Wednesday, May 31, 2017

Skewb Pyraminx Family

Scrambled Skewbs

April 9, 2017
So I have 6 or 7 puzzles that are in the Pyraminx/Skewb family. I call it a family because their guts are the same. At least I think they are. Haven't had them all apart or done extensive research online. I have written posts about some or all of these before and even included videos, but that is all old news. In fact, Solution 1 and Solution 2 below are from years ago. My new interest is in light of a new interest in solving the cube using mainly Up Replace Down, and The Move, aka The Edge Piece Series, aka Al Bob Charlie aka Up Replace Down GoBack. So I wanted to see if I could do the same with Skewbs. The answer: pretty much. The puzzles are pictured and numbered above. 

1. The Pyraminx is easiest. Just some simple twists followed by a few ABCs. (ABC = Al Bob Charlie, my current name for the Edge Piece Series, or The Move)

2. Then comes the Meier-Halpern Pyramid (Meffert's version is popular and known as Jing's Pyraminx). It is like a Pyraminx with centers so there are 4 more pieces to deal with at the end but they are one color each so a Triple-ABC does a double swap if necessary and it is done. This assumes you start by solving it like a Pyraminx, ignoring the centers until the end.

3. Next is the Skewb. It is a cube shaped Meier-Halpern Pyramid. It has 8 corners 4 of which are attached to the core like a pyraminx, which can similarly be solved with a few simple turns. The 6 square center pieces can be solved with ABC just like the edges of a Pyraminx. The catch is that you have to twist the solved corners, not the other ones, while solving the squares, otherwise the solved corners will get scrambled. To solve the last 4 corners if they are not already in the right places use a Triple-ABC to double swap them. Then a couple strategic Double-ABCs can be used to twist them if necessary. The exact strategy came by thinking about the Double-ABC. Which way does it twist which corners? How could the cube be manipulated so that two corners only could be twisted while the others were untwisted? Double-ABC leading with the right hand. Roll the cube so the top corner in back rolls to the bottom left and the bottom right rolls to the top back. Then Double-ABC leading with the left hand. Two of the four twisted corners get untwisted by the left-handed move. And the squares that moved about by the right-handed moves get put back by the left.

4. The Skewb Ultimate is a Skewb in the shape of a dodecahedron. That is a 12-sided Skewb. Four of the small corners can be easily solved like the first four corners of the Skewb. Then the big pieces can all be put into place using The Move. It matters not whether they are oriented correctly at this point since when solving the last 4 corners the big pieces can get flipped. So after solving the last 4 corners flip the big pieces.

5. The Squished Skewb has to be solved like the Skewb Ultimate because its odd shaped center pieces can get flipped. It is also tough to solve because of its large size. And it shape-shifts because of its squishedness. But at least the pieces resemble those of a normal Skewb.

6. The Skewb Curvy Rhombohedron is by far the quirkiest of the Skewbs I own. First I want to say that it is not a rhombohedron. Maybe kite-o-hedron would be a better name, but whoever heard of one of those! At any rate there are six faces all of which are kite shaped. There are 3 different shaped pieces. Six triangles in the center of the kites, two small corners, and six large corners. The six large corners correspond to the six squares of the Skewb. The two small corners and six triangles correspond to the eight corners of the Skewb. Oh, did I mention it shape-shifts? Like the Skewb Ultimate the big corners can flip while solving the last 4 pieces. But then there is something else I have encountered that I did not on any of the other skewbs. Instead of a double swap I have had to twist a face at the end to get the last 3 corners solved. Then I have to resolve the "edges" that shift around. Very quirky indeed. Fun. The reason this happens is because the triangle center/corners don't have obvious orientation like the other skewbish puzzles have. If you make sure all 8 "corners" are solved in the beginning then that won't happen at the end.

7. There is one more puzzle with the word Skewb in the name, but it is not very skewbish in my mind. The F-Skewb. It is cut in such a way that it can be scrambled and solved exactly like a Skewb, but there are additional cuts that allow for non-skewbish scrambling. Four little corners can be solved easily like the first four of the Skewb. Each center Skewb square is elongated and cut in half so there are 2 squares per side. I think they can all be solved using The Move. More testing is required. Then the final four corners are each cut into thirds. I can solve them after all else is solved using a commutator I devised when solving the Face Turning Octahedron. The commutator is very much like the one used to 3-cycle corners of a cube.

And here they are solved.

