2x2 Pocket Cube
My experience solving the 2x2 cube came when I realized that a 4x4 could be mixed in a way that would mimic the 2x2. From there I started working on solving the 2x2.
The solution procedure is basically:
- Solve the bottom layer (bottom 4 cubies)
- Get one corner piece's colors correct (mis-oriented ok)
- Get second corner piece's colors correct (mis-oriented ok)
- If only 2 pieces have colors oriented correctly, use algorithm to swap two other pieces
- Use algorithm to re-orient the positions (basically, same as final step of 3x3)
Solving the Bottom 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.
Case 1: Two corners ok
Case 2: Three corners ok
Rubiks Cubenotes on solving 3x3 and 4x4 Rubik's Cube
Cubes and Solutions:
2x2 Cube: Pocket Cube
4x4 Cube: Rubiks Revenge
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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