Chapter 441

If you want to restore the Rubik's Cube smoothly with the fewest steps, you must first understand a concept - the number of God!

The so-called number of gods refers to the minimum number of steps required to restore an arbitrarily shuffled Rubik's cube.

Since the invention of the Rubik's Cube and its use by mathematicians as a concise teaching tool, mathematicians have been involved in the study of the Rubik's Cube. And the search for the number of God is one of the most important things.

From 0, to 26, to 22, their footsteps never stopped.

It wasn't until 2010 that the mysterious "Numbers of God" that was intertwined with mathematics was finally revealed: the "veterans" Koschenba, the "rookie" Rokic, and two other collaborators who studied the "Numbers of God" announced that the "number of gods" was 20.

The amount of computation required for this proof process is about the same amount of computing resources as Google provides for five years of non-stop computing for Intel's quad-core processors. This number is undoubtedly quite terrifying.

The game uses the Rubik's Cube to be messed up and everyone has seen it, and the position of each of the six colors is opposite, and each edge is flipped in reverse. In the so-called "most chaotic state". The least minimal reduction step is the number of God's Numbers.

What is the number of God that is known, then it is undoubtedly knowing the standard answer. Mr. Cutie Dehua wants to look at the process, not the result, and there is a big difference between the two.

Trying to restore a scrambled Rubik's Cube in 20 steps, although the amount of computation is not as huge as the search for God's number, it is also quite a challenge for a group of doctoral students.

At first, the idea of jumping into my mind was to use the arrangement of six colors to deduce the process, and to use the combination of position colors after each rotation to verify it one by one.

But this idea was just thinking about it, and they quickly shook their heads and gave up.

If dozens of computers were placed here, everyone might try it a little, and it is estimated that an hour would barely be able to push the steps of the performance. But at this time, people don't have any computing devices to use except for a mobile phone, which is tantamount to a dream.

Therefore, this relatively unrealistic approach is unreliable, and the brute force method of 42.5 billion possible attempts is even more inappropriate.

Everyone could only hold their chins and fell into trouble for a while.

Unlike everyone else, Cheng Nuo got the Rubik's Cube and stood directly in front of Mr. Edward with confidence and began to rotate.

In fact, after Mr. Edward explained the rules of the game, Cheng Nuo had a solution in his heart, and when everyone was competing for the Rubik's Cube, he had already deduced the rotation process in his mind.

Cheng Nuo's approach is not to use color arrangement to extrapolate backwards. Even if his computing power is far more than ten times that of ordinary people, it is not comparable to a dozen supercomputers.

Since he was a mathematician, he naturally thought about how to use mathematical methods to solve this problem.

Simplifying a complex problem is the work of mathematics.

Taking the current problem as an example, from a mathematical point of view, the color combinations of the Rubik's cube, although ever-changing, are actually produced by a series of basic operations, and those operations have several very simple characteristics: any operation has an opposite operation.

For example, the opposite of clockwise rotation is counterclockwise rotation.

And for such operations, mathematicians have a very effective tool in their arsenal to deal with it, and this tool is called group theory.

Group theory has a great role in solving various problems in the Rubik's Cube. For the study of the Rubik's Cube, group theory has a very important advantage, that is, it can make full use of the symmetry of the Rubik's Cube.

When we use the knowledge of group theory to look at the huge number of 42.5 billion, it is easy to find an omission, that is, it does not take into account the symmetry of the Rubik's cube as a cube. As a result, many of the 42.5 billion color combinations are identical, just from different angles.

Therefore, the symmetry of group theory alone can easily reduce the color combination of the Rubik's cube by two orders of magnitude.

However, the figure of 42.5 billion is too huge, even if it is reduced by two orders of magnitude, it cannot be calculated by manpower.

So at this time, Cheng Nuo had to use a new tool.

The name of this new tool is Sisslswaite's algorithm, and it can be used for the calculation of the shortest path or the shortest step.

The Sisslethwaite algorithm expands the edges to establish multiple identical computational paths, turning the originally complex computation into a simple repetitive computation.

Cheng Nuo held the "group theory" in his left hand and the "Sissleswaite algorithm" in his right hand, and easily solved this problem.

The amount of computing that originally required more than 20 supercomputers to run for an hour was easily reduced by Cheng Nuo to the extent that an ordinary computer could do it in five minutes.

Squeak-Squeak-

Cheng Nuo's rotation was not loud, so it didn't attract too many people's attention. But it was impossible for Edward, who was sitting in front of Cheng Nuo, not to notice this classmate who had just gotten the Rubik's Cube and was impatient to start spinning.

Edward's face was suspicious. None of the other students got the Rubik's Cube and pondered for a long time before they started to actually rotate, but this one was good, and the Rubik's Cube was not hot in his hand, so he couldn't wait to start the operation.

This game is not a racing game, and even if it is fast, it is not as important as turning steps.

But no matter how much he guessed in his heart, Mr. Edward still looked at the Rubik's cube that kept rotating in Cheng Nuo's hand, and he still silently thought about the number of rotations in his heart.

He also wanted to know how many times this student would need to turn the Rubik's Cube for the first operation.

0 times, or 40 times?

As for 20 times, Edward really didn't believe that Cheng Nuo could find the more than 1 in 400 billion like a blind cat and a dead mouse.

1，2，，...... 8，9，10......

Edward counted the numbers one by one, and as the numbers tended to 20, the six colors of the Rubik's Cube in his sight became more and more regular from the previous mess.

Squeak-Squeak-

In the quiet classroom, many people gradually began to look at Cheng Nuo who was standing in front of him.

Since Cheng Nuo was standing with his back to them, he didn't understand what was happening, but he saw Mr. Edward's eyes widening and widening.

Cheng Nuo rotated the Rubik's Cube extremely fast, and there was already a specific rotation process in his mind, so there was no need for too many pauses at all.

Therefore, Edward was not given much time to think.

A few seconds later, with a click, Cheng Nuo put the restored Rubik's Cube on the table in front of Edward, and said with a smile, "20 steps, the restoration is complete!"