## Friday, May 23, 2014

### Ghost Cube

The Ghost Cube came into my life almost two weeks ago. After the initial greeting, I admired it from a distance for a week. Finally I scrambled it. It was a bugger to find two pieces that went side by side. I was trying to be systematic, but that is really hard. Once though, when I chanced to turn the puzzle around, Bam! A center, edge, and corner had come together without any effort on my part. Yay! A start. As I built my way around the center I had this niggling fear that I might be in for an unpleasant surprise because of the fact that the puzzle when solved is not in 3x3x3 form. Oh, did I mention that during this solve I did not use any reference photos to see what went where? It is now solved and I have several observations.

1. This is a hand mod version, not a mass produced version. During the solve I noticed that one of the centers that ends up as a corner of the solved cube, was not made exactly right. The vertex sticks out a little bit further than it should in one direction.
2. Two of the centers end up as corners of the solved cube. One of these two should be the starting point of the solve.
3. When a weird shaped piece needs to twist in place, I have a terrible time visualizing which way it should go.
4. When I do a 3-cycle of corners on a standard cube I know which orientation two of them are going to end up with. Not so with this beast.

I think before I scramble it again I should try some familiar moves and see what happens. Perhaps I can start seeing more clearly, and rely less on try-it-and-see.

May 25, 2014
I have not made any attempt to memorize what goes where, as it seems that would defeat the purpose of the challenge of this puzzle. But after 3 solves I am beginning to be able to see a little more clearly. I still maintain that one of the two centers that end up on a corner of the cube should be the starting point, although I can't tell them apart so don't know if one or the other would be better. I have also developed a favorite edge to start with—the long one that has three surfaces.

I'm getting a feel for which way to twist corners, and I've noticed a difference between the middle layer edges and the top and bottom layer edges.

Although it is making a bit more sense than at first, there is still an amount of "maybe this one goes there" type thinking.

So far I've been using a straight layer-by-layer approach and after the first layer have to shift back and forth a lot between cube form and 3x3x3 form.

When I first learned how to solve a Rubik's Cube, I learned a working corner technique, a layer-by-layer method, a corners first method, an edges first method, some F2L techniques, and even tried the Petrus method. I can not imagine ever being able to solve the Ghost Cube corners first. When solving a cube now it is usually either F2L or Corners First, so I rarely use the algorithm I learned for placing middle layer edges, but now we are becoming good friends. :D Perhaps I should try some of the other methods.

May 27, 2014
Layer-by-Layer works and is the first method I tried since it allowed me to complete a layer at a time, which was important as I was getting used to seeing how the pieces fit together. But the algorithm for inserting middle layer pieces, although I like it as far as algorithms go, seemed unnecessary once I realized the Working Corner method could be used. In the latest solve the Working Corner method worked well. Instead of R'URU' F'U'FU to insert a middle layer edge, it only took something like RUR'. On the last corner and edge I tried to figure out how to join them and insert them together, but couldn't figure it out, so ended up easily inserting the edge, then using a 3-cycle to put the corner in.

For the last layer, whether I used the Layer-by-Layer method or the Working Corner method, I orient edges, place edges, place corners, orient corners.

Recap of methods: The Corners First method is not going to happen on the Ghost Cube. Edges First might work, but inserting the corners in the first layer is not difficult and is a tremendous help visually. At this point in my familiarity with the pieces, F2L would be a matter of finding a corner, keeping track of it while finding an edge, figuring out how to make them fit together correctly, and inserting them together as a pair. Seems to me like it would be a lot harder than the Working Corner method.

Now what? More Working Corner solves in which I try to insert the last corner-edge pair together.

May 28, 2014
It is settled. After considering each of the solving strategies I am familiar with, the Working Corner Method is my strategy of choice for the Ghost Cube.

I did not start this process by studying the pieces of the cube carefully. Just scramble and go. Needless to say that first solve took a long time, involved much trial and error, and I could hardly tell the difference between an edge and a corner! Since then I have looked at the pieces in the solved state and noticed some similarities and symmetries. Very helpful. It is still the most challenging 3x3x3 shape mod I've ever experienced and I still sometimes have a hard time finding the right piece for a particular spot. But there is definite progress. One major breakthrough came by taking a hard look at the middle layer center pieces in solved state. I no longer have to twist centers as many times as I used to, in order to find the correct orientation. In my last solve I was down to the last 4 corners, but when I looked at them I decided it was cute the way it was, so I declared it a new solved state. I give you Ghost Cube Man—

May 31, 2014
I was curious to know how others solve the Ghost Cube, so I asked on the Puzzle Photography page, but did not get much response. Thank you Otis Cheng for sharing your approach. So I messaged rline and Burgo asking specifically how they go about it. rline has a unique method. I tried it a couple times, at least I tried following the sequence of steps. He did not go into detail as to how he did each step. Although I do not enjoy my implementation of his steps, I feel that I learned something from trying nonetheless and have refined my solves somewhat. Here is what I have now—

Most of Layer 1

• One of the two columns made up of a center-edge pair that make up one edge of the solved cube.
• The other 3 edges around this same center.
• 3 of the 4 corners around this same center.

Use the Working Corner to solve the Middle Layer

• Use the working corner to orient the middle layer centers one at a time.
• Use the working corner to solve the middle layer edges.
• When the middle layer is complete solve the working corner corner.

Last Layer

• Orient edges.
• Permute edges.
• 3-cycle corners.
• Orient corners.
As I have mentioned previously, the middle layer centers can give me fits. Some things I have learned that can be helpful—

Each has a triangle side. The triangle sides of the correct two adjacent centers can be oriented to lie on a plane. The triangle sides of the other two centers lie on a parallel plane. The hexagon shaped pieces go between these centers. The smallest triangle and the largest triangle go together, but if you forget to check that and are just trying to find which two work together, and two look like maybe they are on a plane, but neither hexagon piece will work with them, those centers need to be on the top of the middle layer rather than the bottom.