Solving the Rubik's Cube with Group Theory

on YouTube ↗31m

" summary

Scala code uses the Group typeclass in Cats plus a small custom permutation DSL to model the cube as a subdirect product of an 8-corner permutation and a 12-edge permutation with orientations and parity constraints. The implementation generates commutators and conjugates to produce three-cycles (only ~56 distinct target cycles needed) and searches for algorithms that intersect at one piece. A Bluetooth cube and live coding demonstrate a working solver (edges ignored in the demo, cube sync briefly out of step). The approach leverages cycle decomposition, inverses and group products to convert moves into searchable data.

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" chapters (11)

1. 0:00Intro
2. 0:29Agenda
3. 1:31Group definition
4. 3:03Permutations
5. 6:59Group Theory
6. 7:34Group Permutations
7. 9:15Rubiks Cube
8. 15:25Commutators
9. 17:25Parity
10. 18:34Conjugates
11. 21:19Demonstration

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