brand. The 4x4x4 cube has a total of 96 stickers. | * There are 56 pieces on this cube: 8 corner pieces, 24 edge pieces, and 24 center pieces. There are also some number of hidden internal pieces, depending on the brand. The 4x4x4 cube has a total of 96 stickers. | ||

− | * It is unknown how many moves are required to solve a 4x4x4 cube, but it has been proven to be at | + | * It is unknown how many moves are required to solve a 4x4x4 cube, but it has been proven to be at least 31. |

* The 4x4x4 supercube, the cube where all center pieces are distinguishable, is the only n x n x n supercube where the [[permutation]] of the edge pieces is completely independent of the rest of the cube. | * The 4x4x4 supercube, the cube where all center pieces are distinguishable, is the only n x n x n supercube where the [[permutation]] of the edge pieces is completely independent of the rest of the cube. | ||

* The current single solve record is 21.54 seconds by [https://www.worldcubeassociation.org/results/p.php?i=2009ZEMD01 Feliks Zemdegs], and the average of 5 record is 25.53 seconds by [https://www.worldcubeassociation.org/results/p.php?i=2012PARK03 Max Park]. | * The current single solve record is 21.54 seconds by [https://www.worldcubeassociation.org/results/p.php?i=2009ZEMD01 Feliks Zemdegs], and the average of 5 record is 25.53 seconds by [https://www.worldcubeassociation.org/results/p.php?i=2012PARK03 Max Park]. | ||

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* The 5x5x5 has 12! * 8! * 2^10 * 3^7 * (24!)^3 / (4!)^12 positions. This is about 2.83 * 10^74. | * The 5x5x5 has 12! * 8! * 2^10 * 3^7 * (24!)^3 / (4!)^12 positions. This is about 2.83 * 10^74. | ||

* There are 99 pieces on this cube: one core, 8 corners, 36 edges, and 54 centers. There are also a total of 150 stickers. | * There are 99 pieces on this cube: one core, 8 corners, 36 edges, and 54 centers. There are also a total of 150 stickers. | ||

− | * It is unknown how many moves are required to solve a 5x5x5 cube, but it has been proven to be at | + | * It is unknown how many moves are required to solve a 5x5x5 cube, but it has been proven to be at least 50. |

* The current single solve record is 41.27 seconds by [http://www.worldcubeassociation.org/results/p.php?i=2009ZEMD01 Feliks Zemdegs], and the average of 5 record is 49.32 seconds also by [http://www.worldcubeassociation.org/results/p.php?i=2009ZEMD01 Feliks Zemdegs]. | * The current single solve record is 41.27 seconds by [http://www.worldcubeassociation.org/results/p.php?i=2009ZEMD01 Feliks Zemdegs], and the average of 5 record is 49.32 seconds also by [http://www.worldcubeassociation.org/results/p.php?i=2009ZEMD01 Feliks Zemdegs]. | ||

[[Category:Puzzle theory]] | [[Category:Puzzle theory]] |

## Revision as of 14:21, 26 May 2017

## 3x3x3 Rubik's Cube facts

Here are some 3x3x3 Rubik's cube facts:

- It was originally known as the Magic Cube.
- It was invented by Ernö Rubik of Hungary in 1974, first patented in 1975, and first released in 1977.
- Over 300 million Rubik's Cubes and imitation cubes have been sold worldwide, making it the best-selling toy ever.
- There are 43,252,003,274,489,856,000 ways a cube can be scrambled - that's 12! * 8! * 2^10 * 3^7, 4.3 * 10^19 or 43 quintillion positions! To give you an idea of how big that number is, if there were one cube scrambled for every legal position, they would cover the surface of the earth about 150 times!
- The number of unsolved configurations on a Rubik's cube is a prime number.
- A normal cube has 21 pieces, consisting of one core, 8 corners, and 12 edges, and a total of 54 stickers.
- There exist computer optimal solvers of the Rubik's Cube, and all checked positions have had a solution of 20 moves or fewer, with a small number of positions (such as the superflip) having an optimal solution of 20 moves. An international team consisting of Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge proved that all positions can be solved in 20 or fewer moves, so the exact upper bound is 20.
- The first official World Record for solving the Rubik's Cube was 22.95 seconds by Minh Thai; the current single solve record is 4.73 by Feliks Zemdegs, and the average of 5 record is 6.45 seconds, also held by Feliks Zemdegs.

## 2x2x2 Cube facts

Here are some 2x2x2 Cube facts:

- The official name for this cube is the Pocket Cube or Mini Cube.
- Rubik patented the design for this cube in 1983.
- There are 7! * 3^6 or 3,674,160 positions to this cube. It is equivalent to solving only the corners of the Rubik's Cube.
- A 2x2x2 cube has just 8 pieces, all corner pieces, and a total of 24 tiles. Most mechanisms have a number of hidden internal pieces as well.
- The 2x2x2 cube can always be solved in 11 moves or fewer.
- The current single solve World Record is 0.49 seconds, by Maciej Czapiewski and the average of 5 record is 1.51 seconds by Lucas Etter.

## 4x4x4 Cube facts

Here are some 4x4x4 Cube facts:

- The official name for this cube is Rubik's Revenge, although it was invented not by Rubik but by Péter Sebestény.
- The 4x4x4 has 7! * 3^6 * (24!)^2 / (4!)^6 positions. This is about 7.4 * 10^45.
- There are 56 pieces on this cube: 8 corner pieces, 24 edge pieces, and 24 center pieces. There are also some number of hidden internal pieces, depending on the brand. The 4x4x4 cube has a total of 96 stickers.
- It is unknown how many moves are required to solve a 4x4x4 cube, but it has been proven to be at least 31.
- The 4x4x4 supercube, the cube where all center pieces are distinguishable, is the only n x n x n supercube where the permutation of the edge pieces is completely independent of the rest of the cube.
- The current single solve record is 21.54 seconds by Feliks Zemdegs, and the average of 5 record is 25.53 seconds by Max Park.

## 5x5x5 Cube facts

Here are some 5x5x5 Cube facts:

- The official name for this cube is the Professor's Cube, and it was invented not by Rubik but by Udo Krell.
- The 5x5x5 has 12! * 8! * 2^10 * 3^7 * (24!)^3 / (4!)^12 positions. This is about 2.83 * 10^74.
- There are 99 pieces on this cube: one core, 8 corners, 36 edges, and 54 centers. There are also a total of 150 stickers.
- It is unknown how many moves are required to solve a 5x5x5 cube, but it has been proven to be at least 50.
- The current single solve record is 41.27 seconds by Feliks Zemdegs, and the average of 5 record is 49.32 seconds also by Feliks Zemdegs.