Solved Skewbs


The following was written years ago when I had a different take on the whole thing. My current favorite solution starts out like Solution 1, but when it comes to the last 4 corners is much simpler than the following. There are not cases and no jumping about. Simply permute then orient the corners. I must admit that with the Curvy Kite Skewb I frequently have to 3-cycle corners at the end instead of doing a double-swap. I twist them into place, use the Move to put the three big pieces back and finish it up. As I think on it, I seem to recall a way to avoid this situation. After solving the first 4 pieces check to see if the last 4 need to double-swap or 3 cycle.

Skewb Solution 1: (This is based on the Crazy Tetrahedron Method I learned from rline.)

Centers: First 4 Corners

Get two opposite corners on one face. This takes at most two twists. Get the two skew corners on the opposite face. This takes at most two twists.

Edges: 6 Center Squares

Use EPS making sure you twist the centers solved in the Centers section, and not the Corners that will be solved last. In the Crazy Tetrahedron and the Jing's Pyraminx, it is easy to tell centers from corners, since centers look like centers and corners look like corners, but that is what makes the Skewb challenging. The centers and corners all look like corners and all are centers of rotation.

Corners: Last 4 Corners

Hold the puzzle with a Center forward on the bottom, and 2 corners on bottom with one on the right and one on the left. Another center is on the upper left, and one on the upper right. Call the one on the left L, and the one on the right R. ( L'RLR' ) x 3 will swap the two corners on the bottom with each other, and the two on the top with each other. The colors on the corners on the front faces on the bottom will move to the bottom after the swap, so it is preferable they are the same as the edge on the bottom. The colors on the top of the front top corner and back top corner will stay on top.
Case 1: All are in the right place but at least two are twisted. Hold two twisted corners on top, and do ( L'RLR' ) x 3. Go to Case 2.
Case 2: Double Swap needed.
Holding the two bottom corners and top front corner still, twist the back half of the puzzle so the edge on top matches the color of the top corner that is in front.
( L'RLR' ) x 3 If necessary, go to Case 1.
Case 3: One is in the correct place, and may or may not be twisted.
Twist the Half which will place all 4 corners in their correct spots. They may or may not be twisted. Use setup moves and EPS to re-solve the edges. Go to Case 2.

Solution 2 (This is the solution I came up with on my own originally.)

Notation: Hold the Skewb so one face is facing you, and so there is a corner pointing right, one pointing left, one pointing up, and one pointing down. We will name these corners Rf, Lf, Uf, and Df, respectively. The corners behind these corners are in the back so we will name them Rb, Lb, Ub, and Db. Twists are defined by the corner that is the center of rotation for the twist. Centers can be named Ru, Rd, Lu, Ld, F, and B.

First 4 Corners

  • Get two opposite corners on one face. This takes at most two twists. Get the two skew corners on the opposite face. This takes at most two twists.

Place the Last 4 Corners

  • Rb Lb Rb' Lb' swaps Rf with Lf and Db with Ub, and twists Lf, Ub, and Db counterclockwise.

Twist the Last 4 Corners

  • ( Rb Lb Rb' Lb' ) x 2 twists Rf and Lf anti, and Db and Ub clockwise.
  • ( Rb Ub' Rb' ) Df ( Rb Ub Rb' ) Df' twists Rf anti and Lf clockwise. This is a very easy to see what is happening algorithm. Move Rf up; Twist it; Move it down; Replace it with Lf; Move Lf up; Twist it; Move it down; Move it back.

Place the Centers

  • [ ( Rb Ub' Rb' ) Db ( Rb Ub Rb' ) Db' ] x 2 moves Lu > Ld > Rd. I hold my left thumb on F throughout. I go for 3 centers in a row, rather than 3 adjacent centers, but if I end up with 3 adjacent I can use a setup move when placing the last 3.
  • ( Rf' Lf Rf Lf' ) x 2 Df ( Lf Rf' Lf' Rf ) x 2 Df' moves F > Ld > Lu. That is, it moves 3 centers around a corner without scrambling anything else.

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.)

The Bandage Cube

This section was posted on my Google Site. It says it was updated on September 3, 2011. Below this section is a post I made on WordPress even earlier.

Centers

Since each center is bandaged to an edge, orientation of centers matters.

Edges

Each edge is bandaged to either a center or a corner, so rather than thinking of solving edges, I think of it as solving pieces. One of the edges is bandaged to 2 centers, so this is the starting point of my solution strategy.

Corners

One corner is not bandaged to an edge.

