Puzzled 2: Pyraminx

Wednesday, May 31, 2017

Pyraminx

On January 18, 2010 I posted this on WordPress. Today as I read through it, it made me smile. I guess you could say it made me laugh at myself.

My strategy has changed. Now I solve all the corners with a few twists, then all the edges in no particular order. I still use the Move for the edges.

The Pyraminx is a colorful, twisty tetrahedron, or pyramid.

The little corner tips can rotate, but are always attached to the same pieces, so when I think of a corner piece it is the tip plus the piece it is attached to. There are three edge pieces surrounding each corner. A corner and its edges make up the small pyramid that, along with the base, makes up the whole puzzle. The base is comprised of all the pieces that have the same color. The base has three corners and three edges, one edge between each pair of corners. So if the base has 6 pieces and the small pyramid has 4, there are 10 pieces to the puzzle altogether. You can also see it as 4 corners and 6 edges. Each piece has a home spot. Every piece is home when the puzzle is solved. We call a piece the owner of its home. When the puzzle is scrambled, at least some of the pieces are visitors. That is, they are not in their own home spots, but in another piece's home spot.

In my cube ramblings I sometimes refer to online solutions that I have learned or at least looked at. I have not looked at Pyraminx solutions online. The best solution depends on what you are after. Want a strategy that requires the fewest moves? Want a strategy that is good for speed solving? Or do you want to simply figure out on your own how to solve the puzzle, and develop your own strategy for doing it consistently? That is where I am in my puzzling adventures now, so that is why I no longer look at how other people suggest solving a puzzle. Rarely ever. I have included the explanation of how to solve the Pyraminx below to document for myself how I do it. If you want to compare my method with yours for some reason, it is there for you to try to figure out. Or if you have tried to solve the Pyraminx and need help, then maybe this will help.

Solve One Layer

To solve the Pyraminx I like to start with one of the bases. First I solve three corners relative to one another. I think this can always be done in at most 3 twists. Then with those corners on the bottom I insert the edges into place. This usually takes 4 twists per edge. I'm going to call the small 4-piece pyramid on top, the top, as in the top layer. The 6-piece base is on the bottom. To get a base edge piece home that is on top, hold the puzzle so the home spot is in front and spin the top so the piece is in the back. There are two base corners in front, one on the left and one on the right. The left corner along with the three edges that surround it make up a small pyramid that I will call simply, the left. Guess what I mean by the right.

Now the edge piece that is in the top and at the back has two sides, left and right. If the sticker that belongs on the bottom of the puzzle is on the left, turn the left so the visitor comes to the top. Turn the top to replace the visitor with the owner. Turn the left to take the owner home. Guess what you do if the sticker was on the right.

Continue this process until the base is solved.

Solve the Top—Flipping Edges

Now twist the top to solve the final corner piece. It may be that the top edges are solved. It may be that they are in their correct positions but two of them need to flip. Or it may be that none of them are in the correct place. If two need to flip hold the puzzle so they are both on the bottom layer (the base), and so that one of them is in front. Let's call this piece, Piece 1, and the other edge that needs to flip, Piece 2. Turn the right so Piece 1 moves to the top. Turn the top so Piece 1 moves to the back. Turn the right the opposite direction as before. Turn the left so Piece 1's home moves to the top. Turn the top so Piece 1 comes to the front left. Turn the left so Piece 1 goes home oriented correctly. When an edge is flipped it is not oriented correctly. When it is oriented correctly, it is not flipped. Now turn the base so Piece 2 comes to the front. Turn the left so Piece 2 moves to the top. Turn the top so Piece 2 moves to the back. Turn the left back into place. Turn the right so Piece 2's home moves to the top. Turn the top so Piece 2 comes to the front right. Turn the right so Piece 2 goes to the bottom. Turn the bottom so the puzzle is solved.

Whoa! The above is a 14-move sequence. I like it because it makes sense to me. It is logical. I can follow the piece around the puzzle and see why it is flipping. I can use a similar technique on cubes to flip edges and twist corners. But there is another way to flip two edges that only takes 8 moves. Really it takes 9 if you count the roll of the whole puzzle in the middle. But still that is a big improvement movewise and there is something I like about it too. It uses The Move.

The Move start Right (The Move R) = R↓ L↓ R↑ L↑

Let R↓ mean turn the right counterclockwise, so that the edge on the front right goes to the front bottom.

Let L↓ mean turn the left clockwise, so that the edge on the front left goes to the front bottom.

Guess what R↑ and L↑ mean. Guess what The Move L would be.

Let Roll R mean Roll to the Right, which means roll the whole puzzle so the front spins clockwise 120˚.

OK. To flip the edges at the front left and front right positions you can do The Move R, Roll L, The Move L.

Solve the Top—Cycle 3 Edges

What do you do, though, if when you solved the top corner, you had 3 unsolved edges in the top?

Move one of the edges to the bottom and then around to the same side as the other two. (This is called a setup move.) Once all three edges are on the front they can be moved into their proper places using The Move! Just make sure when you move the piece to the bottom and around, that you do it in such a way that exactly two of the three pieces need to flip as they cycle. Roll the puzzle so the piece that does not need to flip is in the top layer and needs to move to the other top edge in front. If it is on the right do The Move L. If it is on the left do The Move R. Then do the two twists necessary to solve the cube. (That is, undo the setup move.)

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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.