Sunday, May 28, 2017

Pyraminx Crystal

Originally posted April 10-12, 2017 on the BudLCuber Google site.

Recently Roark mastered solving the Rubik's Cube. It is a method that uses The Move, aka Al Bob Charlie, aka Up Replace Down GoBack. He also learned the basic Up Replace Down 3-cycle for corners. And how to twist corners with a Double-ABC. And how to double swap corners with a Triple-ABC.

I got to thinking that he could use the skills he has learned to solve Pyraminx and Skewb puzzles. We haven't tried it yet.

Then I wondered about the Pyraminx Crystal. It was half solved already when I got it out of the closet. I finished it up but wondered what my whole solution involved. I found this note in my Solutions spreadsheet:

White corners; white edges; 4 of the next 5 edges; middle layer lower corners, then last of the edges of the bottom layer; middle layer upper corners; middle layer edges; last layer corners; last 10 edges.

That sounded very familiar. I tried it out. Yes. Very comfortable. As far as all the corners except the last 5 it is all a matter of just putting them in place, or using Up Replace Down to place them. All edges can be done with ABC (The Move). The last 5 corners can be 3-cycled using the Up Replace Down 3-cycle, or double-swapped using Triple-ABC. They can be twisted using Double-ABC. Using the ABC moves on the last layer corners scrambles a few of the middle layer edges, so if wanted, the middle layer edges can be left scrambled until the corners are all solved. Or, of course, my traditional methods for placing and orienting corners can be employed.

Solving it a couple times using the old strategy for the bottom part (white on bottom) and the revised method for the middle edges and last layer was educational. I didn't really like the part of solving 4 of the next 5 edges. I decided to try solving 4 of the 5 bottom middle layer corners instead. It was quite easy. Then using the working face I solved the corresponding edges that go below the corners. Then I solved the last of the 5 corners and inserted the edge. I liked it better for some reason than doing the edges before the corners.

My Current Favorite Method:
1. White Corners
2. White Edges
3. Four of the five Corners in the bottom half of the middle layer
4. The Edges that go below those Corners
5. The last Corner and Edge that go in the bottom half of the middle layer
6. The five Corners of the top half of the middle layer
7. The five Corners of the top layer
8. Remaining Edges

Thursday, March 30, 2017

The Al Bob Charlie Method of Solving a Rubik's Cube

It has been a long time since I had anything to say. It was a long break from puzzling. But my interest has been rekindled this last month. New challenging puzzles have not sucked me back into the puzzle realm although I watch one of Rupert's videos once in awhile. In fact this last month it has been the 3x3x3 cube that has recaptured my attention. I wanted to teach Roark a simple method for solving the cube that he could learn and remember. No algorithm memorizing necessary. It fell into place like this.

First master solving the white edges. I did not require that he do it like I do it. We did not even talk about how to do it. Second, master the middle layer edges. I may have shown him how I do it but for the most part it was up to him to work it out.

Here is where the lessons really began. After mastering the white edges and middle layer edges I introduced him to the working edge—one of the middle layer edge spots. In other words, after solving the white edges, only solve 3 of the middle layer edges. Then solve the final 5 edges together.

Start by using the working edge slot to solve any two of the yellow edges. Each one is done with 3 or 4 twists. In fact, to this point the 9 solved edges have all been done with intuitive moves, and little instruction.

Next I taught him the Edge Piece Series, moves like Ri F R Fi, or U Fi Ui F. Only we didn't write down algorithms, or call it the Edge Piece Series. We called it Al Bob Charlie. To cycle Al to Bob to Charlie where Charlie is the one that needs to flip, you take Al to Bob, Charlie to Al, go back, go back. We discussed the problem of having to flip all three instead of just one. Cycle them the wrong way on purpose, then cycle them home. And we briefly discussed what to do if all the edges were in place but two had to flip. Cycle them out of place then back home correctly. We learned that if after solving two yellow edges, if one of the last three edges was in place and the other two had to swap, then that meant the two solved yellow ones were attached to the yellow center incorrectly. The top had to be twisted 90 degrees and solved again using the Al Bob Charlie method. He got it. He mastered the edges on his own at home over the next few weeks.

I resisted the temptation to try to teach him an algorithm to swap two edges, or to teach him a popular algorithm for 3-cycling yellow edges. We did it all with the simple Al Bob Charlie method. And over the last month or so that this was happening I have used this method myself to solve the cube many many times. I like it. It is fun. It feels good. It makes sense. I even bought a couple more cubes. I had a stickerless speed cube already, but I wanted a genuine Rubik's Cube so bought one on Amazon.com for \$8. One with tiles. I like it. Then I bought a Dreampark cube with black carbon-fiber stickers. I love it. So much so that I got their Pyraminx with black carbon-fiber stickers as well. It is by far the best pyraminx I've ever had. More on the Pyraminx later. Back to the cube.

It was time to learn the corners. At first I tried to teach him to use the same exact movements that I use to whip through some of the aspects of solving the corners, but eventually I decided it was best to let him work out his own ways to twist and turn.

At this point we transitioned from an edges first method to a working corner method. I showed him how to easily solve 3 white corners after solving the first 7 edges. Intuitive Up Replace Down moves were needed to accomplish this. Of course the bottom had to be turned to line up the bottom corners under the working edge, and sometimes we had to deal with a white corner on top that had white on top, but those were not difficult to deal with. Before long he had mastered all the edges plus 3 of the 8 corners. Only 5 corners to go.

Three skills to learn. How to 3-cycle corners. How to double swap corners. And how to twist corners. 3-cycling uses the familiar Up Replace Down move. It cycles two bottom corners and one top corner. The bottom corner that stays on the bottom is the one you move first. It goes Up. Replace it with the corner you are cycling that is on top. Move it Down by undoing the twist used to move the other one Up. Now twist the bottom to replace the corner that moved Down with the other corner that is being cycled. Move it Up with the same move used to move the first piece up. Replace it with the first piece. Move it Down. Move the bottom back. Done. I like this 3-cycle for two reasons. It builds on what is already used—Up Replace Down. And it is flexible. The pieces do not have to be in any certain spots as long as two are on bottom and one on top. You can do it either right-handed or left-handed. And with practice and keen observation you can discover how to cycle corners to avoid having to twist them later.

Twisting them isn't a problem though. It also builds on something already used. Al Bob Charlie. If you Al Bob Charlie the top right edge to the right front edge to the top front edge and do it again it twists the bottom right front corner counter clockwise. The key is that is the only change on the bottom. So then you can turn the bottom layer to replace the twisted corner with another corner that needs to twist. This time Al Bob Charlie the front top edge to the front right to the top right. That twists the second bottom corner clockwise and restores everything else that got scrambled twisting the first corner. Finish by putting the bottom back where it started.

Finally we will cover the double swap. It too is another application of the Al Bob Charlie move. Let's say we need to swap the top right and bottom right corners on the front layer. And we need to swap the back left and back right corners on the top layer. Al Bob Charlie the front right edge to the right top edge to the top back edge. Do those four twists 3 times in a row. That's it!

One other thing. This method relies on two things. Up Replace Down and Al Bob Charlie. Question: How are they related? The double swap explained in the previous paragraph can be thought of like this. Do Up Replace Down GoBack three times in a row. GoBack is simply twisting the top layer the opposite of the way you did on the Replace twist. So instead of calling this the Al Bob Charlie Method we could call it the Up Replace Down GoBack Method.