17 Puzzles

posted Apr 21, 2017, 8:38 PM by Bud Lengtat   [ updated ]

Roriana stayed with us for a few days this week. How fun! One of the things we amused ourselves with was


We brought her home with us after visiting last weekend. When Roark and I were playing catch outside he spotted an osprey. Here he is looking at it through the binoculars with Roriana close by.


Four of the 17 puzzles... well... I haven't played with in quite awhile. The Windmill Cube just takes some getting used to. It is really a 3x3x3 cube, but shape-shifts and requires orientation of the middle layer centers. It is also more challenging to orient the middle layer edges. But it can be solved using the Working Corner Method I have been having fun with lately. The 3x3x3 with circles—all are zero faces, which means that the pieces inside the circle do not move when the layer is twisted. I find that this makes the solve a little more challenging than a 3x3x3. One easy approach though is to start with the edge pieces that are inside the circle. Then use ABC to solve the white outer edges. From there it is pretty much the Working Corner Method. It took me awhile to remember how to solve the corners of the 3x3x2, but I finally did. The Crazy 3x3x2 was beyond my powers of recollection. I was on the right track, but couldn't recall all the details, so I looked it up in my spreadsheet.


Pyraminx Crystal

posted Apr 10, 2017, 9:45 PM by Bud Lengtat   [ updated Apr 12, 2017, 11:07 PM ]

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 
  

  
 

 


Pyraminx / Skewb Family

posted Apr 10, 2017, 4:41 PM by Bud Lengtat


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.




The Move Revisited—Al Bob Charlie aka The Edge Piece Series aka Up Replace Down GoBack

posted Apr 9, 2017, 10:45 PM by Bud Lengtat

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.

54 Puzzles Solved in January 2012

posted Feb 1, 2012, 12:45 AM by Bud Lengtat

Some with notes; some without.
40 I want to solve again in 2012; 14 I don't.

I currently have 2 puzzles I haven't solved yet.
  • Dayan Gem IV
  • Gear Pyraminx

Mosaic Cube

posted Dec 19, 2011, 1:20 PM by Bud Lengtat   [ updated Dec 17, 2012, 1:14 AM ]

(When I first got it I wrote) I fiddled around with the Mosaic Cube enough to see how to cycle 3 pieces. During my first solve attempt, it fell apart. For a week it was in pieces on the desk waiting to be put together again. One rainy weekend I reassembled it with the help of a video at MeffertsPuzzles YouTube. It was a bit dicey at the end when the guy on the video used a screwdriver! I tried but failed to do it that way, but finally figured a way to get the last piece in. After assembling it, I reviewed the 3-cycles I had figured out, then scrambled it. My first solve: Corners first, then one side. Then all the centers, which are really sort of like edges only they aren't on the edge. Then the edges. Second solve: Corners first, then one side. Then some centers. Then all the edges. Then finish the centers. I stumbled upon a 5 move 3-cycle for the centers. The same thing on a normal cube scrambles two sides pretty bad.

(December 18, 2011) It has been months since I played with the Mosaic Cube and now I have no idea how to solve it, or where the notes are. 5 move 3-cycle? No idea!

(December 19, 2011) Right after I went to bed last night it hit me. I may have made a video. Got up and looked in the Movies folder. Nope. Looked in iPhoto. Nope. But there was a photo of it partially assembled that was the key to understanding. Now I can do a pure 3-cycle of centers with EPS! And a pure 3-cycle of edges with EPS. Since each corner is one twist from solved, this pretty much covers it.

4x4x4 Octahedron

posted Sep 26, 2011, 12:57 PM by Bud Lengtat

Page added.

Revisiting the Crazy 4x4x4 II

posted Sep 18, 2011, 11:43 PM by Bud Lengtat   [ updated Sep 22, 2011, 3:46 PM ]

In adding the family of 4x4x4 puzzles to the spreadsheet and this site, I eventually had to face once again, the Crazy 4x4x4 II. As I reviewed all the notes I had written before and all the solution strategies I had worked through, I wondered how in the world I ended up with the supposedly most favored strategy.

As I have re-worked through some of the strategies, something else has come to mind, inspired at least partially by something I think rline uses in some of his 4x4x4 solves—building edge pairs and moving them out of the way using EPS.

