Pocket Cube
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Image:Pocket cube solved.jpg Image:Pocket cube.jpg Image:Pocket cube tilt.jpg The Pocket Cube is the 2×2×2 equivalent of a Rubik's cube. The cube consists of 8 corner cubelets, and no other types of cubelets.
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Permutations
Any permutation of the 8 corner cubelets is possible (8! positions), and 7 of the cubelets can be independently rotated (37 positions). There is nothing identifying the orientation of the cube in space, reducing the positions by a factor of 24. The number of possible positions of the cube is
- <math>\frac{8!\,3^7}{24}=7!\,3^6=3674160</math>
which factors as <math>2^4 3^8 5^1 7^1</math>.
The maximum number of twists required to solve the cube is up to 11 full twists, or up to 14 quarter twists. An optimal (least number of twists) solution from any position can be found by a computer with a brute force algorithm.
The number f of positions that require n full twists and number q of positions that require n quarter turn twists are:
| n | f | q |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 9 | 6 |
| 2 | 54 | 27 |
| 3 | 321 | 120 |
| 4 | 1847 | 534 |
| 5 | 9992 | 2256 |
| 6 | 50136 | 8969 |
| 7 | 227536 | 33058 |
| 8 | 870072 | 114149 |
| 9 | 1887748 | 360508 |
| 10 | 623800 | 930588 |
| 11 | 2644 | 1350852 |
| 12 | 782536 | |
| 13 | 90280 | |
| 14 | 276 |
Records
Gunnar Krig holds the world record for the fastest time solving the pocket cube in competition, with a time of 3.94 seconds set at the Swedish Cube Day 2005 competition. The record for the fastest average of five cubes is held by Shotaro "Macky" Makisumi, with a time of 6.29 seconds set at the Horace Mann Spring Competition 2005. [1]
See also
- Rubik's Cube (3×3×3)
- Rubik's Revenge (4×4×4)
- Professor's Cube (5×5×5)
External links
- Pocket Cube Solver - a browser-based CGI solver
- http://www.ganpuzzle.com/vcube222.htm Solve by learning 2 simple tricks with step by step animation accompanied by detailed descriptions of each move.fr:Pocket Cube