Puzzled 2: Bandage Cube Kit

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)

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)

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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Rubik's Cube Books

I got my first Rubik's Cube in the early nineteen eighties. The only way I could solve it was to take it apart and put it back together solved. Until, that is, I got some little books that explained sequences of moves that could be used to put pieces where you want them without messing up what was already in place.

The Simple Solution To Rubik's Cube
by James G. Nourse
Notes on Rubik's Magic Cube
by David Singmaster
Solve That Crazy, Mixed-up Cube Puzzle
by Don Frederick.

I think I put together my own strategy using bits and pieces gleaned from all three books. Eventually I lost interest and forgot how to complete the cube, forgot I had those books, and lost track of the cubes.

Mark Jeays' Working Corner Method

http://jeays.net/rubiks.htm

In 2007 my interest in Rubik's Cube was rekindled when I watched the movie The Pursuit of Happyness. Marae found my 1980s cube for me and I tried to solve it. Huh-uh. I could do part of it, but not the last layer. Looking online I found various tutorials. Mark Jeays included YouTube videos with his Solution 2. This method worked for me and although I no longer use it in its entirety, nor could I, as I have forgotten the yellow edges sequences, I still find the basic working corner technique helpful, and use a slightly modified version of his corner twisting technique at times.

In the summer of 2014 we packed 30 or so puzzles and flew to visit Raymond and Fam in the Czech Republic. Breann, who had learned this method and no other, made some comment about bubururu or something like that, and it piqued my curiosity. What were those algorithms, and how similar are they to the EPS technique I use now when using a working corner? So I looked them up. Actually, the three algorithms were for dealing with the two last edges solved, which either needed to be swapped, or flipped, or swapped and flipped. The swapper is very similar to the one I have learned and used since, but I actually like it better in one sense, with a slight modification.

To swap UR and FR without flipping:

U' R U' R' U' R U' R' U'

To swap and flip UR and FR:

F' U' F U' F' U' F U2

To flip UR and FR:

F' U F U' R U' R' U

Will I actually learn and use these? Probably not. But I like them. :)

There is a slightly different implementation of the Working Corner Method. Arnaud van Galen calls it the Keyhole Method. I like his demonstration better than the one I originally learned. It just dawned on me why he is able to get away with doing it the way he does. He goes ahead and finishes the F2L before going to the last layer, unlike the way Jeays uses the working corner (keyhole) to also get the last layer. Since I no longer use the working corner to get the last layer, I should implement Arnaud's technique.

Jasmine's Scalable Method

http://peter.stillhq.com/jasmine/rubikscubesolution.html

This was the next method I learned. For awhile the idea of speed cubing appealed to me. This promised to be a good beginner's method for those that wanted to go on to faster method's later. Now that I know what I know, I wouldn't recommend this method if your goal is to be able to consistently solve the cube in less than 30 seconds. Rubik's Speedsolver Champion Leyan Lo presents a beginner's method that I like the looks of although I've never learned it. I have recently watched Arnaud van Galen's complete beginner's method video series and recommend them. Gilles Roux presents a beginners' method that is very close to one of my favorite ways of solving the cube. The simplicity and comprehensibility make this method a good place to start if you want to understand the Rubik's Cube. Also, if you are interested in speedcubing you should check out this YouTube video.

After trying for months to get under a minute with both Jasmine's Method and the Corner's First Method—and failing, I finally decided to quit trying and just enjoy cubing at a nice slow pace.

Don't get me wrong. Jasmine's Method has its merits. The sequences for orienting the last layer edges and corners, and permuting the last layer edges are still in my arsenal of useful algorithms.

Adam Cheyer's Corners First Method

Philip Marshall's Ultimate Solution

http://helm.lu/cube/MarshallPhilipp/
After learning to solve the cube corners first, what is next? An Edges First Method! This was a very difficult tutorial to follow, but once I got it, it was my favorite way to solve the cube for awhile. It uses only a few algorithms, and when you are finished solving the cube you feel like you've solved the puzzle, not just used memorized sequences to unscramble it.

Gilles Roux presents a beginners' method that could be used to solve the cube edges first. The simplicity and comprehensibility make this method a good place to start if you want to understand the Rubik's Cube. His technique is much easier to follow than Marshall's.