Pocket Cube
From Wikipedia, the free encyclopedia
The Pocket Cube (also Mini Cube, Junior Cube or Ice 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.
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[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
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] Records
Javier Paris holds the current world record of solving the pocket cube in competition, with a time of 1.63 seconds set at the Murcia Open in 2008.
[edit] Variants
At Rubik's online store, an easier version of the Pocket Cube exists, dubbed the "Junior Cube". This version has only two colors, with a picture of a monkey on one face.
[edit] 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
- Combination puzzles
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