Strategy

  1. Orient the centers. Hold the cube so the orange is on the bottom and the white is on the back. Orient all the centers accordingly.
  2. Get Blue-White (5). The BW move: F' U L F U L' U2. If BW is at GO or YW start with R U. Then do the BW move until BW is home. Then if you started with R U, do U' R'.
  3. Get Green-Orange (6). The GO move: R U F R U' R2 F'. This is also a 5-cycle. If GO is at GY, it won't get cycled, because the 5-cycle I use doesn't hit that spot. So I use a double swapper to get the GO to the RB spot. Then the GO move takes it right home. The double swapper is (R U2 L' U) (R' U2 L U'). It swaps the piece at GY with RB, and the piece at RG with RY.
  4. Get Yellow-White (8). The YW move: (R U R' F') (U L' U' L) (F U'). This is a 3-cycle that moves the pieces on top around. On a solved cube it would move RY to GY to YW. If the YW is not on top I simply move it to the top with the double swapper, then use the YW move once or twice as needed. The double swapper is (R U2 L' U) (R' U2 L U').
  5. Get Red-Yellow (1). The RY move: (R U2 L' U) (R' U2 L U'). This is the double swapper used previously when necessary. If RY is at RG it takes it home. If RY is at GY it takes it to RB, where it can be moved to RG, then double swapped home. To move it from GY to RB use the Step 6 3-cycle.
  6. Get last 3 with a 3-cycle (743). The GY-RB-RG 3-cycle: (U2) (L F' L' F) (U') (R' F R F') (U').

Bandage Cube Scrambles

Thanks to James the "thebackflipmaster" for the following list of scrambles.
02-----U F'L'U L U'F'L F U'F R2U2L'U2R'F'U F U'R'U F'L'U2 Good scramble. 
03-----R U2F'L'U L U'F'L F U'F R U L'U R'U F U F R'F L'U' Good scramble. 
04-----F'U L2F2R'F L'F2R F2L'F2R2U2L'U R'U'R'U2L F'L'U L Good scramble. 
06-----U F2R F'U2R'U F R'F'R U R'F2L F'R F'U'F'U'R U'L F2 Good scramble. 
09-----U F2R F2L'U2R'U2L F'L'U L U L U'F'L F L'U2F R F R' Good scramble. 
10-----F'U L2F2R'F L'F2R2U F2L'F U L'U'L F U L U'F2L'F U2 Good scramble. 
11-----U2L U2R'F R F'U'R U2L'U2R U R'F'U2L2F L'U R'U F U' Good scramble. 
13-----R U R U2L'U R'U L F2R'F'R U F'L'U R'U2L2F U'R'F'R' Good scramble. 
15-----U2L F U'R'F R F2L2U2R U R U'L U2R2F2L F L F'R F2L2 Good scramble. 
16-----F R2U R'F'U2L U2R'F'U'F R2U R'F'U F U L'U'F U'R'F' Good scramble. 
17-----F R2U R'F'U F'L'U L U'F'L F L'U2F R U'R'U2L2F2R'F2 Good scramble. 
18-----F R U F'L'U'R U'L U2R2F'U2L U'F'L F L'U'L F2R'F2L2 Good scramble. 
19-----R U2F'L'U L U'F'L F2U'R'U L'U2F'U L2F L'U2R U'L F2 Fell into place at the end but was a long time getting there.
21-----F R2U R'F2L F U'R'F'U F2R U F'L2U'L F U'F'U L2F2R2 Good scramble. 
23-----F'U L U L F'L'F U L'U'F U'R'F'L F'R F'U'F'U'R U F2 OK scramble. 743 was done, but I had to do a 743 earlier anyway. 
24-----F'U L2F'R F2L2U'F R U R'F'R'F'U2L U'F'L F L'U2F R 
25-----U2L F U'R'F2L'F R U2L'U'L F U2R'F R F'U'R U R'F2U 
26-----U2L F U'R'F R F'U'R U2F'L2U2R U'L U2R2F2L F'R F'U2 
27-----R U R'F'U2L U'F'L F L'U'F U'R'F R2U2F'L'F'L'U L U 
28-----U2L U'R'F2L F'R F2L2U'F R U'L U'F'L'U2F R U L'U2R' 
29-----R U'L U'F2L'F U L'U'L F L'U2R U'L U2R'U2L U'F'U L2 
30-----R U2F U'R'U'R'F R F'U'R U2F'L'U L2F U'R'F2L F2R'F2 
31-----F'U L F U'R'F R2U R'F'R U F'L F L'U'L F2R'F'R'F L2 
32-----R U R U2L'U R'U'R'U2L2F2R'F'R U F'L'U2R U'L U'F2L' 
33-----R U2F U'R'U F'L'U L U2R'F R2U F2L'U L U'F'L F2U'R' 
34-----U F2R F'U2R'U F R'F'R U R U F'U L U2R'F2L'F U L F' 
35-----R U R'F2L F2U F U'R'F R F'U'R U F'U L F'L2U2F R U 
36-----U F'L'U L U L U'F'L F L'U'L F'R F2L2U'F R'F'U F2R 
37-----R U'L U'F'L'U'F2R U'R2F'U F R'F'R U F'L'U'L F'R F 
38-----U L'U2R U R U'L U2R'F'U L F U L'U R'F R2U R'F'R'F' 
39-----F'U L2F L'U2R U R'F'U F'L'F2R U F U'R'U F'L'U'R U2 
40-----U L'U2R U'L2F U'R'F2U'F R2U R'F'U L F L'U'L'U'F2R' 
41-----F'U L U L F'L'F U L'U'L F L'U2F R U'R'U F R'F'R U' 
42-----F'U L2F'R F2L'F U'R'F'U'R U R'F'U2L F'L'F U L'U2F' 
43-----F'U L2F2R'F L'F2R2U F'L F L'U'L F2R'F L2U'F U F'L' 
44-----U2L F'L2U'L F2R'F'R U F'L F U2R'F R2U F2L'U'F R U2 
45-----F R2U R'F'R U2L'U R'U2L U2R'F'U L2F2R'F L'F2R2U F2 
46-----F'U L U'F R2U R'F'U L F L'U R'U2L F'L'U L F'L'F U' 
47-----F R U'R'U F R'F'R U2F'L'U L U2R'F R U F'L'U L U2R' 
48-----F R2U R'F'R U2L'U R'U L F U2R'U F R'F'R U2F'L'U2R' 
49-----F R2U R'F'U'R'U L'U2R U2L F U2R'U F R'F'R U F'U2R' 
50-----F R2U R'F'R U2L'U R'U L F U'R'F'U L'U2R U R U'L U'

