I have 1 question: I used U2 B as pre-moves, shouldn't the undo premoves be B' U2?
I was wondering that same thing
Actually, it worked out right. Your pre-moves should be the moves at the end of your solve. The idea is this - because you applied the pre-moves, it means your "solved state" after the scramble is whatever the cube looked like when you first applied the scramble. But you figure out how to solve it to a normal solved state first. Now, to get back to the original state of the cube before applying the scramble, you need to apply the exact same moves you applied as pre-moves, which means you apply U2 B, just as you did before the scramble. That gives you a cube that looks just like it did before you applied the scramble.
What I don't understand is how you saw that you could do those pre-moves and get such a nice easy solution. What was your logical progression to think of it?
It is pretty hard to explain this, but I will try:
1. Perform the scramble with white on top and green on front.
2. D' makes a perfect column of orange-blue on the left. It also makes a line of green with red-orange on both sides. Red and orange are opposite colors, so this green line is also correct. Together this makes a pseudo 1x2x3 block.
3. Realize that to turn this pseuse 1x2x3 block into a pseudo 2x2x3 block all that is necessary are two more edges in the S-slice.
4. Realize that the best two positions for those two edges are UL and UR because the pseudo 1x2x3 block can be positioned at Up-Front with the green line correctly placed.
5. R2 puts an edge into the UR position with the correct orientation.
6. F2 moves the pseudo-1x2x3 block out of the way for the next edge.
7. B' L puts an edge into the UL position with the correct orientation and relative position compared to the UR edge.
8. F' finishes the pseudo-2x2x3 block.
9. Now to find out how to do the premoves you need to see that the green line is alread positioned correctly. So all you need to do is find the shortest move sequence that positions the white line and the blue-orange column
10. U2 positions the white line.
11. B positions the blue-orange column
12. Now that we know the premoves, undo all the moves (B' U2 F L' B F2 R2 D and undo the scramble.
13. Perform the premoves U2 B and do step 2 to 8 again. You can see that all pseudo-blocks are now real blocks.
After writing/reading step 9 to 13 it is also clear to me why I should finish wit U2 B and not B' U2
Chris: Before I tried to find a solution to your "big premove sequence + short triple extended cross F2L" I ran it through cube explorer. That found 15 moves optimal, so I decided not to try and find it. You already used 6 premoves and 5 regular moves, so the chances of me finding anything better than my own 27 move solution means I had to find a perfect solution and/or some cancellations. You just had bad luck with your last pair and no oriented edges on the last layer. All I could see was the obvious D R D' to form 3 last layer pairs and orient 2 last layer edges, but that only reduced the optimal solution to 14 moves.
