## Monday, January 4, 2010

### How I Found The Ultimate Solution

A few years ago...I'm 11 years old, and someone gives me a Rubik's cube for a present. I proudly take it to school to show people. Someone messes it up. I twist and turn and try to get it back. The someone laughs. I cry. That ends my relationship with the Rubik's Cube.

Over 20 years later, and now I decide that for goodness sake, I should be able to do the RC, and I'm intelligent enough, etc etc etc. So I ask for one for a present. This time the internet exists, and I do some research on how to solve it. Having assumed there's pretty much only 1 way to solve it, I'm surprised to find a multitude of ways, some related, others in a class of their own.

I see videos of people like Jessica Friedrich solving it in 15 seconds and nearly give up. I read about how she worked out billions (well, a lot, anyway) of algorithms to solve it. So "anyone can solve it in 2 easy steps: 1) learn all the algorithms, 2) solve it".

Then I find pages like Cubefreak, which list a number of different ways, and make me realise I'm not alone in my quest. Sites like Dan's Cube Station, Cube!, Joel's Speedcubing Page, and Dan Knights - On Speedcubing all confirm this. By this time, I decide I want to be a speedcuber. A day later I give that thought up.

By now I've learned to slowly solve the cube by following algorithms. Some methods use lots of algorithms; some use less. But at the back of my mind there's a nagging feeling that solving the cube by working through algorithms is a bit like the Maths teacher who tells his students they don't need to understand what they're doing, just follow the instructions. I feel like I'm cheating.

My quest begins to find a method which is simple to do, and which makes intuitive sense. On the bottom of the page How to solve the Rubik's Cube, there are links to alternate methods. Among these are methods by Lars Petrus, Matthew Monroe, and a method by Philip Marshall called Rubik's Cube: The Ultimate Solution. The Marshall method intrigues me because it says it uses only 2 algorithms. Two algorithms??? That must be a typo. How could something as complex as the cube use only 2 algorithms?

I take a look at the site and two things immediately hit me:

1. The claim is true. There really are only two algorithms required.
2. Using those algorithms to solve the cube is nearly impossible because the explanation of the site isn't overly clear.
I encourage you to take a look at Philip Marshall's site. You'll probably find what I did: the site is very wordy and takes many reads of each part to fully grasp what the author is saying. Yes, there are pictures of cubes, but overall, it's not like most of the other RC sites out there, which have fancy java applets, and easy to read chunks of text. That being said, a lot of the material on those sites is algorithms.

After about a week of doing not much else but working on understanding this method, I can safely say that I get it. It's a brilliant method; genius, even. But a few google searches convince me that not many others are using it, probably because people can't understand what he was writing. (That certainly is a common theme among the few forum entries I find.)

Now that I'm on board with the method, let me make a few observations about it
1. It's not for speedcubers. If you're looking to reach that sub-20-second time, this is not the method for you and my site won't help you. I suggest trying some of the other links above.
2. It always works.
3. It's actually very easy to grasp and quite intuitive. I hope to use this site to convince you of that.
4. It's challenging. Not because of all the algorithms to learn, but because working out where to use the two algorithms is not always a piece of cake.
5. It's by far the most satisfying way to solve the cube. Every time I've finished a solve, I've felt good! It's good to know that I'm not mindlessly following a multitude of algorithms. With this method, I really do understand why it's working.
6. His claim that  "It is so simple that, once learned, one cannot forget the moves. You will not have to twist the cube incessantly in order to figure out how the moves are made. " is entirely true.

A quick word about its creator.

I had a good poke around the site and read what I could. I even sent an email to Philip using the address on the site, to thank him for the method and ask some questions about it. That bounced straight back. Then I read on one of the pages: That let's me out. All I can do is about 1.5 turns per second; but then I am 75 years old. Judging by the fact that the latest date on the site is 2004, I'd say Philip is now at least 80 years old (it's 2010 as I write this). That probably explained the bounced email.

The purpose of my site, then, is to try and make what I think is a fantastic method completely clear and understandable to anyone else who's interested. I'm not Philip Marhsall, I've never met him nor communicated with him. I hope he doesn't mind me making this site.

The standard RC notation is never used in this method; sometimes, though, I'll use it to make things clearer. For completeness, here it is:

F-front face
L-left face
R-right face
U-upper face
D-down face or underneath face
B-back face

Putting a dash after any of those means to rotate anticlockwise (pretend you were looking at the face straight on).

