Pocket Cube
The Pocket Cube (also known as the Mini Cube) is a 2×2×2 combination puzzle invented in 1970 by American puzzle designer Larry D.
In February 1970, Larry D. Nichols invented a 2×2×2 "Puzzle with Pieces Rotatable in Groups" and filed a Canadian patent application for it.
Nichols was granted U.S. patent 3,655,201 on April 11, 1972, two years before Rubik invented the 3×3×3 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.
The 2×2×2 Rubik's cube, has eight permutation objects (corner pieces), three possible orientations of the eight corner pieces and 24 possible rotations of the cube, as there is no unique top side.
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 (similar to what happens in circular permutations).
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 largest order of an element in this group is 45.
[4] 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: The two-generator subgroup (the number of positions generated just by rotations of two adjacent faces) is of order 29,160.
[6] 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.
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.
One layer is built with correct permutation similarly to normal CLL, however one corner piece can be incorrectly oriented.
The rest of the cube is solved, and the incorrect corner orientated in one step.
[12] It starts by building a face like in the Ortega method, but then solves the rest of the puzzle in one step.
Top-level speedcubers may also 1-look the puzzle, [13] which involves inspecting the entire cube and planning out the best solution in the 15 seconds of inspection allotted to the solver before the solve.
Notation is based on 3×3×3 notation but some moves are redundant (All moves are 90°, moves ending with ‘2’ are 180° turns): [14] The world record for the fastest single solve time is 0.43 seconds, set by Teodor Zajder of Poland at Warsaw Cube Masters 2023.
[15] The world record average of 5 solves (excluding fastest and slowest) is 0.86 seconds set by Yiheng Wang (王艺衡) of China at Chengdu Spring Open 2025.
[16] An average of 0.78 seconds was set by Wang previously with times of 0.74, (0.70), (0.97), 0.78, and 0.81 seconds, but frame-by-frame analysis revealed his use of 'sliding,' a technique breaking several of the World Cubing Association's (WCA) regulations.
After deliberation between the WCA's Board of Directors and WCA Regulations Committee, Wang was retroactively penalized with additional seconds added to four of his solves.
