2018/January/Rubiks Cube

Rubiks cube projects and progress, January 2018:

• Started rubiks notes repository: https://charlesreid1.com:3000/notes/rubiks-notes
• Started repo for investigating order of permutations: https://charlesreid1.com:3000/charlesreid1/rubiks-cube-cycles
• Learning terminology/notation needed to solve this problem

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

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

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

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