Below is not only a basic strategy, but also a story complete with dates.

My Basic Strategy

Hold the cube so orange is down and white is back. Solve the centers and get the top configured as shown in the photo.

Bandage Cube showing blue side
Bandage Cube showing green side

Piece 5 (Left Back Down)

  • 14735 if piece 5 is at 3 or 7 (Fi U L F U Li) (U2)
  • 37415 if piece 5 is at 1 or 4 (U2) (L Ui Fi Li Ui F)
  • 34865 if piece 5 is at 6 or 8 (R U) (Fi U L F U Li) (U Ri)

Piece 6 (Right Back Down)

  • Green up if 6 is at 1; 78416 (R U F) (R Ui R2 Fi)
  • Red up if 6 is at 3; 87436 (R U F) (R Ui R2 Fi)
  • Yellow up if 6 is at 4; 38146 (R U F) (R Ui R2 Fi)
  • Red up if 6 is at 7; 87436 (R U F) (R Ui R2 Fi) three times
  • Yellow up if 6 is at 8; 38146 (R U F) (R Ui R2 Fi) three times

Piece 8 (Left Back Up)

  • 13/47 if piece 8 is at 3 or 4 (R U2 Li U) (Ri U2 L Ui). Now 8 is on top.
  • 178 until 8 is home (R U Ri Fi) (U Li Ui L) (F Ui).

Piece 1 (Left Front Up)

  • 13/47 if piece 1 is at 3 or 7 (R U2 Li U) (Ri U2 L Ui).
  • 743 if piece 1 is at 4 (U2) (L Fi Li F) (Ui) (Ri F R Fi) (Ui). Now 4 is at 3. Do 13/47.

743 (The last three)

  • 743 (U2) (L Fi Li F) (Ui) (Ri F R Fi) (Ui).

