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I had a prof in college describe solving a rubik's cube as group conjugation (e.g. f * g * f^-1). For example, you find a way to swap two pieces on the top lay
by dunham 2y ago
I had a prof in college describe solving a rubik's cube as group conjugation (e.g. f * g * f^-1).
For example, you find a way to swap two pieces on the top layer and mangle the bottom (f), turn the top (g), and then do the opposite (f^-1), swapping a different pair and un-mangling the bottom. Between complementary swaps, edge flips, and corner rotations, you can build an entire solution with this technique. (My current version of this does the edges first, ignoring any damage to corners and then does corners.)
Somewhat related - many years ago there was a tutorial of the Gap computer algebra system that analyzed the rubik's cube group. I can't find the original, but there is a translation to Julia here: https://oscar-system.github.io/GAP.jl/stable/examples/ https://oscar-system.github.io/GAP.jl/stable/examples/
- eddd-ddde 2y agoYes! This is also how I learnt to solve Rubik's cubes. You eventually develop the intuition to solve any move without having to "memorize" anything.
- tripplyons 2y agoThis is exactly how the Old Pochmann method works for solving a Rubik's cube blindfolded! You can effectively come up with and memorize a sequence of corner swaps and edge swaps. It is probably the simplest method for solving a Rubik's cube sighted as well because of how simple it is.