2018/January/Rubiks Cube: Difference between revisions
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* Notes on permutation notation and factoring into pieces, with intention of writing cycles, LCM | * Notes on permutation notation and factoring into pieces, with intention of writing cycles, LCM | ||
Rubik's Cube: Part 1: | Rubik's Cube: Part 1: Representation | ||
* Introduction: purpose, group theory, experiments, uncover behavior | * Introduction: purpose, group theory, experiments, uncover behavior | ||
* How does the Rubik's Cube work - pieces, colors, and faces | * How does the Rubik's Cube work - pieces, colors, and faces | ||
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* Tuple representation of a Rubik's Cube | * Tuple representation of a Rubik's Cube | ||
Rubik's Cube: Part 2: Permutations | Rubik's Cube: Part 2: Permutations | ||
* Introduction: Study sequences and the permutations that result | * Introduction: Study sequences and the permutations that result | ||
* How do we represent a particular permutation? Start with n-tuple representation from prior post | * How do we represent a particular permutation? Start with n-tuple representation from prior post | ||
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* Sequential application of transformations result in new tuple, unique to cube permutation | * Sequential application of transformations result in new tuple, unique to cube permutation | ||
Rubik's Cube Part 3: Cycles | Rubik's Cube Part 3: Cycles | ||
* Introduction: studying behavior of cycles and predicting order of move sequence | * Introduction: studying behavior of cycles and predicting order of move sequence | ||
* Intercalation product | * Intercalation product | ||
Revision as of 09:21, 11 January 2018
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
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