After a couple solves I decided to share my enjoyment of this puzzle on the twistypuzzles.com thread. I noticed that Burgo listed the Bandaged YZ as a difficult puzzle. I couldn't believe it. So I checked the pictures and noticed that the three little tiles across the middle of the green side are supposed to be one long tile. Maybe I should graduate from my very simplified one to his Unbandaged one before attempting the terribly bandaged one!
Burgo's Unbandaged YZ (below) didn't seem difficult either, although he lists it as difficult. Perhaps I should have scrambled it and solved it several times to see if there were any hidden surprises. But the blue and white faces could be turned from the get-go so 3 of the 5 edges and 4 of the 5 corners that need to be solved are easy to handle. And turning the blue face 180° makes the orange yellow corner edge pair easily accessible. Furthermore doing blue' yellow' puts all little ones on top in such a way that all manner of EPS and Sunes can be done. I even had to swap two edges and it was no problem at all with my standard edge swapper algorithm—U' R U' R' ....
At first Burgo's Bandaged YZ (see below) seemed like it was going to be another relatively easy solve.
- Bandaged pieces—easy
- Permuting Corners—easy
- Orienting Corners—required coming up with an all new technique that I've never seen before which uses a combination of Edge Piece Series and a Corner 3-cycle.
- Bandaged pieces—easy
- Permuting Corners—not easy, but not difficult
- Orienting Corners—interesting
- Need to twist 1, 2, 5, 7
- Did 1 with 3-cycle and 3-cycle' (2)
- Did 5 with 3-cycle and 3-cycle' (4)
- 3-cycle 2 to 3
- Double swap 3 to 1 and 7 to 2 (Triple-EPS)
- Twist 2 and 7 with 3-cycle and 3-cycle' (2)
- Noticed I now needed an n=1 3-cycle, so didn't have to undo steps 4 and 5. :D
3-cycle: (RUi RiU) x n Ri RUiRi Di RURi D R (UiR URi) x n
- n = 0 moves UFL > URF > RDF
- n = 2 moves UFL > RFU > RDF
- n = 4 moves UFL > FUR > RDF
- n = 1 moves UFL > FRD > RUB
The idea is that you can twist corner 1 by cycling it to 2 with n = 0, then cycle it back with n = 2 or 4 depending on how it needs to twist. Notice the UFLs and RDFs above? But the piece at 2 twists. That is the key. Same thing works for corner 3. Cycle 3 to 2, then back to 3 with the proper twist. 2 takes care of itself since you can't have just one twisted corner.