Wednesday, July 29, 2015

Dayan Gem V Solution

In the fall of 2013 I participated in a discussion at the forum about how to solve the Dayan Gem V. The solution I came up with originally was OK, but by the end of the discussion I had come up with a better way. I don't think it incorporated anything from the discussion. The discussion simply spurred me on to find a better way.

Here is the complete method as presented on the forum.

1. Get all the centers—small triangles, large triangles, and if you have stickerless v1 as I do, the thin strips on the square faces. All 8 triangles can be solved with either 0, 1, or 4 moves. I do not mean each! I mean that after either 0, 1, or 4 twists all 8 triangles are solved!

The 6 thin strips take me up to 3 Double-EPS, or 24 twists. I use Double-EPS to maintain centers. Rarely it takes three of them. Rarely are they already solved. Usually it takes two Double-EPS to solve all 6 pieces.

2. Place all the small edges (corners) from the bottom up. Uses an Up-Replace-Down technique. Some people call this truncated EPS, since it is the first 3 twists of the EPS. 

3. Use [3,1] commutators to solve the large edges.

And in an earlier post I said:
doctor twist wrote:
I am left with 3 unsolved center pieces. How you can deal with that?

In my solution outlined directly above, I deal with all 8 of the triangle centers, and all 6 of the thin strip centers of the square faces in step 1, so that I never end up in the situation you describe of being left with 3 unsolved center pieces. My motto: Deal with parity as early as possible so you don't have to unsolve and re-solve at the end.

So, here is how I deal with the centers in a little more detail. Starting with a scrambled puzzle,

1. I hold the puzzle so there is a square face on top, and the large red triangle is on the upper half of the front, and the large purple triangle is on the upper half of the back. This is totally arbitrary, but it is what I am used to looking for and it defines for me the color scheme of the whole puzzle. (It is sort of like when I am solving a Rubik's Cube I start by holding it with the white center on the bottom.)

2. With the Red Triangle in front, I can see 3 small triangles. By looking at these 3 I can tell whether they are solved, or whether they need a double swap, or whether I need to do one twist that will solve them. If the one twist is required I do it. If the double swap is required I do it. (So I deal with the "3 unsolved center pieces" before anything else on the puzzle is solved

3. Since I have the stickerless version, there are colorful thin strips on the square faces. I place them next using Double-EPS moves. I use Double-EPS instead of just EPS so that the 8 triangle centers don't scramble during this phase. So if I need to move thin strip A to thin strip B to thin strip C, I go the opposite way twice! C to B to A twice is the same as A to B to C, and with each EPS there is a double swap of center triangles, so doing it twice leaves them solved. :D

So that is how I deal with it. But what if someone handed me a puzzle with everything solved except for 3 triangle centers? Then what would I do? I would do a single twist that solved them, then re-solve the puzzle from there. What a pain! That is why I like to insure at the very beginning that this will not happen.

As I read through the forum topic today some interesting things came out. themathkid originally solved the Dayan Gem V like he solves the Vulcano, Konrad solves it like the F-Skewb, and I originally thought of it like the Jing's Pyraminx. 

The thing that got me into this puzzle today is that I left it downstairs where Alex could reach it and Annie brought it to me in pieces. Three pieces had fallen out. She brought the puzzle and the pieces to me upstairs. It popped back together easy enough but I'm not sure the pieces are oriented correctly so I have to solve it to find out. I've solved it a few times already this summer using the abbreviated guide in my spreadsheet, but something told me I had recorded more about it so I went looking and found it at the forum.