Because Social Media isn't Verbose, and CLL isn't as common in 1982.

 People have complained to me on more than one occasion that I am verbose. As far as I know, this is a completely undesirable trait most of the time. However, I am always found wanting more information and specificity when I ask about things, so I have attempted to learn how to (mostly) politely interrogate people so that I get the sort of answers that I'm looking for.

When I'm the person giving the answers, it's terrible, but mostly because I have given more answer than the other party wanted, and even sometimes to questions that the other party only wanted a meaningless superficial answer to. I have been told on more than one occasion that I talk too much or overexplain, and even once have been told in response that "people aren't going to read my @#$%^$%$$% novel" when I typed out a thorough answer to something.

Every once in a while, I see something that's a tiny bit underexplained, and it bugs me, but I usually have enough sense to not cause problems. What follows is a byproduct of me now fixing something that was a little bit under-explained (or oversimplified, you pick) and I finally bothered to sort it out myself.

So the first Rubik's cube official record was Minh Thai's 22.95. 

 

https://www.youtube.com/watch?v=WJTZhgrbgt8&t=325s

And, thanks to reddit users /u/qqwref and /u/BrestCubing, a lot of important solves have been reconstructed - including this one - and we'll get to that.  Most of the modern solves are done with a method that everyone is more familiar with, what used to be called Fridrich and is now referred to as CFOP. But, Minh's solve is done with his own method, and it's even well documented. ("The Winning Solution", ISBN 0-440-09795-9, 1982.) 

Minh's book was a step ahead of many things that were available at the time because he had individual orientation algorithms for the second set of corners, when nearly every other solution book had some sort of incremental method for orienting the second set of corners. It was one of the first published cube books to explicitly detail and demonstrate the idea that if you had more algorithms at your disposal you could solve faster.  Interestingly enough, there were also a handful of extra algorithms in the examples that started to make me consider the idea that Minh had actually been able to orient and permute second layer corners in a single algorithm.

So, that leads me to the reconstruction. Michael Gottlieb's (qqwref) reconstruction is as follows:

U L2 D' B2 U' R2 B2 F2 D' F2 L2 R2 F R2 D L2 R2 B' L' D' R F' 


x2 y // inspection 
D' R u D R' y' D' R D R' // FL corners + 1 edge 
y D r' E' L // FL center + 2nd edge 
z2 U y l D R' z' R' x z' r' R2 U2 z D R2 D2 // CLL 
R' l' z M D2 M' // FL 3rd edge 
z2 y R z' M z R' // LL 1st edge 
z' r' L' z D R' E R // LL 2nd edge 
U' u' R E' R' // LL 3rd edge 
u R' E' R E2 R E R' // LSE 
R2 E E' r2 E M2 E' // centers

 

This is typical of modern reconstructions. The scramble is shown first, starting from a solved cube with white on top and green on front, moves are shown in standard Singmaster notation, including cube rotations, and double slashes at the end of a line to give a place to put comments.  So, at the end of line four there, it says "CLL". The implication there is that Minh solved both permutation and orientation in a single algorithm. However, that's not the case. Also, it's largely overlooked because it's typically more move-efficient to orient first before permuting. So, here's my marked-up version of the reconstruction. I added notes in one color and comments in another so I could keep track. The Stage/Section references are from Minh's solution guide.

 

U L2 D' B2 U' R2 B2 F2 D' F2 L2 R2 F R2 D L2 R2 B' L' D' R F'

x2 y // inspection  yellow top, red front 

D' R u D R' (y' D') R D R' // FL corners + 1 edge ends with orange corners on top but still yellow top red front 

(y D) r' E' L // FL center + 2nd edge ends with orange on front, red corners need diagonal swap 

 z2 U y l D R' z' R' x z' r' // corners in correct cycle, orange on bottom 

This is equivalent to the permutation algorithm in Stage 2, Section 1, C3, (LFUF’U’L’) with cube rotations and wide moves.  This is permutation only, so I wouldn’t exactly count this as CLL. 

 R2 U2 z D R2 D2 // CLL corners oriented, orange on left  

This is equivalent to the orientation algorithm in Stage 2, Section 2, T7, (R2 F2 R F2 R2) with one cube rotation. 

R' l' z M D2 M' // FL 3rd edge 

z2 y R z' M z R' // LL 1st edge 

z' r' L' z D R' E R // LL 2nd edge 

U' u' R E' R' // LL 3rd edge keyhole piece is at ‘dr’ for the LL edges 

u R' E' R E2 R E R' // LSE 

R2 E E' r2 E M2 E' // centers

Taking another look at this reconstruction solidified two things for me - one, the confirmation that he wasn't doing full CLL, and second, that he rarely performs any sort of F or F' moves despite how often they appear in his solution guide. I had already gotten a sense of that from some other video of him, but it was nice to have the confirmation from a good reconstruction.

