Puzzled 2: Red Blue Yellow Balls on Intersecting Circles

Showing posts with label Red Blue Yellow Balls on Intersecting Circles. Show all posts

Tuesday, May 26, 2020

Rubik's Rings—Red Blue Yellow Balls on Intersecting Circles (not to be confused with Rubik's Magic)

I know, I know. Yesterday I told myself I was going to put it away and not think about it. But today I felt compelled to get it out and experiment and see if I could codify it. So...

R' moves the right ring down one. R'2 moves it down 2. And so on.
R moves the right ring up one. R2...
L moves the left ring down one. L2...
L' moves the left ring up one. L'2...

If most of the yellows are in the inner section and if your moves do not pull any red or blue up from the bottom, then the only changes will be at the top.

The right outer section has 11 balls. Let's call them 1x to 11x starting at the top.
The left outer section has 11 balls. Let's call them 1y to 11y starting at the top.
Let's call the inner top ball T, and the inner bottom ball B.
Left inner balls we will call -1x to -5x.
Right inner balls we will call -1y to -5y.

The following 5 pictures were each taken after doing the given sequence to a solved puzzle.

R' L R L'

1x > T > 1y

2R' 3L 2R 3L'

2x > T > 3y

6R' 5L 6R 5L'

6x > T > 5y

R' (L R' L' R) R
1y > 1x > 2x

2R' (3L R' 3L' R) 2R
3y > 2x > 3x

After all this analysis I was feeling pretty confident, so gave it a good scramble and started solving. But before long once again I was dazed and confused and all my wonderful analysis was not helping. Directly. But then. Bam! It hit me. Solve the yellows first! That is the key step that I had forgotten. Basically the whole solution strategy is to solve the yellows then use The Move to solve the reds and blues.

So I did it and it was easy to solve. Another scramble. Yellows first. Reds and blues... Now this is interesting...

Tried The Move but they were too far apart and a yellow got outside, so I solved the yellows again then resolved the blues and reds. So, no, I don't have a perfect strategy for solving the above case. Yet.

After fiddling a while longer I can say two things. I'm still a bit confused. But I am confident I can solve it within a few minutes every time.

Sunday, May 24, 2020

Last Two Scrambled Puzzles

The one on the right is another Pentahedron. Uranus, to be exact. I followed the instructions in my Solution Guides Pre Fall 2013 and it was super easy. Here they are:
Anti-clockwise Algorithm
RU'RU L RDRD' L cycles the bottom corners anti-clockwise.

Explanation of Algorithm
RU'RU is an EPS from DR to UR to UL. It also cycles 5 corners.
RDRD' is an EPS from UR to UD to DL. It also cycles 5 corners.
In other words the second EPS puts the edges back.
It also puts some of the corners back, resulting in a corner 3-cycle.

Clockwise Algorithm
LULU' R LD'LD R to cycle corners clockwise around the bottom.

Solution Strategy

Yellow and Purple Circle Edges. At most 3 twists.
Blue, White, Orange Circle Edges. At most 2 twists.
Yellow and Purple Outer Edges. Use The Move.
Middle Layer Outer Edges. Use The Move.
Corners. Use the 10-move 3-cycles built from The Move. (The algorithms above)

The puzzle on the left above is called Rubik's Rings. I remember that I mastered it a couple summers ago when we were in Czechia. But now? I'm still trying to figure it out. When I Google Rubik's Rings I do not get this puzzle. Instead Rubik's Magic comes up. Dumb.

I finally solved it. But have I mastered it again? Far from it! I just fiddled and fiddled. Tried this and that. Finally I tried moving a ball to the other end. It messed up something else. I fixed the top and bam! It fixed the bottom as well.

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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.