3x3x3 Fewest Moves:
yD2R'UF2R'FL2FL2RUF2R'F'RF'B2R2U'B2L2F2D' (25)
yD2R'UF2: Obvious 1x2x3.
R'FL2FL2RU: There are of course other promising opposite 1x2x3, but no other that prepares following steps so nicely.
F2R'F'RF'(L2): In the "Sune" class, it's the best sequence for the edges.
From here (17 moves), there's still a 3-cycle of edges needed. Maybe you can try to insert it before to optimize. I don't like insertions.
Time: About 30 minutes.
Gilles.
Excellent, Gilles! After rewriting it without cube rotation, it's this
= D2 B' U R2 B' R F2 R F2 B U_R2 B' R' B R' L2 B2 U' L2 F2 R2 D' (23)
I didn't know you count cube rotation as 2 moves ;-)
An alternative continuation based on 9-move edge flipping and corner rotations would be:
_ (U R U2 B U B2 R B R2) B' R2 B F2 (23) which also has three more modifications
_ U R U2 B U B2 R_ F D2 B' D2 F B2 (23)
_ U R U2 B U B2 R_ B2 F' U2 B' U2 F'(23)
_ U R U2 B U B2 R_ F2 B' L2 B' L2 B' (23)
If you add a requirement stating that no more than two quarter turns can appear in sequence in solutions, here they are.
I wondered whether there is one shorter finish. Cube Explorer finds what I cannot:
U F' U B' F U2 F R B' R B2 F -> (22)