Extras

When I was first trying to solve the Bandage Cube early on it helped to categorize the pieces. Much like it is good to realize something about the three different kind of pieces in a normal cube, it helped to think about the different pieces of the bandage cube and how they worked.
The first challenge was simply in scrambling the thing. Because of the restricted movement caused by the “bandages” it is quite challenging to mix it up. But before long mixed up it was indeed. And as I just tried to solve one side it got scrambleder and scrambleder. I finally solved it a couple times but couldn’t really tell you how. I was trying to keep track and analyze it but it was tough. I experimented with different strategies that I thought would work. In the course of a week I was able to come up with a lot of algorithms through trial and error, being careful to record how to do what. I tried several approaches before finally coming up with the strategy above which is the easiest for me to remember without my notes. Below are some of the algorithms I figured out that are not part of the basic strategy, but may be useful in isolated cases.
436: R 234 Ri 12
367: U2 L Ui R 234 Ri U Li U2 18
143: 743 13/47 19
173: 13/47 743 19
176: U L F Ui R U Fi Li U2 R U Ri Fi U F Ui Ri 17
678: 34786 743 18
146: (red-yellow switch) F U2 L U2 234 U2 Li U2 Fi 18
17/48: (R U Ri Fi U F) (Ui Ri Fi) (L Fi R) (F2 Li Ui) 15
35/78: (R Ui L) U2 (Ri U Li) U2 8
36/48: R U 13/47 Ui Ri 12
34865: R U Fi U L F U Li U Ri 10
68435: R Ui L Ui Fi Li Ui F Ui Ri 10
78635: R U2 L F Ui Ri Fi U Li U2 10
36875: U2 L Ui F R U Fi Li U2 Ri 10

