2018/January/Rubiks Cube: Difference between revisions
From charlesreid1
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===blog post part 2=== | ===blog post part 2=== | ||
Rubik's Cube: Part 2: Permutations | <s>Rubik's Cube: Part 2: Permutations</s> | ||
* <s>Introduction: Study sequences and the permutations that result</s> | * <s>Introduction: Study sequences and the permutations that result</s> | ||
* <s>How do we represent a particular permutation? Start with n-tuple representation from prior post</s> | * <s>How do we represent a particular permutation? Start with n-tuple representation from prior post</s> | ||
* <s>Now, when we rotate a piece, we can map the pieces involved in the rotation</s> | * <s>Now, when we rotate a piece, we can map the pieces involved in the rotation</s> | ||
* Sequential application of transformations result in new tuple, unique to cube permutation | * <s>Sequential application of transformations result in new tuple, unique to cube permutation</s> | ||
===blog post part 3=== | ===blog post part 3=== | ||
Revision as of 08:08, 15 January 2018
projects
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
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
https://charlesreid1.github.io/4x4-rubiks-cube-part-1-representation.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
Rubik's Cube: Part 2: Permutations
Introduction: Study sequences and the permutations that resultHow do we represent a particular permutation? Start with n-tuple representation from prior postNow, when we rotate a piece, we can map the pieces involved in the rotationSequential 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
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