From charlesreid1


Rubiks cube projects and progress, January 2018:

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


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


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