The Story

December 10, 2009: What is a Bandage Cube? It is a 3×3×3 cube that has tiles applied that restricts movement of the layers. There are 14 1×1 tiles, and 20 2×1 tiles. There are 4 center-edge pieces. There are 7 corner-edge pieces. Then there are 2 unique pieces. One is a single corner. The other is a center-edge-center piece. At first I thought the challenge was to scramble it! After awhile it was barely scrambled and I tried to get the green side solved. It just kept getting scrambleder and scrambleder.
Perhaps the best strategy is to try to use the red-yellow-green corner piece strategically to move the orange-white 2×1 pieces to the big orange-white center-edge-center piece. If that is even possible. hmmm…
The strategy worked, to a point. This cube sort of reminds me of trying to solve the 3×3×3 cube using the Petrus Method, only not. I ended up with 3 pieces that needed to cycle. After an attempt to cycle them it ended up needing 3 different pieces cycled. And again. Then I got back to the original situation. Sad thing is, I’m not sure what I’m doing. So close. I’m afraid one of these times it is finally going to fall into place, but I won’t know exactly how I did it.
December 12, 2009: It took a couple days to finally solve it for the first time. I tried to figure out some algorithms. I have a few notes and a few videos, but I do not have it all figured out yet. Now that it is solved I want to think hard about it before scrambling it again. A strategy that might work:
  1. Get the first two layers with orange down and yellow up. Mostly. For the left side get it so the greens are pointing down like all the other edges. Then at the end do Li to complete the solve.
  2. Line up the yellow-blue center-edge so the blue is on the white side.
  3. Cycle the 3 corner-edge pieces into place.
  4. Twist the yellow layer so everything lines up on the sides.
Steps 2 and 4 are trivial. Step 1 I was able to do the first day I attempted it. I think I can solve the first two layers a piece at a time. It might be smart to look for a systematic way to do it. For Step 3 I need the yellows in the E formation. You hold the cube so yellow is on the left and the little cube is on the front top left. (Li Ui L) switch (R Ui Ri) D (R U Ri) switch (Li U L) Di
It moves the bottom-front-left to the bottom-back-left to the top-back-left.
December 13, 2009: Overall the strategy outlined yesterday may work. I’m not sure yet. But I should mention in Step 1 that it is probably best to hold white in front and get the front and side corners and edges before going for the back ones. In other words, fill in the 4 pieces to the sides of the white-orange foundation piece.
This puzzle is hard. It may take a couple more days to get Solve #2, and then I still might not understand!
December 14, 2009: Got it! Solve #2. But have I developed a strategy for systematically solving it? Not yet. In the meantime, another puzzle that has recently caught my attention is the 2×2×2. I’ve been attempting to solve it with as few looks as possible. I have been doing so for a few days. Some of my progress is documented in gmail. Basically I can usually get it in 2 or 3 looks. I would like to be able to study it for a minute or so, then solve it completely without looking.
December 20, 2009: I was practicing what I knew after Solve #2 and accidentally scrambled it. It was back to the beginning.
After much trying, failing, trying something else, failing, etc. something finally worked and everything was solved except the red layer. A new idea came to me that enabled me to solve the red layer with a bit more understanding. Since then I have solved it multiple times and recorded sequences of moves that do various double swaps, 3-cycles, and even a couple 5-cycles that may prove useful. A strategy that seems to work:
  1. Hold the cube so orange is down and white is on the back.
  2. Solve the centers.
  3. Solve at least one piece by… uh… pulling and planting posts. First put the little cube over the visitor. Pull it up. Put the little cube over the owner. Pull it up. Take it home with either U or Ui and one of the L’s or R’s or F’s. If anything else is simple to move home, do it. If it isn’t scrambled in such a way that this is easy to do, skip right to the next step.
  4. Write down the cycles needed to move the remaining owners home.
  5. Figure out how to go about it using the following notes compiled through much experimentation.
In order to help keep track of what I have figured out so far, I have numbered the corners thusly:
  1. top front left
  2. top front right
  3. bottom front right
  4. bottom front left
  5. bottom back left
  6. bottom back right
  7. top back right
  8. top back left
(At this point in my notes there was a long list of 3-cycles, swaps, and 5-cycles.)
One really cool thing about the 3-cycles is the extensive use of The Move. Yes, The Move that I discovered worked so well with the Jing’s Pyraminx. The Move that I ran across when figuring out the Skewb. I read somewhere that it can also be used to solve the edges of the Pyraminx. I hadn’t approached the Pyraminx that way before, but perhaps now I will. And the 3×3×3 cube—remember the Edge Piece Series of the Ultimate Solution by Philip Marshall? What he calls the Edge Piece Series, I have been calling The Move.
December 21, 2009:
  1. Hold the cube so orange is down and white is on the back.
  2. Solve the centers and get the top configured as shown in the photo.
  3. Move piece 5 home using one of the algorithms given below.
  4. Move piece 6 home using one of the algorithms given below.
  5. Move the last 5 pieces home using one of the algorithms given below.
There is much flexibility in steps 3, 4, and 5. It may be better after step 2 to find both 5 and 6 and consider which order they should be moved in, or if they can both be moved home simultaneously using one of the extra 5-cycles. Or perhaps moving 6 first, then 5 makes for a more pleasing solution. For example, if 5 is at 4 and 6 is at 3, then doing 436 moves 6 home and moves 5 to 3. It is only 7 twists to get 5 home from 3 as opposed to 14 from 4.
December 28, 2009: Another strategy, not necessarily a better one. I like puzzle solutions that do not require a lot of memorizing or a lot of notes. I have taken a lot of notes during experimentation, but now would like to look for a way to simplify the strategy. It may require more twists and turns, but fewer different sequences.  So instead of 5 different sequences of moves to choose from to get piece 5 home, there is a way to use one of only two.
The disadvantage is that sometimes I’ll end up doing a lot more twisting and turning than necessary. For example, let’s say 5 and 6 are home. If 3 is at 1 and 4 is at 4, if I did 713, which is 18 moves, I’d be done with 3 and 4, but if I use this alternate strategy, I will do the 8 move swap to get 3 home, then have to do a 19 move cycle to get 4 home, for a total of 27 moves.
The advantage of this alternate strategy is that if I can cut back on the number of sequences I use to solve the cube, then maybe I’ll be able to internalize them and be able to do it without the notes.
The Basic Strategy
1. Hold the cube so orange is down and white is back.
2. Solve the centers and get the top configured as shown in the photo.
3. Move piece 5 home by repeated use of one of the following:
  • 14735 if piece 5 is at 3 or 7 (Fi U L F U Li) (U2)
  • 37415 if piece 5 is at 1 or 4 (U2) (L Ui Fi Li Ui F)
  • 34865 if piece 5 is at 6 or 8 (R U) (Fi U L F U Li) (U Ri)
4. Move piece 6 home by using one of the following:
  • Green up if 6 is at 1; 78416 (R U F) (R Ui R2 Fi)
  • Red up if 6 is at 3; 87436 (R U F) (R Ui R2 Fi)
  • Yellow up if 6 is at 4; 38146 (R U F) (R Ui R2 Fi)
  • Green up if 6 is at 7; 14876 (F R2 U Ri) (Fi Ui Ri)
  • Red up if 6 is at 8; 34786 (F R2 U Ri) (Fi Ui Ri)
5. Move piece 3 home by one of the following:
  • 178 if piece 3 is at 8 (R U Ri Fi) (U Li Ui L) (F Ui). Now 3 is at 1.
  • 13/47 if piece 3 is at 1 (R U2 Li U) (Ri U2 L Ui)
  • 743 once or twice if piece 3 is at 4 or 7 (U2) (L Fi Li F) (Ui) (Ri F R Fi) (Ui)
6. Move piece 4 home by one of the following:
  • 178 if piece 4 is at 1 (R U Ri Fi) (U Li Ui L) (F Ui). Now 4 is at 7.
  • 874 once or twice (R U) (Fi L F Li) (Ui F Ri Fi) (U F R) (U Fi U2 Ri)
7. Finish up with one or two times through the following:
  • 178 (R U Ri Fi) (U Li Ui L) (F Ui)
January 3, 2010: The problem I have run into with the Basic Strategy I worked out, is in step 6. The 874 move. It is too long for me to remember easily. What to do? Save 3, 4, and 7 for the last step. This makes sense because I already know the 743 cycle. But it only makes sense really if there is an easy way to get 8 and 1.
(At this point the solution strategy presented at the top was fully developed.)

