I got a 5x5 cube a while ago and was reading about how to solve it, and came across a nice, concise description of how one might invent moves which can be combined into algorithms which let you make incremental progress on a cube. I can't find it again, now!
Some of it was along the lines of (1) Figure out how to do something A to a single layer (while messing up the rest of the cube). (2) Observe that if you do A, then rotate the layer R, then undo A (A'), you have an operation B = A R A' which does something to only one layer of the cube. I assume that most moves in most common algorithms can be expressed in terms of a couple of fundamental techniques like this (probably using the words "commutator" and "conjugate"). Does someone have a link or reference that gives you the general meta-technique (even if it involves incompletely-specified things like "figure out an interesting sequence of moves in terms of their effect on a single layer")?
I'm interested in this because I'm not really interested in learning (again) and forgetting (again) any particular existing method for solving the cube, but it would be fun to be able to fiddle around with it in a less-than-random way and eventually arrive at a method, based on some higher-level principles.
I spent a disenjoyable 45 minutes one afternoon trying to learn the basics of solving; somehow, I could never get the cube "solved". Eventually, I discivered my daughter had rearranged a few of the stickers, resulting in an unsolvable cube.
There's actually a parity to the positions of the pieces that most people don't seem to know about. If you flip an edge or twist a corner, the whole cube becomes unsolvable.
You can also make it unsolvable by swapping stickers because each piece is unique. There is only one red/white/blue corner and only one green/yellow edge. Assuming standard color arrangement, there is no piece with both yellow and white, or both blue and green, or both red and orange.
The guy I learned to speedcube from was so good that we would secretly flip a corner or edge on his cube, challenge him to a race, and he would solve it to the point where only one piece was flipped, curse at us, fix it himself, and still beat us all by at least 10 seconds.
Yep, it would be readily apparent by that point. You wouldn't even need to "solve" it first; you would see pretty much instantly that the last layer was in an impossible position.
Source: I got into speedcubing for a couple years in high school and averaged in the 30s, with a record of 26 seconds.
A friend of mine got into a Rubik’s Cube in college. As a prank, we swapped the stickers on his cube and were amazed when he noticed it in a few seconds and correctly identified what was swapped. Familiarity with the invariants
The Heise method might be a great fit for you. Unlike most methods, it requires no memorization. And, unlike most methods that require no algs, it can be quite fast. AND it forces you to learn about how the cube actually works and to think in commutators and conjugates: https://www.ryanheise.com/cube/heise_method.html
Do you mean the short-term memory needed to apply the commutators or the conjugates? Otherwise you only really need to "memorize" the steps of the method.
I learned this method around 10 years ago, and I can still solve the cube without applying any memorized algorithms because of it. It really is the only fun way for me to solve the cube after all this time.
This. I used to forget the algos whenever I didn't touch the cube for 6 months. Then learnt Ryan's method. Picked up the cube 4 months later and found I can still solve it.
There's a method entirely based on group theory, a version of the original computer algorithm created to solve the cube (the Thistlewaite algorithm) simplified for use by a human [1]. It iteratively solves the cube into simpler groups that need a smaller moveset to solve (the last step uses only half turns on each face, no quarter turns). It requires only a bit of memorization, and you can understand exactly how the algorithm works. It's not a great speedsolving method, but you can get relatively fast with it: in [2] there's a solve below 30 seconds.
Some of it was along the lines of (1) Figure out how to do something A to a single layer (while messing up the rest of the cube). (2) Observe that if you do A, then rotate the layer R, then undo A (A'), you have an operation B = A R A' which does something to only one layer of the cube. I assume that most moves in most common algorithms can be expressed in terms of a couple of fundamental techniques like this (probably using the words "commutator" and "conjugate"). Does someone have a link or reference that gives you the general meta-technique (even if it involves incompletely-specified things like "figure out an interesting sequence of moves in terms of their effect on a single layer")?
I'm interested in this because I'm not really interested in learning (again) and forgetting (again) any particular existing method for solving the cube, but it would be fun to be able to fiddle around with it in a less-than-random way and eventually arrive at a method, based on some higher-level principles.