2018/January/Rubiks Cube
From charlesreid1
projects
Rubiks cube projects and progress, January 2018:
 Started rubiks notes repository: https://charlesreid1.com:3000/notes/rubiksnotes
 Started repo for investigating order of permutations: https://charlesreid1.com:3000/charlesreid1/rubikscubecycles
 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 96tuple (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/4x4rubikscubepart1representation.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/4x4rubikscubepart2permutations.html
Rubik's Cube: Part 2: Permutations

Introduction: Study sequences and the permutations that result 
How do we represent a particular permutation? Start with ntuple 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
Flags
Rubiks Cube notes on solving 3x3 and 4x4 Rubik's Cube
Cubes and Solutions: 2x2 Cube: Pocket Cube 3x3 Cube: Rubiks Cube · Rubiks Cube/Layer Method 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
