Pocket Cube
From Wikipedia, the free encyclopedia
The Pocket Cube is the 2×2×2 equivalent of a Rubik's cube. The cube consists of 8 corner pieces, and no other types of cubies.
Contents |
[edit] Permutations
Any permutation of the 8 corner cubies is possible (8 positions), and 7 of the cubies 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
which factors as 24385171. Or simply 3,674,160 permutations.
The maximum number of turns required to solve the cube is up to 11 full turns, or up to 14 quarter turns. An optimal (least number of turns) 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 |
[edit] Solutions
One method of solving the Pocket Cube is to consider it as a simplified Rubik's Cube; that is, one with all the center and edge pieces removed. Thus, the Pocket Cube can be solved by any method used to solve the regular Rubik's Cube by disregarding all steps that specifically deal with the permutation or orientation of the edge pieces. However, since the Pocket Cube lacks center pieces, this version is regarded as a little bit trickier than the 3x3x3 version.
[edit] Records
Anthony Hsu, from the USA, holds the world record for the fastest time solving the pocket cube in competition, with a time of 3.55 seconds set at the Trumbull Spring competition 2006, in Trumbull, Connecticut, USA. The record for the fastest average of five cubes is held by Łukasz Ciałoń, from Poland, with a time of 4.69 seconds set at the Polish Cube Fest 2006, in Poland. [1] [2]
[edit] Trivia
A Pocket Cube is visible on Brian Fantana's desk in the film Anchorman. This is presumably to emphasize his stupidity: he would be unable to even attempt a 3×3×3 cube.
[edit] See also
- Rubik's Cube (3×3×3)
- Rubik's Revenge (4×4×4)
- Professor's Cube (5×5×5)
- Speedcubing
[edit] External links
- Previous cubes - Nichols' 2×2 Cube used magnets to hold it together.
- Brief history of Erno Rubik's famous cube
- Rubik's Cube Tutorials - A absolute beginner's tutorial to gain insights into solving Rubik's cube.
| Rubik's Cube Edit |
|
Inventor Normal Rubik's Cube Cubic variation Non-cubic variation Derivative Notable player of Rubik's Cube Solutions Mathematics |
