Thursday, August 7, 2014

Bandage Cube Kit—Cross Road Cube

We traveled from Prague to Sacramento on the 5th of the month. Along the way I worked on the Cross Cube and documented the adventure in a binder. Here's the story—

A lot like the Meffert's Bandage Cube, or the Bicube, only the 2x2x2 block of pieces diagonally opposite the 1x1x1 of the Bicube is unbandaged, so is indeed more 2x2x2 ish.

Since I have had the Meffert's cube for a long time and am somewhat familiar with the screwy color scheme he used, I tiled the Cross Cube to match, so as to avoid any confusion.

On the first scramble the blue-white and orange-white edges fell into place as I oriented the centers. The big challenge was pairing up the blue-orange-white 2x1x1. After that I solved it as the Bicube with no problem.

On the second scramble I made sure each piece was scrambled. Getting the 2x2x2 corner was somewhat challenging but I finally got it and went to my Bicube solve. All was going well until I got to what should have been the last step—the 743 3-cycle. But instead, 7 and 3 had to swap and flip. Huh?!?

Figuring it had something to do with the 2x2x2 corner, I used it to twist one of the pieces to the other one. Things were pretty messed up so I re-solved and 7 and 3 were no longer swapped. 7 and 8 were! But at least they weren't flipped. :D

Decided on a new approach. Point greens down since with the little ones on the blue side they could be pointing back without pointing them back. Then put the 1x1x1 on top on the left and do a mirror solve. By the time I did what I could do, I put the greens at the back and fixed the top and... found 3 and 6 were swapped.

Tried something else—don't remember what—ended up needing a 4-cycle, which is not any better than a swap. So I did a 5-cycle to see what would happen. 4 and 6 were swapped. Did the place #5 algorithm. It then needed a 6-cycle. Did it repeatedly, and it just cycled through a bunch of 6-cycles until it came back to the single swap.

A little background. I got up at 4 AM in Prague to get ready to go to the airport and fly home. We flew to London. Had a several hour layover. Flew to Dallas. Had an even longer layover. On the flight to Sacramento I wrote:
Altogether it has been a very long day. In Dallas I scrambled the 2x2x2 corner and couldn't get it back. During the biginning of the flight to Sacramento I tried and failed and was getting frustrated. Being awake for 24 hours may or may not have something to do with it.
After forcing down a can of Ginger Ale I tried to sleep. I slept some although I dept waking up. Finally I decided to get the cube out, solve it as much as possible, then retile the pieces I couldn't solve. But instead of the red-yellow-green corner, I was using the blue-white-orange one as the #2 corner. After several tries through the #5 routine I noticed the blue-white-orange had twisted and was paired up perfectly with the blue-white edge. I put them home. Then #6, #8, and #1. I don't think I had to cycle 743. It was solved! No pair swapped! Somewhere in the trying to solve the 2x2x2 corner I suppose, I remedied the swap problem. 

Played around with it for a bit more. Somehow twisted #2 clock and #8 anti. All else was still solved. How? I had an idea, but hadn't written it down. Started writing. 

Fi U L F U Li U2 (#5)
F R U Fi Ui
Fi U L F U Li U2 (#5)
Ri
Fi U L F U Li U2 (#5)
Double swap; 743; double swap; 743 x 2

The above twists #2 anti and #8 clock.

I still do not know how to systematically fix the situation in which 2 pieces need to swap.

August 7, 2014
Today I saw that
Fi U L F U Li U2 (#5)
F R U Fi Ui
Fi U L F U Li U2 (#5)
Ri
Fi U L F U Li U2 (#5)
times two twists #2 clock and #8 anti. Can that be?

And after more experimentation and solving, I finally scrambled it in such a way that I got the single swap again. And still have no idea how or why or what to do about it.

August 8, 2014
OK. I have an idea. An intelligent guess. From solved I did R Bi Ri. That took the orange-white edge out of place. Then I tried to keep track of things but got hopelessly lost eventually, but managed to get the orange-white edge back home without turning B 90°. Upon solving the cube from there, I ended up with 2 swapped pieces, 3 and 4. I just don't have a nice neat algorithm for doing it. I think the single 90° turn of B key to the single swap situation. It isn't polished but I got something.

R B Ui L Ui Fi L D2 L2 does a 90° turn of B then restores the blue-orange and white-orange edges. It wasn't easy to unlock the resulting bandages on F and R, but eventually got it and solved the puzzle! Yay!

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