My 4x4x4 Story

On June 29, 2008 I uploaded this to Scribd.
On January 15, 2010 I posted it on WordPress.

Understanding the Puzzle and Solving it Too

On June 24, 2008 I published the following booklet on Scribd. 
On January 15, 2010 I posted it on my WordPress site.

Old Puzzle...New Puzzle...Home Job...New Tool

Happening
 Originally posted May 21, 2017 on BudLCuber Google site.

Old Puzzle This last week for some reason that escapes me now I busted out the Crazy 4x4x4 and solved it. I tried solving it from memory, but the problem is there are too many memories to choose from. Huh? I really got pretty far in the solution but then messed up and looked up my notes from years gone by. I had a nice method worked out, but then at some point looked to see what others said about it and decided to go down a different path. But now as I look back on the two methods I prefer my original one.
  1. The squares inside the circles. Use 2-layer turns to solve them. It is just like solving a 2x2x2 cube.
  2. White and Yellow circles can be solved like the Corners First white and yellow edges.
  3. Middle Layer Circles can be solved like 4x4x4 middle layer edges.
  4. Pair up outer edges and use The Move to place them like solving a cube Edges First. Sometimes an 8-move edge 3-cycle is the easiest way to pair them up at the end. Sometimes 2 paired edges need to swap at the end. This is simply a double swap of individual pieces and can be handled with the 3-cycle.
  5. Corners using the 3-cycle.
To see how I did it for a while see below.

New Puzzle For years I have wanted a good stickerless 6x6x6 cube that I felt I could afford. It is finally here. Cyclone Boys is the one I got this last week. In the picture some of the red, orange, and yellow center pieces are still scrambled.

Home Job I think it was 2011 when I first started hiring the weeds done each Spring. I was working 40 hours a week in the machine shop at the time. Since then I have done part of the job myself while having a pro finish it up. But this year I have much more time than money and I dropped 30 pounds off my weight during the first few months of the year so have done all the weed eating on my own. It didn't stop there. I want to really clean it up so have gone nutso on pruning and thinning as well as you can see in the background.

New Tool There are quite a few branches that could be turned into small firewood as a result of this and other woodcutting tasks. Although I do not want a gas powered chain saw I decided an electric one might be just the thing to get the job done. Got it yesterday.

In September 2011 I posted a different way to solve the Crazy 4x4x4 on my Google site. Here it is—

Crazy 4x4x4 II
Centers
2x2x2 inside the 4x4x4 supercube. The squares inside the circles. Use 2-layer turns to solve them. It is just like solving a 2x2x2 cube.
4x4x4 Supercube
Non-white and non-Yellow inner edges. The inner edges of this Crazy puzzle correspond to the centers of a 4x4x4 supercube. The inner edges move in pairs. So the inner edge pairs that have no white or yellow correspond to the white and yellow centers. When solving a 4x4x4 cube you start with the white and yellow centers. Use techniques like with the white and yellow edges on the 3x3x3 Corners First Method, only hold white and yellow on the sides, and only do half the pieces.

Corners
Solve the corners like a 3x3x3 or 4x4x4. Corners First works. Corners can easily be matched to inner center/edges after all X's are done. Move the 2 inner layers 90 ̊, make the required adjustment, and move the inner layers back.

Edges
White and Yellow outer edges. Just like the Corners First Method.
Middle Layer Outer Edges. Just like a 4x4x4 cube.