So, a sequence like F R' D U' F2 means
1. rotate the front face 1 turn clockwise
2. rotate the right face 1 turn anticlockwise
3. rotate the down face 1 turn clockwise
4. rotate the upper face 1 turn anticlockwise
5. rotate the front face 2 turns

1. Brillant...keep it up...when I was 11 years old and got my first Rubiks cube...I worked on it and memorized sequences to certain patterns...I managed to do it in under a minute...Now I am 42 years old and for the past year I have rekindled my interest in solving the cube but to find out that my memory is just not what it was 600 000 000 000 neurons ago. Since I have much less of them now...it takes my time to understand and memorize...I have begun to read your site...I am motivated and excited to start again...I just bought the Rubiks tower and thats how I found your site. So I guess I will just start by doing the simple cube first. Wish me like...I will keep u posted...If I succeed...it will be because of you...Thanks

1. Brilliant!

I do wish you luck, but you'll need hardly any of it. This method is so simple. Even some of the much harder puzzles (eg. Crazy Mars Pentahedron) I can do (and will be uploading videos) using only a basic edge piece series. It constantly amazes me how adaptable it all is. I'm just like you, in that I don't have the ability, nor can I be bothered, to learn algorithm after algorithm.

2. This comment has been removed by the author.

3. Best of luck! I didn't know there are so many shapes of cubes :\
I never heard of 2 algs solution, however isn't it making it harder than the regular solve (the seven steps - solution) because you have to do more moves "yourself"??
Ben.

4. Hi Ben,
Difficulty is subjective. You're talking about "more moves", which is clearly about the number of moves, not about difficulty. I'm not quite seeing how a solution which has 7 steps could be simpler than a solution which has 2...

5. Hi chareaves
I've been looking for this kind of solution for a long time.

I think it can be made even more intuitive as follows.

Say your basic Edge Piece Series is
U'RUR'
This affects a T shaped subsection of the cube

Then the Corner Piece Series can be written in terms of the Edge Piece Series
(U'RUR') L' (U'RUR')' L

(When you write it out L and R commute and you get what you're using namely U'RUL'U'R'UL)

In fact the form I prefer would be
L' (U'RUR') L (U'RUR')'
(You are throwing the FLB bottom corner in to the T shape, doing the Edge Piece Series to it and then pulling it out again and finally undoing the Edge Piece Series)

Thanks again, a long search is over.

1. You are absolutely right. All I've done here though is to try and present Marshall's solution. I don't use his exact solution anymore.

6. It turns out that you really only need the Edge Piece Series (what I have been calling "down, down, up, up"). You don't need the Corner Piece Series at all.

1. Use down-down-up-up (EPS) to get all of the edges in the right places, so that you have "plusses" on each side.

2. Use (EPS)^3 to move the corners into the right places, since doing EPS three times swaps two pairs of corners. Do this until all of the corners are in the right place, but possibly wrong orientation.

3. Twist the corners that need twisting by using EPS twice (which messes up three edges and twists four corners, but leaves them in place), swap out one of the corners with another one that needs twisting in the opposite direction, and then undo the EPS's you did to get everything back to normal again. (This step is harder to describe in words.)

And there you have it: 3x3x3 solved using only the EPS. :-)

1. Correct! And thanks for commenting. I've just tried to present Marshall's solution here. When I show people how to solve myself, I do something similar to yours.

7. @chareaves and Chris Pine

Great stuff. Solving the cube with just one move plus setups.
(A single 1,1 commutator and its conjugates.)

Nice description Chris. Just one point that probably should be dealt with in more detail; chareaves has put up a video of solving the corners just using EPS
but there is one tricky configuration at the end - everything solved except for two corner pieces in position but twisted.

One of these corners is moved out of the way of an EPS involving the other corner. This other corner is then moved around by multiple applications of the EPS until it is in place and correctly oriented.
Then the first corner is temporarily moved to the second corner's original (and also final) location and itself moved in to place.

chareaves uses repetitions of the EPS instead of it's inverse (EPS^5 = EPS') which I also prefer.

Great work both of you.

As a final step in making this truly the idiot's solution I would like to break down Marshal's four cases for the top edge pieces (Step 3) in a way you wouldn't have to remember cases at all.
I'd like to have one target case, namely case 3 - two correct and beside each other. We can finish from there in one EPS.
The rest of the time I would like not to have to think in terms of cases but just look and see how to get to case 3.

For example with case 2 - two correct and opposite each other - I'd ignore the elegant solution and instead stick with an EPS to get to case 3. Am I correct in thinking this is always possible?

As far as I can see it is also true that in both case 1 and case 4 a single EPS brings you to case 3.

Is there a counterexample to any of these claims?

8. Hi,
Thanks a lot for your clear explanations!
I searched for a good solving method that would be simple for me to learn and remember by heart, and I decided that the Phillip Marshall method sounds like the best candidate. Only two simple and clear 'series' to learn.
However, then I got confused by his website and video, and I'm happy to see that you figured it out, and orderd your insights in a clear way, and put them on the web for everybody to see.
Thanks!