Pocket Cube

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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 1 Permutations 2 Solutions 3 Records 4 See also 5 External links

[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.

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

[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 Gunnar Krig, from Sweden, with a time of 5.38 seconds set at the Chalmers Open 2006, in Gothenburg, Sweden. [1]

[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

• 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.
• Previous cubes - Nichols' 2×2 Cube used magnets to hold it together.
• Pretty Patterns - A collection of pretty patterns for the Pocket Cube.
• Rubik's Cube Tutorials - A absolute beginner's tutorial to gain insights into solving Rubik's cube.