So, that's not to say that _nobody_ was doing CLL in the 80's, it just wasn't Minh Thai. Mark Waterman has a well-documented (on the web, at least) corners first solution that has a CLL step.

The next time we take a swing at this, I will have to look at the "LSE" step.

Yes, I still cube. Sometimes I type, too.

So I found out in the last month or so that I'm no longer in the top 100 in Florida on 3x3x3, the standard regular Rubik's cube. Also, I didn't get to sign up for a competition in June that I kind of wanted to go to because I was being distracted by life. But, competitions aren't really my everyday focus at this point. I think that I have more to say when I'm showing someone about cubing, and making it more accessible to them from an intellectual standpoint.

I managed to make it out to one of our local Mexican food places with the wife just the other night. We hadn't been out to dinner in a while, and I thought maybe I could do better than Taco Bell. They make guacamole right at the table. When he asked us if we wanted mild, medium, or spicy, we're joking about whether or not he means authentic medium or chardonnay-drinking-housewives-listening-to-Coldplay medium. We're seated outside, and it's warm enough out that we're enjoying the fact that we have both Mexican Coca-Cola and water to drink because we're sweating just sitting there. Some random guy showed up around the same time as our guacamole technician with a large Labrador and just wants to have it sit with someone while he goes in and gets alcoholic beverages. The people next to us who were just finishing seem to have enough room near them to accommodate the dog, and our guacamole tech commented about how the dog is being good. I turn my attention to the cube I have on the table for a moment, and since I was looking down I saw a person walking a dog on the other side of us, and predictably the Labrador was no longer just sitting there, but charted an intercept course to find the other dog. The Labrador reappeared, and then went to have a word with some people at the other tables about what it was that they were having for dinner. One of the servers had enough sense to bring the dog some water, and it sat back in its original spot, but now the people sitting there were really looking to go at this point - both because of the dog awkwardness and because they had been finished with their food for a bit already. Thankfully the gentleman whose dog it was reappeared, and talked with everyone again. He even asked how old our guacamole tech was, and said how proud he is of him for being a 16-year old with a job.

We went on to enjoy our guacamole and chips, ordered some tacos, and the couple watching the dog can now leave, and the servers went about the business of rearranging two tables so that a somewhat larger group could sit there. The group of six was an older man, and his wife, and a collection of  twenty-something children and perhaps a girlfriend. or My wife and I enjoyed our meal, talked about how customer service is supposed to work, and talked about how we are both readjusting to how our jobs have changed over the last couple of months. It isn't until the check was done and we're about to leave, that the one person sitting in the group of six that can see (the presumed father of the family) that I have a cube at the table mentioned it to the person that's closest to me but has his back to me. So, I brought the cube over, and the father mentions that the person closes to me, a bearded college-age person, could solve it.

At this point, my focus went to the college age person. I asked him how long it takes him to solve it, and what method he uses. Since he does something that's between a beginner's method and what we now refer to as CFOP, and takes around a minute and a half, I showed him the 80's corners first method that I do. I talked through most of it, and I probably wasn't that fast. He was intrigued, but he wasn't exactly impressed that I could tell. I was concerned that I had flubbed my demonstration, but was ready for followup questions. I did not get to do followup questions, because the young woman diagonally opposite him at the table immediately reached for the cube to scramble it again. Perhaps I had impressed her more, or she had seen it less. I try to nonchalantly stand around while she's scrambling it and not watch her scramble it, but I'm still trying to stand close enough to listen to make sure that nobody's hand-twisting corners or popping the cube apart. Thankfully there were no shenanigans. So now, I usually for a second demo try to do CFOP, and show how it's different because of looking for more than one piece at a time during the first two layers. This solve went noticeably faster, even despite me talking through it. The young woman got to watch the solve up close this time, and the bearded young man was more impressed this time. Then, while I'm still standing at the far corner, I do a silly cube trick just as comic relief. All it is you do R2 U2 R2 U2 R2 U2 to a solved cube, and you will see that you have two pairs of edges swapped. If you grip the cube properly, and only are touching the unsolved edges, you can perform that same move again without letting go of the cube and so it goes from unsolved to solved and it seems like your hands are exactly where they started (but they aren't). She even had me do the silly cube trick again so she could video it. (No, I don't know where it ended up yet.) So as I'm walking back around the table, I turn the cube a few times in my and ask the bearded young man if he had heard of Steven Brundage, which he had. I showed him the scrambled cube in my hand, explained a little bit about what it was that Steven Brundage does, and using the cover of the high back chair next to him, I then was able to fix the cube quickly and produce it for the group solved again. So, now, I didn't have to worry if he was impressed or not because I think he definitely was by then. We definitely had to go at that point, because I can't really take questions after doing the Brundage trick.

