The title says it all. What’s the best strategy for solving a Rubik’s cube?
Like this.
Okay. That’s for the 3x3x3 cube. Now, how do you solve the 4x4x4 & 5x5x5 cubes?
For those and the original I dismantled mine and put it back together in the “correct” way. I know not the way it is supposed to be done but while I liked various puzzles growing up I for some reason found Rubik’s Cube incredibly boring. Pulling it apart and reassembling it was the most fun thing I found to do with it.
The generic strategy is to find a normal tower of subgroups of Rubik’s group G with G[sub]0[/sub] the trivial group and G[sub]n[/sub] Rubik’s group itself. Optimally, each group G[sub]k[/sub] is a semidirect product of G[sub]k-1[/sub] and Z[sub]4[/sub], with the generator of Z[sub]4[/sub] being a twist in G. Then find such a tower of minimal height.
The same strategy can be applied to “magic” polyhedra of all kinds, replacing Rubik’s group by the group of maneuvers on the polyhedron and Z[sub]4[/sub] by the cyclic group generated by a basic maneuver.
Thanks for clearing that up. 
An impossibly vague question gets an impossibly vague answer. What is “best”? Memorizable? Shortest path? (what do you consider “a move”?) I’ve got a sequence that’s only provably below 120-some moves, but I find it rather elegant. Others have provably shorter algorithms that require memorizing larger basic chunks. Thistlethwaite is down to 45 moves, but it’s pretty much impossible for a human to implement it. There’s no evidence that “God’s Algorithm” (which would get down to 22-23 moves) is anything other than a giant lookup table.
If the OP wants an algorithm, Google awaits with dozens upon dozens of them for the taking. If he can find it, Jeffrey Adams’ solution by commutators is especially nice (G/[G,G] = Z[sub]2[/sub]!). To explain notation and the large chunks of primitive maneuvers any algorithm uses would be prohibitive here. The only reasonable response is to give a solution schema, which I’ve done.
Well, yes. I was mostly joking; to a non-mathematician (which I’m assuming the OP is, given the nonspecificity of the question) your reply makes as much sense as if you’d started hopping up and down wildly while screaming “ooga mo booga woogoo foo!” Just sayin’.
Play around with a Rubik’s cube long enough and eventually you discover that there are certain patterns of moves that switch or flip only 2-4 subcubes at a time, leaving the rest of the cube the same as it was. By switching and flipping subcubes you can eventually shuffle all the subcubes into place.
Yeah, seriously, mathochist…
I always liked to peel the sticker off the center square, take the screw out, disassemble and reassemble “solved,” now that’s elegant,
Larry
Actually, the easier way is to spray paint each side with the required color!
or like me just take all stickers off and replace accordingly with the proper colors all together…my mom thought I was a smart kid…for like a week.
My brother got really good at Rubik’s cube solving. He got it to under a minute, a few times. Not especially unique, but it sure impressed people like me, who couldn’t do it at all.
I preferred to disassemble somebody else’s cube, rotate one corner so that it was now unsolvable and then smirk whilst they valiantly tried. I think this may have been born of either envy or disdain for those with the patience to persevere.
Well, while nowhere near as elegant as the
listed above, disassembly was also my favoured method. However, I used to do it by rotating the top and bottom through 45 degrees and then twisting hard in a vertical direction, which would cause the thing to come apart without the need for tools or disturbance of stickers. 
I’ve always wanted to report this: I once dreamed about solving the cube and had a sort of solution come to me, at least about one side of it. And when I woke up I tried it, and darned if it didn’t work. Now, I realize that getting one side of the cube isn’t much of a big deal, but I was so excited about having a solution to a problem come to me in a dream that I was just jazzed for weeks and weeks. Not quite the benzene ring, but we all have to start someplace, don’t we? I’m going to take a nap now and when I get up, look out, Fermat.
In Soviet Union, Rubik’s Cube solves you!
I did almost the same thing. Got one of those books with the moves you need to solve it. Memorized the moves, and could consistantly knock the thing out in under 3 minutes. Not world record time but fun to impress friends with.
Can’t do it anymore though since I forgot all the moves.