Inspired by
What I did do was look at Lars' guide, just looking at the goals of each step in sequence without looking at the moves to get there. Here's how it progressed:
2x2x2 is easy.
2x2x3 is also easy.
Rotating the edges I figured out quite quickly.
2x3x3 takes me a long time but it's basically doable. I found this stage to be a bit random in progress towards the goal.
That leaves just the top layer to do. Here's where I departed from Lars' method a bit.
I figured out a few different variations of moves for manipulating the top layer which permute edges and corners and also turn corners, leaving edges unturned. This stage was a bit random. In fact very random. But I had a strong feeling that between the various moves I knew, some combination would solve the cube. I started by doing edges first and then corners, and ended up with all solved but 2 corners incorrectly rotated. I could also get 3 corners incorrectly rotated, or all 4, but I couldn't get none. (Just one is also impossible for parity reasons). Then I went back to Lars' steps and noticed he does corners before edges. So I tried that instead. And finally a solution occurred.
Having solved it, I checked Lars' actual moves. What he calls a Sune I had discovered also. And many variations thereof which do various things to the top layer.
I also have a different method from the old days: rather than starting with 2×2, 2x2x3, etc. I start with a layer (blue of course being the One True Layer) then proceed to the second layer. I have a move that is much easier to me than the 15-puzzle style second layer alignment I did when following Lars' steps. It leaves the top edges incorrectly rotated, but a variant of it can also be used on the top layer (multiple times if need be) to end up with 2 layers solved and top cross correctly rotated. From there it is just a matter of applying my move to permute 3 corners, then the Sune & variants to rotate corners and edges correctly.
I'm usually solving the cube in around 5 minutes. That'll do.
“It was wonderful, to see how, after only a few turns, the colors became mixed, apparently in random fashion. It was tremendously satisfying to watch this color parade. Like after a nice walk when you have seen many lovely sights you decide to go home, after a while I decided it was time to go home, let us put the cubes back in order. And it was at that moment that I came face to face with the Big Challenge: What is the way home?”
– Erno Rubik
I applaud your efforts, and congratulate you on your success. It's been fun following your trials, however brief. Your quick with puzzles. The inventor was 29 when he create and solved the cube, but the solving bit took about a month, a time during which he remained uncertain it was possible to find a method back to the solution. When you explained your found method for permuting 3 corners, I was quite impressed, but decided not to mention anything about how Lars' method contained this step – didn't want to taint the experiment 🙂 I was extra pleased that you seemed to find an alternative way to accomplish it. This is why I asked you for the sequence – I was quite curious. Have you compared since, and does your 3-corners trick create the same result? On a final note, 5 minutes is impressive.
I have a rather quick way from 2x3x3 to 3x3x3 if you're interested. Though it's not quite a set move, it does reduce it to far less than even a bit random. I imagine it's what Lars sees, or intends, but as I didn't quite pick it up directly from his instructions, it remains one of the few bits of the solution to which I feel I've contributed.
(http://livejournal.com/users/greatbiggary)
For doing the second layer, my move is as follows:
The first layer is the top. Say the top is blue and you are trying to get the red/yellow edge in position. Assume the red/yellow edge is somewhere on the bottom layer (and you can almost always choose the next edge to attack such that this is the case; if you can't then just do this move and then you will be able to).
Further assume, without loss of generality, that we are looking at the red face and the red/yellow edge is at the bottom of the face with yellow on the bottom and red facing us. What we basically want to do is move that edge anticlockwise so that it ends up between red and yellow.
The move to do this is:
L'U'F'ULF'BF
(http://livejournal.com/users/elbeno)
Er that B should be a D. L'U'F'ULF'DF.
(http://livejournal.com/users/elbeno)
*burbles*
(http://livejournal.com/users/sylvene)