  1. Center squares—2x2x2
  2. White and yellow "inner edges"—non-white/non-yellow "centers"—use techniques like with the white and yellow edges on the 3x3x3 Corners First Method.
  3. Pair up outer edges—move two pieces together then use EPS to replace them with an unmatched pair before moving back. At the end it may be necessary to use the edge 3-cycle to get the last few pieces.
  4. Solve the outer edges just like a 3x3x3 turning only outer layers.
  5. Solve the corners using 3-cycles. If 2 need to swap at the end, you have to re-solve edges after a 90˚ twist of an outer layer to make the corners solvable. Let's try something else.
  1. Center squares—2x2x2
  2. White and yellow "inner edges"—non-white/non-yellow "centers"—use techniques like with the white and yellow edges on the 3x3x3 Corners First Method.
  3. Pair up outer edges—move two pieces together then use EPS to replace them with an unmatched pair before moving back. At the end it may be necessary to use the edge 3-cycle to get the last few pieces.
  4. Solve the corners like a 3x3x3 using the Corners First Method. Nope. No good. It scrambles the pieces solved in step 2.
  5. Solve the edges like a 3x3x3 using the Corners First Method.
  6. Solve the remaining circle pieces.
  1. Center squares—2x2x2
  2. Blue, Red, Green, and Orange "inner edges"—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.
  3. Pair up outer edges—move two pieces together then use EPS to replace them with an unmatched pair before moving back. At the end it may be necessary to use the edge 3-cycle to get the last few pieces.
  4. Solve the corners like a 3x3x3 using 3-cycle commutators.
  5. Solve the edges like a 3x3x3.
  6. Solve the remaining circle pieces.
Wait! Although pairing up edges is kind of fun, I think it is better to just solve edge pieces one by one. This takes me back to the strategy I liked most about a year ago. The very very very appealing thing about it is that it is the same steps as solving a normal 4x4x4 cube from step 2 on. So there is not a totally new strategy to learn.
  1. Center squares—2x2x2
  2. Blue, Red, Green, and Orange "inner edges" = 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.
  3. 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.
  4. Solve the edges like a 4x4x4.
  5. Solve the remaining circle pieces.
I decided. A new page has been added.

4x4x4 Family and Parity

posted Sep 9, 2011, 8:47 PM by Bud Lengtat

When I first got a 4x4x4 Cube I think I probably started by trying to solve centers first, or layer by layer. Either way I would end up sometimes with a problem at the end that I came to know after some online research as parity. How did it show itself? Two edges needed swapped. This is impossible with a 3x3x3. I don't remember if I figured out a way to deal with it on my own, or if I picked my favorite of various solutions I found online. But then I found online a way to solve the 4x4x4 centers last and I never had parity problems as long as I stuck with it. I have tried to learn and relearn exactly what parity is and why it happens, but I haven't really fully understood because today I was thinking that with a 4x4x4 supercube, in which the center pieces each has a specific home spot, there wouldn't be a parity problem at the end of the solve. Wrong! I tried solving the supercube centers first, and when I got to the end had to swap 2 edges. Time to revisit Ryan Heise's page. Chris Hardwick explains it like this: "This is the parity that is caused by solving the centers such that the edge permutation is odd. If the scramble has the edges in an even permutation and you solve the centers in an odd number of inner face quarter turns you will cause the orientation parity. If the scramble starts with the edges in an odd permutation and you solve the centers in an even number of inner face quarter turns then you will also cause the parity.

This parity is not caused by the centers. I've seen that erroneously stated on many different sites and posts on the group. The one-edge flipped parity is caused by solving the centers such that the edge pieces are in an odd permutation." This is on his website here.

His algorithm is much shorter than the method I worked out, and fixes everything in the process, but it would be one more algorithm to learn, and I am not into learning more algorithms at this point. So I will stick with working it out the way I know, and avoid having to for the most part, by solving the centers last.

Skewb Family

posted Sep 6, 2011, 2:27 PM by Bud Lengtat

Pages have been added for the Skewb, the Tetraminx/Pyraminx, the Jing's Pyraminx, and the Vulcano. They join the Crazy Tetrahedron Standard, which is also in the Skewb Family. Yet to come: Crazy Tetrahedron Mars, which I have attempted, but not yet solved. And Crazy Tetrahedron Saturn, which I have not yet attempted.

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