Puzzled 2: Curvy Rhombohedron Skewb

Monday, February 17, 2014

Curvy Rhombohedron Skewb

The first couple solves I just started putting pieces together that looked like they needed to be put together. Eventually a 3-cycle or a twist or two needed to be done to finish up and I drew from my Skewb Family Arsenal of Algorithms (I just made that up).

But then Kevin asked how I solve the Skewb, so I got out the Skewb Cube and solved it. Then the Tetrahedral Skewb. Then the Squished Skewb. Then I intentionally tried to use the same strategy to solve the Curvy Rhombo Skewb.

Documented Scramble #1: DNF
After getting the first 8 pieces solved, leaving only 6 to go, the thing still looked scrambled! After using a setup move and the 3-cycle to place 2 of the 6 pieces, and not being able to see how to undo the simple setup move, I decided that although it is possible to solve in the same way, a more intuitive approach would be better.

Documented Scramble #2:
After solving the yellow layer, including the green and purple triangle center pieces, one twist of the black layer was needed to solve the 3 remaining triangle center pieces. That left the 3 remaining edges out of place and the remaining corner twisted. After using Double-EPS to place the edges instead of the pure 3-cycle, both of the diagonally opposite corner pieces needed twisted. I don't think it is possible to twist them together, so I twisted each one with a triangle using an algorithm that hadn't been used in any of the previous posts' solves. I will not even attempt to type it out.

So it turns out I not only demonstrated the algorithm. I also showed what happens when unexpected results happen, and one way to solve mysteries! :D

Documented Scramble #3:
Very difficult to get the yellow layer this time. The first several times I tried it this way it seemed almost trivial to get a layer solved. But this time, either it was a different scramble, or my mind wasn't in sync with the puzzle as before. This can be a problem when solving intuitively rather than with a systematic strategy. I ended up using Triple-EPS a couple times to swap pieces into place on the yellow layer.

After solving most of the black layer as described in #2, once again I ended up with the 2 small corners twisted. Two lessons to learn. First, if I would use the same steps as I do with other Skewb puzzles, I wouldn't have this problem at the end. So is it worth it to work through a more visually challenging solve at the beginning to make the endgame go more smoothly?

Secondly, it dawned on me that one conclusion I made in #2 above is incorrect. I said "I don't think it is possible to twist them together," because one is in the corner role and the other in the center role (thinking of the Tetrahedral Skewb). But what did I learn in the video above? I can twist 1 corner and 3 triangles, in the unshapeshifted puzzle, and 2 of the triangles are centers! So I can twist a corner and a center together! Yay!

In conclusion... well, is it ever really concluded? Let's just say that after several more solves I have decided that at this point I rather like solving it using the same basic approach taken with the other Skewb Family puzzles. That is, get the 2 small corners and the 6 triangles first. This only takes a few simple twists. Maybe 1 EPS. So with half a dozen twists or less more than half the puzzle is solved! Then 3-cycle the 6 big pieces home.

If a corner needs twisted without disturbing triangles, up twist down replace up twist-the-other-way down go-back works well and is pretty simple. Let's see.

Bottom line though, with this puzzle, as with any puzzle, there is no right or wrong, easy or hard, better or worse, way to solve it. I may decide on a favorite way to solve it tonight, but 6 months from now pick it up and take a whole different approach. I suppose I should demonstrate the Preferred Method applied to this one, so

Documented Scramble #4:

3 comments:

Julian SMarch 7, 2014 at 2:14 PM
What is the Double-EPS? How is it different than a 3-Cycle?
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UnknownMarch 8, 2014 at 9:18 AM
An EPS on this puzzle does a 3-Cycle plus double-swap. Doing the same EPS twice in a row does a 3-Cycle, and swaps back the other pieces, so it does only a pure 3-Cycle. So the answer to your question: no difference! But when solving skewbs, I sometimes use a 3-Cycle that is not a double-EPS.
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Julian SMarch 13, 2014 at 1:00 AM
Thank for the reply. Even though I wasn't entirely sure about what it was, I experimented using my limited knowledge of a 3-Cycle and figured it out much to my pleasant surprise and now I can follow along with better understanding. Once again, I appreciate the reply. And the good news in the end is that I can now solve the Skewb Curvy Rhombohedron puzzle. The important keys were the two algorithms you showed; one for cycling the edge pieces, and the last for rotating the remaining two edges. Thank again for the tutorial.
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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.