I also got to do a little bit of a demo for my corner gas station/vape shop/convenience store the next day, and I think I learned from the night before not to end with the tricks, but I also had enough time to show off a Roux solve. So that one went 80's - CFOP - Roux - What is an Inverse?. I told them that there would be a quiz next time, but I think that's an idle threat unless they start selling cubes there.

This is what I like to do, though. I really enjoy doing these small demos for people. Honestly, I hope that the fact that I've been doing it is why I'm not in the top 100 in Florida any more. I hope that enough new people have gotten into cubing as a byproduct of people like me making it more accessible that the pool of people competing has grown in size.

In other cubing news, I finally purchased a Rubik's Tactile Cube which means I can now finally say that I've solved a cube without looking at it. I was very happy with the choice of shapes on the opposite sides. I was also very happy that even though it's the modern Rubik's mechanism that's harder to pop, it was set up just loose enough that it was a delight to turn the first time out of the package.

"What's the secret?" they ask...

...and more often than not, I respond with "How do you get to Carnegie Hall?"

It's not a question that I get all the time, but if I'm out walking around with my Rubik's cube and a bystander asks me that question, it's the question that's the most likely to get me to stop.

I think the most common misconception about the Rubik's Cube is that people think there's more going on that what there is. Visually, there are 54 stickers (or colored tiles). It usually takes me showing a person specifically what an edge and what a corner is to get them to realize what they're looking at. More or less, this is the rundown that I give them.

Ok, so the first thing that you want to see is that the center pieces don't move relative to each other. On this cube, red is always opposite orange, white is always opposite yellow, and blue is always opposite green. These six pieces are on a center spindle like a U-Joint in your car, and can't go anywhere. The next thing is that you want to notice is that each edge piece and each corner piece is unique. For example there's only one orange and white piece, and there's a one-to-one correspondence between the colors on the piece and where it has to go when the cube is solved.

At this point I would turn the cube so that the orange and white piece is in the right place.

When I was using older cubes, I often took one of the edge pieces out at this point to show that you can't really change the pieces and that it really was a matter of getting the selected piece in the right place.


So now, you can see that the place that the orange and white piece has to go is that spot between the orange center and the white center. That piece goes at the intersection of those two faces.

While I turn the cube to show the position of the piece, I'm looking for one of the two adjacent corner pieces.


Here's the corner piece that goes next to it. Orange, white, and green. 

That piece has to go at the corner that corresponds to the orange, white, and green centers. There are twelve edge pieces with two colors each, and eight corner pieces with three colors each. So now, for every piece on the cube, you can say: Is the piece in the right place, and is it turned around the right way?

If I think that I've lost them, I pick a different piece and place it in an incorrect orientation in the correct location, and if I haven't lost them I try to extrapolate a little more.

So this now means that if you do one side, like most people try to figure out first, it's not going to just be that side. If you have one side done correctly, it's going to be an entire layer solved.

From here it's usually dependent on the person and how we're doing and what follow-up questions that they're asking.

Another nice version of this interchange is that every once in a while (and it's becoming more frequent) I get to watch someone else solve a cube, and I'm able to offer some pointers, or recommend what to work on next or what to look up. The majority of the time is still me trying to demonstrate and explain as much as is requested to people that are unfamiliar.

Sometimes it's hard to know when we're done, but sometimes it's really easy. Once in a while after a solve demonstration, especially since I'm not as fast as whatever they may have seen on the internet or TV, they say things like "Did you see that there are some kids that can do it really fast, but they're doing it mathematically?" The last time that someone did that, I just walked off.

Had you seen it yourself, you might have thought that I assumed that it was the two people talking to each other and I was no longer in the conversation, since I didn't have a polite response prepared. And then you go - Hey, wait a minute, isn't there math here? What's your problem with the question? So, maybe I should explain.

1) Practically nobody successfully solves a cube without a plan. Even if you don't start with a plan, you're going to need one by the time you finish.

2) Nobody solves a cube fast without a plan, and having memorized algorithms beforehand and putting time into executing those algorithms as efficiently as possible.

3) Nobody solves a cube really fast without a plan, memorized algorithms, and lots of practice at piece tracking - looking ahead at finding the pieces you're going to need for the next algorithm by the time you finish the one you're doing.

