Puzzled 2: Square-1

Saturday, June 20, 2020

Square-1

I don't think I have ever felt like I had the Square-1 mastered. Maybe I can spend enough time with it now...

Here it is scrambled.

And solved.

Here is a "map" I made years ago to help navigate from scrambled to solved.

The solution strategy in the old Solution Guide goes something like this.

Use the map to get it back to cube shape.
Get all the white corners on top.
Use Corners First algorithms for 1 pair and 2 pairs and even 0 pairs to solve the corners. Here is what the 2 pairs algorithm looks like in Square-1 notation. (0,-1) / (0,3) / (-2,-2) / (2,-1) / (0,1) swaps the front ones on top and the front ones on bottom.
Solve Edges with this double swap algorithm. (1,0) / (3,0) / (-1,-1) / (-2,1) / (-1,0) swaps UL with UB, and DR with DB.

If one pair of edges need to swap at the end, there is a parity issue. Go to 44 44, swap 3 on top with 3 on bottom, go back to cube. Fix everything.

The above is in my Solution Guides Pre Fall 2013 spreadsheet. On June 27, 2015 I blogged "...today I set out to discover and document how to fix parity with a minimum of damage to the solve. Found it. When you make the swap of 3 pieces make sure you move the same number of yellows down that you move up. For example: / (3,3) / (–1,–2) / (–2,4) / backtrack"

Earlier in June 2015 I posted this diagram that I had painstakingly made.

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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.