Sunday, August 6, 2017

e-mail To The Boys—My BLD Edge Method Explained

Let's see if I can break it down into baby steps. Do you have a solved cube? 
  1. Hold it with white on top and orange in front. 
  2. Do Ri U R Ui R2. Remember what that means? R means Right clockwise. Ri means Right inverse or counterclockwise.
  3. As you do R2 roll the cube so green is now in front. White is still on top.
  4. Do Li Ui L U. 
  5. As I do the final U I roll the cube so orange is on top and yellow is front.
  6. Do R U Ri Ui R2.
  7. As I do the R2 I roll the cube so orange is in front and white is up.
  8. Do Ui.
The moves in steps 2, 4, 6, and 8 are each pretty simple and can be done quickly and smoothly. If you did it correctly only 4 pieces were affected. The 2 corners in back on the top swapped, and the right top edge and left top edge swapped. Doing steps 1-8 takes me less than 10 seconds.

Now let's talk about the edges. Roll the cube so blue is front and yellow on top. Where did the two swapped edges go? They are on the bottom. One in front; the other in back. Where did the two swapped corners go? They are on the bottom right. One in front; the other in back. I call the above algorithm The Swapper, for obvious reasons. We will get back to it in a bit, but first we need to name all the edge surfaces. I saw a couple different ways of doing it online but ended up with my own, slightly different, method of naming them.

A = yellow surface of the yellow green edge. That is, the one in the back on top.
B = yellow surface of the yellow red edge. That is, the one on the right on top.
C = yellow surface of the yellow blue edge.
D = yellow surface of the yellow orange edge.

Note that when I think of these surfaces I am also thinking about where they belong when solved. So A is the top surface of the top back edge. In other words, there is an A surface and an A location. On a solved cube all the surfaces are in their proper locations. On a scrambled cube most if not all the surfaces are not in their correct locations. Surface B may be at location L for example.

E, F, G, and H are all on the left side. E at top, F in front, G on bottom, and H in back, but all on the left face of the cube. So they are all orange the way I hold the cube.

I, J, K, and L are all blue. All on the front. I top, J right, K bottom, and L left.

O, P, R, S are all red. All on the right. O on top, then go clockwise as with the others.

U, V, W, Y are all green. All on the back. 

1, 2, 3, 4 are all white. All on the bottom. 1 in front, then go clockwise.

If you have related all of this to an actual cube I trust there is nothing confusing about it. Just trust me that to solve the cube with my eyes closed I had to name every surface of every edge of the cube. Now, remember The Swapper algorithm? What two edge surfaces got swapped? 1 and 3.

Now let's look at a scrambled cube. Let's say the green-red edge is at the bottom back with green down. In other words the surface at location 3 is Y. With 3 twists I can get the piece at Y to location 1. Then I roll the cube over so white is up and orange front and do The Swapper. Then I roll the cube back over so yellow is up and blue front and do 3 twists to put Y home. And now the piece at 3 is the one that started at Y. Let's say it is the red surface of the red-blue edge. That is S. 

Before I go on there is one very important thing I have not mentioned yet. The corners that get swapped by The Swapper have to be the same corners every time. That way those two corners just go back and forth as you solve the edges and don't move around the cube during the solve. So although it is possible to move S to 1 with one twist, that moves one of the corners out of place so you can't do that.

When I first started developing this method I put every piece to spot 1 to swap it with the piece at spot 3, but not long ago I realized there is a better way. There is not only a better way to get to spot 1 for some of the pieces, but I can also put a piece that needs to swap at A, move A to W and 3 to K with the inner vertical slice, do the Swapper, put things back, and it accomplishes the same thing only with easier and often fewer moves. 

So I can get S ready to swap with 4 moves. After the swap and putting everything back S is solved and the piece where S is, is now at 3. Let's say it is the piece that goes to V.

To solve the first 3 edges I have to remember Y S V, so I make up a little sentence that I can remember like Yolanda serves veggies. Then I close my eyes and move Y into position, swap, move Y home, move S into position, swap, move S home, move V into position, swap, move V home. And continue the process until all 12 edges are solved.

There are some things that can happen that complicate the process a little bit but once you get the hang of it it isn't that hard to deal with. Like what if the piece that lives at 3 is the next piece after V. Then it doesn't need to swap. It is already home. So you pick another piece that hasn't been solved yet and swap it to 3 then swap it to its home and continue the process. 

I'll tell you what. When you start with a scrambled cube, close your eyes, start twisting, and 10 minutes later you open your eyes and the cube is solved, it feels good.

Questions? Comments? Anyone inspired to dance?

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