Old Treasures and Blasts From The Past

 

I posted this Skewb Collection a couple days ago on Craigslist.

Dino Skewb, Ultimate Skewb, Curvy Rhombohedron, Squished Skewb.

Apple//e Software

Calendar Maker was a program I wrote to print out calendars on a dot matrix printer for Dad. He was really into birhtday calendars.

I had a program published on Softdisk! Loose Change. They totally reworked the graphics and I didn't even feel like it was mine any more, but the idea was mine for sure. When I taught algebra at FLCS we had some word problems that gave a given amount of money made from an known number of coins. The object was to use two equations with two unknowns to figure out how many of each coin there is. I had left a problem on the board one day and after school Rory, when he was 12 give or take, quickly figured it out in his head, no algebra required. I started giving him problems like this for fun and programmed a computer game for him based on these problems. 

IO Silver was a game we liked published by Beagle Bros. Software in 1984. All I remember is using 4 keys on the keyboard to make the little guy run around the screen collecting things.

The Rory and Raymond disks were... hmmm... I seem to recall making a game disk for each boy. When you booted it up it ran a math practice thing or something that they had to pass in order to get to the fun games. I think that is how it worked.

Loderunner. Ahhh. Loderunner. How many hours I spent playing the 150 levels and making levels of my own. A quick online search uncovered an online version so I can play the Apple //e version on my Chromebook! Lode Runner Web Game

Dino Eggs. One of the games that came on Softdisk. I think we played it quite a bit but I have no recollection of the details. Good news. Some guy made a video on YouTube. Dino Eggs And in the description there is a comment by the original creator and a link to his story about making the game.

Super Boulder Dash. Did it come from Softdisk too? Don't recall. It was fun and engaging enough to have and keep but I do not remember it either. Again, it can be found on YouTube.

Championship Lode Runner. This added another 50 levels to the original 150. I was so pleased that I could pass them all I documented it on the label. 

AppleWorks 4. Oh oh oh. AppleWorks on the //e. Fond memories. 

Math Blaster. This was the best version of Math Blaster in my opinion. The Mac version did not appeal to me at all. I loved the Apple //e Math Blaster game. Rory was the Math Blaster Champion.

The Beagle Bros. !!! I had quite a collection of their software for the Apple //e.

I learned about Fractals on an Apple //e. Oh yeah. Green monitor. Relatively slow processor. I would start one before I went home for the day and hope it would be finished by the morning. But I was fascinated by the math behind the graphics.

If I remember correctly Myst was for the //e, DuelTris was for the Apple 2gs, and obviously the book was written for Mac users. I think I completed Myst. DuelTris was a fun 2-player form of Tetris. And the book was very influential in teaching me how to take advantage of the Mac word processor instead of trying to type on the computer as if it was simply a typewriter.

In 2003 the boys and I made up a new Frisbee Golf game on our home course of 15 "holes". We called them holes even though they were really trees, rocks, a ditch, and a swingset. Over the years we played a lot of Frisbee Golf. And for the most part we used normal Frisbees, not the new fangled disc golf discs. Sometimes we played each person against the others. Usually we played teams. Sometimes one team against another, but usually the team was all of us. We were seeing how low a score we could get. At one point in our history of Frisbee Golf games we played Speed Frisbee. I'd time the game on my wristwatch and we would play as a team, usually Rory and I throwing and Raymond blocking to keep the Frisbees as close to the holes as possible. We would combine the times and scores to get the final score. I kept track in a little notebook. But in 2003 we made up a new game. How many throws does it take to get all ones? Our bests:

Ro & I: 66 on September 6, 2003

Rory, Robert & I: 54 on October 21, 2003

Raymond & I: 62 on October 8, 2004

Rory & Raymond: 38 on August 4, 2007

As far as I know we haven't tried since.

Skewb Pyraminx Family

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.

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.

Curvy Rhombohedron Skewb

The first couple solves I just started putting pieces together that looked like they needed to be put together. Eventually a 3-cycle or a twist or two needed to be done to finish up and I drew from my Skewb Family Arsenal of Algorithms (I just made that up).

But then Kevin asked how I solve the Skewb, so I got out the Skewb Cube and solved it. Then the Tetrahedral Skewb. Then the Squished Skewb. Then I intentionally tried to use the same strategy to solve the Curvy Rhombo Skewb.

Documented Scramble #1: DNF
After getting the first 8 pieces solved, leaving only 6 to go, the thing still looked scrambled! After using a setup move and the 3-cycle to place 2 of the 6 pieces, and not being able to see how to undo the simple setup move, I decided that although it is possible to solve in the same way, a more intuitive approach would be better.

Documented Scramble #2:
After solving the yellow layer, including the green and purple triangle center pieces, one twist of the black layer was needed to solve the 3 remaining triangle center pieces. That left the 3 remaining edges out of place and the remaining corner twisted. After using Double-EPS to place the edges instead of the pure 3-cycle, both of the diagonally opposite corner pieces needed twisted. I don't think it is possible to twist them together, so I twisted each one with a triangle using an algorithm that hadn't been used in any of the previous posts' solves. I will not even attempt to type it out.

So it turns out I not only demonstrated the algorithm. I also showed what happens when unexpected results happen, and one way to solve mysteries! :D

Documented Scramble #3:
Very difficult to get the yellow layer this time. The first several times I tried it this way it seemed almost trivial to get a layer solved. But this time, either it was a different scramble, or my mind wasn't in sync with the puzzle as before. This can be a problem when solving intuitively rather than with a systematic strategy. I ended up using Triple-EPS a couple times to swap pieces into place on the yellow layer.

After solving most of the black layer as described in #2, once again I ended up with the 2 small corners twisted. Two lessons to learn. First, if I would use the same steps as I do with other Skewb puzzles, I wouldn't have this problem at the end. So is it worth it to work through a more visually challenging solve at the beginning to make the endgame go more smoothly?

Secondly, it dawned on me that one conclusion I made in #2 above is incorrect. I said "I don't think it is possible to twist them together," because one is in the corner role and the other in the center role (thinking of the Tetrahedral Skewb). But what did I learn in the video above? I can twist 1 corner and 3 triangles, in the unshapeshifted puzzle, and 2 of the triangles are centers! So I can twist a corner and a center together! Yay!

In conclusion... well, is it ever really concluded? Let's just say that after several more solves I have decided that at this point I rather like solving it using the same basic approach taken with the other Skewb Family puzzles. That is, get the 2 small corners and the 6 triangles first. This only takes a few simple twists. Maybe 1 EPS. So with half a dozen twists or less more than half the puzzle is solved! Then 3-cycle the 6 big pieces home.

If a corner needs twisted without disturbing triangles, up twist down replace up twist-the-other-way down go-back works well and is pretty simple. Let's see.

Bottom line though, with this puzzle, as with any puzzle, there is no right or wrong, easy or hard, better or worse, way to solve it. I may decide on a favorite way to solve it tonight, but 6 months from now pick it up and take a whole different approach. I suppose I should demonstrate the Preferred Method applied to this one, so

Documented Scramble #4: