Pocket Cube/Solution Method
Solution Method for Pocket Cube
The solution method for the pocket cube is as follows:
- Solve one corner of first layer(trivial - just orient it)
- Solve the remaining three corners of the first layer (i.e., finish one complete face of the cube and have half of it solved)
- Solve the top layer permutation (three possible cases: one corner solved, two corners solved, or all four corners solved)
- Solve the top layer orientation
A brief primer on move notation for the 2x2
Solve one corner of first layer
Trivial, but also important for orienting your mental model of the cube.
Solve remaining three corners of first layer
The 2x2 has a few patterns that can be applied from larger cubes, starting with the bottom.
In the process of solving the 3x3 using the beginners method, you start by solving the cross on the bottom, and then by moving the corners into place. The moves that help with moving the corners into place are useful in forming the bottom 4 cubies of the pocket cube - you basically have a cross-less cross.
So, solving the bottom layer of the 2x2 is largely intuitive.
Solve top layer permutation
There are four corner cubies on top layer, and three possible scenarios for the top layer permutation (arrangement of pieces relative to one another):
- One OK corner case - one of the four top-layer pieces is in its correct final solved position (not necessarily its final solved orientation); the remaining three pieces are not in their correct final solved positions.
- Two OK corners case - two of the four top-layer pieces are in their correct final solved position (not necessarily their final solved orientation); note that this scenarios is only possible if the two OK corners are adjacent pieces on the cube face. They will never be located on opposite sides of the cube face.
- Four OK corners case - you lucky duck! All four of the top-layer pieces are in their correct final solved position (but not necessarily their final solved orientation). You may skip this step entirely.
We provide algorithms for the first two scenarios.
(TBA: algorithms for 2x2 parity scenarios)
Solve top layer orientation
The last step, where the corners of a cube are all re-oriented together, can be done using the exact same algorithm sequence as on a 3x3, 4x4, or 5x5:
R' D' R D
Rubiks Cubenotes on solving 3x3 and 4x4 Rubik's Cube
Rubiks/Todo - task list for things to do on the wiki related to the rubiks cube pages
Combinatorics and Permutations:
Counting cube permutations: Rubiks Cube/Numbers
Representation of cube permutations: Rubiks Cube/Tuple
Permutation Algebra: Rubiks Cube/Permutations
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