2018/January/Rubiks Cube: Difference between revisions
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* Notes on how the Rubiks Cube works and how to represent it with a 96-tuple (hint at square redundancy) | * 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 | * Notes on permutation notation and factoring into pieces, with intention of writing cycles, LCM | ||
Rubik's Cube: Part 1: Tuples and 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 and Move Maps | |||
* 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 and Sequence Orders | |||
* 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== | ==Flags== | ||
Revision as of 09:20, 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: Tuples and 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 and Move Maps
- 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 and Sequence Orders
- 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