Centers Last
Final Inner Edges. Use commutators that do not scramble anything else. That means do not use 2-layer twists for the inner layers.

Skewb Adventure

Originally posted on May 9, 2017 on BudLCuber Google site.

Roark and Roriana were here for the weekend. They seemed to have a lot of fun with Legos and watching movies and a little puzzling. Roark and I discussed different methods of solving the Cube and we took another look at the Skewb. I showed him again the method that utilizes ABC a lot. But then I got to thinking. He knows how to do a 3-cycle on the cube. Using a 3-cycle on the Skewb makes it a much easier solve in my opinion. So I showed him how to solve the Skewb using my original method. He liked it. When I was putting puzzles away today I wondered if my old method was good for the other Skewbs. I tried it on the Skewb Ultimate. Yep. I tried it on the Kite-o-hedron. Yep.

It was fun figuring out how to solve a Skewb using only ABC with no 3-cycle, but in the end, the method with the 3-cycle is far better for me.

My season of exploring different puzzles is over for a while. I put everything away except my 3 3x3x3 cubes and the Skewb. I have a lot of weed eating to do this spring, and am keeping up with Yahtzee with Buddies. This is also the year of the Bible Project videos.

My New Walking Shoes

I decided I needed some shoes for when I wear shorts this summer—shoes for going on outings where there will be walking. I even bought myself some of those short socks to go with them.

My New Walking Shoes

Tuesday, May 30, 2017

Dayan Gem V version 1


Dayan Gem 5 v1
Originally posted May 2, 2017 on my BudLCuber Google site.

After restoring the 17 to order once again the last few days I longed to get out another to add to the mix. I picked up a few but decided on the Dayan Gem 5. It is stickerless. Instead of looking up my notes immediately I wanted to take a fresh look at it in light of Al Bob Charlie and my cubing adventures of late. Probably because of all the Skewbing I've done lately it struck me right off that this puzzle is very Skewb-like. It has 4 small triangles that are like the first four corners of a Skewb. It has 4 large triangles that are like the last 4 corners of the Skewb. It has 6 square sections, each made up of 3 pieces, that are like the 6 squares of the Skewb. Then it has 12 pieces that complete the big triangle "corners." After solving it I scrambled it and solved it without twisting the faces with the small triangles. It was exactly a Skewb! 

But the first solve was a bit of an adventure. It started out scrambled. I had no idea what the final color scheme would be. It has 8 hexagonal faces and 6 square faces, so 14 faces. The six square faces are the standard Rubik's Cube colors. 6 of the 8 hexagonal faces are too. Then there is a pink and a purple side. After solving it I saw that opposite colors were just as they are on a cube. But it isn't at all obvious when the beast is scrambled. I started by putting together the square sides. Then I could see where they went in relation to the small triangles. URD and ABC were about all that was required. The 12 final small pieces could be placed one or two at a time using the URD 3-cycle that I use on the FTO and on the F-Skewb. 

Following are the notes I made in my Solution Guides spreadsheet years ago.

114 centersThe 8 central triangles can be solved in either 0, 1, or 4 twists. 1 EPS is the worst case scenario.
The 6 central strips on the square faces can be solved using Double EPS. Use Double EPS rather than simply EPS so the triangles stay solved. At most 3 D-EPS will be needed.
212 small edges (corners)Start with the whites on bottom. Whites in the middle layer can be solved with 1 or 3 twists. Whites on top can be solved with 3 or 4 twists.
Next solve the 6 pieces in the middle layer. 3 or 4 twists each if they are in the top layer.
The remaining top 3 pieces will take 0 or 1 twist to solve.
312 large edgesHold any triangle on bottom. Twist a large triangle layer as either R or L. You don't want to move a small edge to the top layer. Do an URD 3-cycle.
Sometimes squares get built but need flipped. The up-back-down-switch-up-forward-down-replace-go back edge flipper works great.
NotesWhen I first got this puzzle I worked out a solution that used a bit of reduction, and a 3-cycle that used an inner slice. I watched rline's tutorial, but it seemed unnecessarily difficult. But the one thing it did have going for it was no inner slice moves. So after some bantering with Konrad online I set out to come up with a solution that was better than my original one, and better, in my opinion, than rline's. The above is it.
In my original method I started by building square faces, checking large triangles, solving the reduced edges (square faces), solving the 4 centers that hadn't been solved since the beginning, and finally using my slicy 3-cycle to place all the little edges (corners).

I tried it. I like it. A lot.