I have a bad memory and I don't want to keep looking up algorithms, so is there any way to solve it without algorithms?
P.S. I'm sorry if this is a stupid question... I just can't seem to find it on Google and I also don't care about speed.
P.P.S. I usually use this to solve it because of my terrible memory:
http://novakowski.net/cubesolvr/
If you don't care about speed, then you can do what I do, which uses
commutators. It's slow, but easy to remember, and if you want to solve other puzzles (such as Megaminx) then you can often use the same ideas without having to look up anything. I don't claim this is an original method at all, just something cobbled together from the basics.
First a word about what "without memorization" means to me. To me, it means all the move sequences you need, you created yourself without having to look them up, so if you forget them, you can recreate them again. To use commutators you do need to be able to remember the move sequence you used long enough to invert it, so you end up re-using sequences so that you don't get confused, but to me that's a different thing than memorizing a move sequence you read somewhere.
If you haven't ever solved a cube before, try solving one face a few times to build your intuition.
Outline:
1. Intuitively solve edge positions & orientations everywhere except one face.
2. Use commutators to solve edge positions.
3. Use commutators to solve edge orientations.
4. Use commutators to solve corner positions.
5. Use commutators to solve corner orientations.
For step 1, I solve edges on one face, then do the other 4. This is easy to do intuitively.
For the steps using commutators, the only commutators you need are with U, so, for a move sequence M: M U M' U'. (U2 or U' will work with the same sequences.)
So, to do steps 2,3,4,5, you need to find sequences to make each necessary adjustment while preserving on the U face all the earlier properties. Specifically, you will need to create sequences for:
2. Swap adjacent edges on U face, preserving other edge positions on U face.
3. Change one edge's orientation on U face, preserving edge positions on U face & other edge orientations on U face.
4. Swap adjacent corners on U face, preserving edges on U face, and preserving other corner positions on U face.
5. Rotate corner on U face, preserving edges on U face, corner positions on U face, and other corner orientations on U face.
The fun part about solving without memorization is creating these yourself, so I suggest doing that. A tip for doing that is to solve the U face intuitively first, then try to intuitively make the adjustment you want, and pay attention to which moves you did to do it. For completeness, here are the ones I use most often, but you should use whatever makes sense to you:
2. R' F R F2
3. R' U F' U'
4. R' D' L D L' R
5. R' D2 R F D2 F'
(Here's where the philosophical question of "what counts as memorization" comes up, and I would say these don't require memorization, because each is the most braindead obvious way to do it.)
When using these inside a commutator, whatever operation you're doing happens twice, so for the swap movements, you need to get comfortable with how two swaps combine into a length 3 cycle.
As an example of how these work inside a commutator, if I wanted to flip the orientation of the two closest U face edges, I'd do (R' U F' U') U' (U F U' R) U.
When you get comfortable, then learning to use conjugates can help make the corner re-positioning a bit less tedious. It's still a very slow method though.
