Sunday, May 19, 2019

Extremely simple solution for 3x3 Rubik's Cube - just two steps

Introduction

It is not fake. It really works!

Recently I tried to solve Rubik's Cube by myself and I found it very complicated. After 30 minutes I could not solve it and I found beginner's solution on the internet like this. It is very complicated for a normal person and it is almost not possible to remember it. Why this solution so complicated? Why do I need to remember a lot of algorithms? Hopefully, there are some automatic solution finders on the internet :)

I decided to find my own solution, but it should be very simple, that everyone can repeat it and remember. Of course, I read about God and Devil algorithms and that nobody could find a very simple solution so far. But really, 3x3 Rubik's Cube beginner's solution has 7 steps and 9 algorithms which have to be memorized. Some of the algorithms look like this R U R' U R U2 R' U (8 moves of the cube). Who can remember this? Only some real geeks or nerds.

Note: Please do not expect to use the solution mentioned in this post for very fast solving/speedcubing. It will not work. This solution is simple but relatively long. It was designed to solve Rubik's Cube with simple and easy to remember algorithm without time limitation.

What is needed to apply this simple solution?

After I found a simple solution for 2x2 Cube like explained here, I started working on a simple solution for 3x3 Rubik's Cube. Unfortunately, the same solution as for 2x2 cube does not work in some cases, sometimes I manage to solve 3x3 by the same solution as 2x2, but not always. In a 1 month, I finally found a simple algorithm, which can solve any 3x3 Rubik's Cube. I called it Russian Flag Solution or Z-Solution. It consists of 2 steps and only 2 things have to be memorized, in order to solve it.

What has to be remembered?

1. How to solve one face properly.

2. This Color Sequence: White, Blue, Red, Yellow, Green, Orange. (let's call it "Russian Flag Sequence").









Optionally it is good to remember which color is opposite to which, like White-Yellow, Blue-Green, Red-Orange, but it is not necessary. It will just make it a little bit faster.

"Russian Flag Sequence" is easier to remember because the first 3 colors make Russian Flag and the rest are the colors opposite to Russian Flag colors.

What are the steps (brief description)?

Step 1. Solve all the corners and middles.
Solve corners and middles only on one face in the order defined by "Russian Flag Sequence" and after some time all the corners and middles will be solved by themselves. Of course, after solving corners in one face, the previous face will be broken, but it is expected, in the end, all corners will be fine. To solve corners in one face, the same algorithm "how to solve one face properly" (explained in this video) can be used. It is even easier to solve only corners and just skip what is in between the corners. Detailed description.


Step 2. "Around the White".
Solve only one face which is close to white, then solve next face close to white in clockwise or counterclockwise order. This is why I call it "Around the White" algorithm. But do not break the corners. Usually, it is very easy. In other words, it is making faces one by one following the color sequence Blue, Orange, Green, Red or opposite.






After some time full cube will be solved. Detailed description.

Note: Solved corners and middles state is very stable and robust structure, it is very difficult to break it.

Detailed explanation.

How to solve one face properly.

First, I want to put some pictures and explain what does it mean "How to solve one face properly". It should look like shown in the pictures below. If there are some difficulties to solve cube to this state, this video can help.

It is one state of the cube shown from different sides.

It is one state of the cube shown from different sides.


How to solve all corners with the detailed illustrations (Step 1).

Here as I mentioned above the Russian Flag algorithm will help. Only corners on one face have to be solved in a specific order. And again, it has to be solved properly. Below are the pictures showing what is "properly solved corners for one face" and what is "wrong".

It is one state of the cube shown from different sides.

It is one state of the cube shown from different sides.
To achieve this, the same algorithm as to making one face can be followed. And again, if there are some difficulties to make this cube state, this video can be helpful.

Now corners have to be solved in the "Russian Flag Sequence" like shown in the pictures below.

Iteration 1 (white corners).

 Iteration 2 (blue corners).

 Iteration 3 (red corners).

 Iteration 4 (yellow corners).

Iteration 5 (green corners).

 Iteration 6 (orange corners).
and after orange color (Iteration 6) everything should be repeated again from white color (Iteration 1). Of course, if white corners are solved, while solving blue corners white will be broken, but it is ok. And after some time all the corners will be solved automatically.


Most probably other sequences will work as well (most probably opposite direction like Orange, Green, Yellow, Red, Blue, White), but for me, Russian Flag is easier to remember and I did not try other sequences. This color sequence is chosen because these are colors in one of the corners if I go through them clockwise. I believe any other color sequence will work if they are from the corner and make a clockwise or counterclockwise sequence.



How to solve faces "Around the White" with the detailed illustrations (Step 2).

Now one full face has to be solved which is attached to a white and then next face attached to white in counterclockwise order. It is shown in the pictures below. And again while solving one face, previous will be broken, but it is ok. Also after each face, it has to be checked, that corners are not broken. If corners become broken, everything should be restarted from the beginning.

Iteration 1 (blue face).


Iteration 2 (orange face).

Iteration 3 (green face).

Iteration 4 (red face).

and after red color (Iteration 4) everything should be repeated again from blue color (Iteration 1).
This video shows the whole process.

How much time will it take?

Interesting question, how much time it will take? Maybe it will take years to go through all possible combinations?
Actually, I did it many times for 3x3 Rubik's cube and it takes from 5 to 20 minutes. It is approximately the same time for Step 1 (all corners) and for Step 2 "Around the White". For example, 5 minutes for Step 1 and 5 minutes for Step 2. In terms of how many times it is required to make different faces, I can tell that from my statistics after 10 to 30 iterations corners will be solved and similar for step 2 "Around the White".

Why does it work?

Do not ask me why it works, I have no clue :) I found this solution accidentally, by just playing with 2x2 Rubik's cube with the thoughts "Let's do one face after another and see what will happen". And after this, I made a similar solution for 3x3 cube.
The only explanation I have is about entropy reduction. Every step I decrease entropy a little bit and in the end, it leads to full order and zero entropy. Maybe it will lead to some new development in the Group Theory or even Solid-state Physics.

Does it work for other Rubik's cubes?

So far (based on 19 May 2019) I could not manage to find a similar algorithm for the 4x4 cube. All corners algorithm works fine for the 4x4 cube, but step 2 does not work. I will put an update here or new post if I will find a simple solution for the 4x4 and bigger cubes.

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