# 2018/January/Rubiks Cube

### From charlesreid1

### projects

Rubiks cube projects and progress, January 2018:

- Started rubiks notes repository: https://git.charlesreid1.com/notes/rubiks-notes
- Started repo for investigating order of permutations: https://git.charlesreid1.com/charlesreid1/rubiks-cube-cycles
- Learning terminology/notation needed to solve this problem

### blog post

Blog post plan:

~~Notes on how the Rubiks Cube works and how to represent it with a 96-tuple (hint at square redundancy)~~- Notes on permutation notation and factoring into pieces, with intention of writing cycles, LCM

### blog post part 1

Link: https://charlesreid1.github.io/4x4-rubiks-cube-part-1-representation.html

~~Rubik's Cube: Part 1: Representation
~~

- Introduction: purpose, group theory, experiments, uncover behavior
- How does the Rubik's Cube work - pieces, colors, and faces
- Computer representation of a Rubik's Cube
~~Tuple representation of a Rubik's Cube~~

### blog post part 2

Link: https://charlesreid1.github.io/4x4-rubiks-cube-part-2-permutations.html

~~Rubik's Cube: Part 2: Permutations~~

~~Introduction: Study sequences and the permutations that result~~~~How do we represent a particular permutation? Start with n-tuple representation from prior post~~~~Now, when we rotate a piece, we can map the pieces involved in the rotation~~~~Sequential application of transformations result in new tuple, unique to cube permutation~~

### blog post part 3

Rubik's Cube Part 3: Cycles

- Introduction: studying behavior of cycles and predicting order of move sequence
- Intercalation product
- Factoring a permutation using Theorem A
- Factoring Rubik's Cube permutations
- Least common multiple and order
- Caveats

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