So the question you have to ask yourself, is that math? I would say that it's just pattern recognition and execution of specific operators that have some basis in set theory or group theory, but you're not doing any set theory while you're solving the cube (unless you're working it out slowly from scratch like case #1 above.) Considering how infrequently set theory and group theory come up in casual conversation, I don't even have a good feel for what people would say is or is not math. Perhaps that can be left as an exercise for the reader to determine what is, or is not math here. (I'm not suggesting that set or group theory isn't math, I'm suggesting that those are the sort of things about which a layperson might be inclined to say, "No, I mean like real math.")

It would also appear that I really need to watch that movie about Edward Snowden. I was disappointed to find out he doesn't have a WCA ID.

What is the opposite of solved?

My holiday cubing was noteworthy this year. I spent some time working on solving large cubes, although I haven't managed to migrate to a modern solution yet. It was nice to knock three minutes off of my 5x5x5 solve time, although it's not really that noteworthy since I'm just down to 10 minutes from 13. I couldn't really do much with my 4x4x4 time, since I'm still using a Rubik's Revenge from the 80's and the stickers slide around a lot and I'm worried about losing one. Both of those were just warmups for the VCube 7x7x7 that I got this Christmas, but my only solve time for that was nearly three-quarters of an hour, and I'm nervous about the stickers on that as well as they're very small and I've managed to rough one of them up already. I'm not quite ready for anything bigger until I refine my solution, since nobody wants to sit around for hours while I solve a cube. (At least I'm not working on a 17x17x17.)

As a result, the 3x3x3 still has to be the go-to cube for going out in public and talking about cubing. It's still the most mechanically robust design, and it's what people are familiar with anyway. So, that's what I'm always carrying around with me. Last Friday night at a small gathering of friends, I was asked about something unusual - something quite the opposite of what's usually done with the cube. I was asked if it was possible to get all six colors on each of the six sides. I was pretty sure that it was, but I didn't have a ready answer because I didn't seem to be in the right frame of mind. (I had fumbled a question about the meaning of the Apple logo despite having just listened to an episode of The Nerdist with Benedict Cumberbatch the week before.) I knew that there should be several possible positions that satisfied these conditions, but it worried me a little because in my head I started with the most extreme case - throwing stickers on a blank cube and then wondering if it meets conditions of solvability afterwards.

If you take a cube apart and reassemble it at random, you have a one in twelve chance of having a solvable cube. If you start from a blank cube and apply stickers at random, you have a much lower chance of having a solvable cube. If you put the six centers on first, assigning random stickers, you have less than a 1 in 48 chance of having a solvable cube since all six have to be different. It just gets worse from there. Clearly, this was the wrong approach for the problem. So, as I walked back home, I imagined what you could do with conventional patterns, hoping that I could figure out something that wasn't too bad, but nothing came to mind. I could guarantee three or four easily, but once I put more one place, I would always have a side that came up short.

When I got home, I did a quick internet search, thinking that this was already a solved problem and I was just going to reinvent the wheel. While I found a couple people asking the question rather easily, I did not find the answer there. It was hard to find people that even understood the question, since I don't always hold out a lot of hope for Yahoo Answers on questions of this type. But, in the minute or two that I looked, I also didn't find anything that overtly stated that it was an impossible position, so I decided that I would stop checking the internet and leave it as a problem for Saturday

Often when presented with a problem like this, I find myself working on it even when I'm not working on it. As I put my head down to go to sleep, I have this overwhelming thought - "Superflip!" Now, this is not the entire solution, but it puts you a lot closer without much difficulty. The position referred to as the superflip is the state of the Rubik's cube where all of the pieces are in their correct places, the corners are all correctly oriented, but none of the edges are correctly oriented.

So, with the superflip, you automatically have 5 different colors on each side - the corners and the center are the regular color of the face, and the four edges are the colors of the four adjacent faces. The only thing left to do are things that manipulate centers or corners that mix colors from opposite faces. If you move centers around, you can either move six centers to adjacent faces, which we don't need, or you can move four centers to opposite faces, which gets us 2/3 of the way there.

The cube on the left is the superflip cube from the first picture with the centers moved, the cube on the right is a cube with only the same four centers manipulated.

So, I am left with only two sides that need a piece from the opposite side, and no available tool to move centers around. So, what can I use to manipulate some corner pieces without disturbing the edges? The first thought I had was one of the zigzag patterns.

So, once you do that, then the finished cube ends up like this:

So, now we have all six different colors on all six of the sides. If you need the cheat code to get here, try using B' D2 L2 B L' R' D B F' L' F2 R' B2 R' D' U' F2 R2.