Pocket Cube
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.
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
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 |
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, because you don't know what each face's color needs to be (while in the 3x3x3 version the center pieces inform you of that). This is just a minor bother, though, because you can simply remember the cube's color configuration.
Records
Mátyás Kuti, from Hungary holds the world record for the fastest time solving the pocket cube in competition, with a time of 2.73 seconds set at the Czech Open in 2007.[1]
Trivia
At Rubik's online store, an easier version of the Pocket Cube exists, dubbed the "Junior Cube." [1]. This version has only two colors, with a picture of a monkey on one layer.
See also
- Pyramorphix, a pyramidal puzzle that uses the same mechanism
- Rubik's Cube (3×3×3)
- Rubik's Revenge (4×4×4)
- Professor's Cube (5×5×5)
- Speedcubing
Notes
- ^ "World Cube Association Official Results". Retrieved 2007-09-22.