## Wednesday, July 23, 2014

### Bandage Cube Kit—Bandaged YZ Family

I don't know why exactly, but I like this configuration a lot. It is just fun to play with. Maybe it is the three 2x2x1 blocks. Maybe it is because edges can be solved with EPS and corners permuted with Triple-EPS, and oriented with Sune/Mirror. Perhaps because although setups are needed to get around the bandaging, they are not overly complex. There is just something about the feel that is enjoyable.

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.

First Solve:
1. Bandaged pieces—easy
2. Edges—easy
3. Permuting Corners—easy
4. 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.
Second solve:
1. Bandaged pieces—easy
2. Edges—easy
3. Permuting Corners—not easy, but not difficult
4. Orienting Corners—interesting
Orienting Corners—
1. Need to twist 1, 2, 5, 7
2. Did 1 with 3-cycle and 3-cycle' (2)
3. Did 5 with 3-cycle and 3-cycle' (4)
4. 3-cycle 2 to 3
5. Double swap 3 to 1 and 7 to 2 (Triple-EPS)
6. Twist 2 and 7 with 3-cycle and 3-cycle' (2)
7. Noticed I now needed an n=1 3-cycle, so didn't have to undo steps 4 and 5. :D
Throughout the solve I hold green on the left and white up.

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
3-cycle': (RUi RiU) x n Ri Di RUiRi D RURi R (UiR URi) x n

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.