Pocket Cube

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A scrambled Pocket Cube

The Pocket Cube (also known as the Mini Cube) is the 2×2×2 equivalent of a Rubik's Cube. The cube consists of 8 pieces, all corners.

History[edit]

Solved versions of, from left to right: original Pocket Cube, Eastsheen cube, V-Cube 2, V-Cube 2b.

In March 1970, Larry D. Nichols invented a 2×2×2 "Puzzle with Pieces Rotatable in Groups" and filed a Canadian patent application for it. Nichols's cube was held together with magnets. Nichols was granted U.S. Patent 3,655,201 on April 11, 1972, two years before Rubik invented his Cube.

Nichols assigned his patent to his employer Moleculon Research Corp., which sued Ideal in 1982. In 1984, Ideal lost the patent infringement suit and appealed. In 1986, the appeals court affirmed the judgment that Rubik's 2×2×2 Pocket Cube infringed Nichols's patent, but overturned the judgment on Rubik's 3×3×3 Cube.[1]

Permutations[edit]

Pocket cube with one side tilted

Any permutation of the eight corners is possible (8! positions), and seven of them 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. This is because all 24 possible positions and orientations of the first corner are equivalent due to the lack of fixed centers. This factor does not appear when calculating the permutations of N×N×N cubes where N is odd, since those puzzles have fixed centers which identify the cube's spatial orientation. The number of possible positions of the cube is

The maximum number of turns required to solve the cube is up to 11 half or quarter turns, or up to 14 quarter turns only.[2]

The number a of positions that require n any (half or quarter) turns and number q of positions that require n quarter turns only are:

n a q a(%) q(%)
0 1 1 0.000027% 0.000027%
1 9 6 0.00024% 0.00016%
2 54 27 0.0015% 0.00073%
3 321 120 0.0087% 0,0033%
4 1847 534 0.050% 0.015%
5 9992 2256 0.27% 0.061%
6 50136 8969 1.36% 0.24%
7 227536 33058 6.19% 0.90%
8 870072 114149 23.68% 3.11%
9 1887748 360508 51.38% 9.81%
10 623800 930588 16.98% 25.33%
11 2644 1350852 0.072% 36.77%
12 0 782536 0% 21.3%
13 0 90280 0% 2.46%
14 0 276 0% 0.0075%

The two-generator subgroup (the number of positions generated just by rotations of two adjacent faces) is of order 29,160.[3]

Methods[edit]

A pocket cube can be solved with the same methods as a 3x3x3 Rubik's cube, simply by treating it as a 3x3x3 with solved (invisible) centers and edges. More advanced methods combine multiple steps and require more algorithms. These algorithms designed for solving a 2x2x2 cube are often significantly shorter and faster than the algorithms one would use for solving a 3x3x3 cube.

The Ortega method,[4] also called the Varasano method,[5] is an intermediate method. First a face is built (but the pieces may be permuted incorrectly), then the last layer is oriented (OLL) and lastly both layers are permuted (PBL). The Ortega method requires a total of 12 algorithms.

The CLL method[6] first builds a layer (with correct permutation) and then solves the second layer in one step by using one of 42 algorithms.[7]

The most advanced method is the EG method,[8] named after Eric Gunner. It also starts by building a layer (in any permutation), but then solves the rest of the puzzle in one step. It requires knowing 128 algorithms, 42 of which are the CLL algorithms.

World records[edit]

Vicente Albíter of Mexico solving it in 1.55 seconds at the Mexican Open 2008

The world record solve is 0.49 seconds, set by Maciej Czapiewski of Poland on 20 March 2016 at Grudziądz Open 2016.[9]

The world record average of 5 solves (excluding fastest and slowest) is 1.35 seconds, also set by Maciej Czapiewski on 24 February 2018 at Warsaw Cube Masters 2018, with the times 1.25, (1.14), 1.31, (2.00) and 1.50 seconds.[10]

Top 5 solvers by single solve[edit]

Name Fastest solve Competition
Maciej Czapiewski 0.49s Grudziądz Open 2016
Michał Rzewuski 0.52s Grudziądz Open 2016
Mats Valk 0.56s Kaohsiung Open 2016
Rami Sbahi 0.58s Canadian Open 2015
Kim Roger Høyland Larsen 0.58s Sandnes Open 2016

Top 5 solvers by average of 5 solves[edit]

Name Fastest average Competition
Maciej Czapiewski 1.35s Warsaw Cube Masters 2018
Kevin Gerhardt 1.37s Hessen Open 2018
Will Callan 1.39s Tea Time Spring 2018
Rami Sbahi 1.45s Michigan 2017
Andy Denney 1.48s Coach Pigeon 2018

See also[edit]

References[edit]

External links[edit]