Chapter 441: Number of gods

Chapter 441
If you want to successfully recover the Rubik's Cube with the least number of steps, you must first understand a concept of God's number!
The so-called number of gods refers to the minimum number of steps required to restore a random puzzle.
Since the Rubik's Cube was invented and used as a concise teaching tool by mathematicians, there have been many mathematicians devoted to the research of Rubik's Cube. The search for the number of Gods is even more of the most important.
From 30, to 26, to 22, they never stopped.
It was not until 2010 that the mysterious "number of Gods" interwoven by this game and mathematics finally came to light: the "veteran" Kossamba, the "rookie" Rokic, and two other collaborators announced This proves that the "number of God" is 20.
The huge amount of calculation required for this proof process is almost equivalent to the computer resources required by Intel’s quad-core processor for 35 years of non-stop computing provided by Google. This number is undoubtedly quite scary.
Everyone has seen the scrambled state of the Rubik's Cube for the game. The position of each piece of the six colors is relative, and each edge piece is reversed. In the so-called "most chaotic state." The least reduction step is the value of the number of God.
Knowing the number of Gods is undoubtedly knowing the standard answer. What Mr. lovely Dehua needs to look at is the process, not the result. There is a big difference between the two.
If you want to recover a scrambled Rubik's Cube with 20 steps, although the amount of calculation is not as large as the search for the number of God, it is also a considerable challenge for a group of doctoral students.
The idea that jumped into my mind at the beginning was naturally to use the arrangement of six colors to reverse inference, to derive the process through the results, and to verify one by one by using the combination of position and color changes after each rotation.
But everyone just thought about this idea, and quickly gave up.
If dozens of computers are placed here, everyone may try it a little bit. It is estimated that one hour can barely deduced the rotation steps. But at this time everyone doesn't have any computing devices that can be used except for a mobile phone. This idea is tantamount to a dream.
Therefore, this relatively unrealistic method is unreliable, and the brute force method of 432.5 billion possibilities is even more inappropriate.
Everyone can only hold their chins and get into trouble for a while.
Unlike everyone else, Cheng Nuo got the Rubik's Cube and stood in front of Mr. Edward with confidence and began to turn it.
In fact, after Mr. Edward explained the rules of the game, Cheng Nuo had a solution in his mind, and when everyone was fighting to get the Rubik's cube forward, he had already deduced the turning process in his mind.
What Cheng Nuo adopted is naturally not a method of reverse inference using color arrangement. Even though his computing power is far more than ten times that of ordinary people, he can't compare with a dozen supercomputers.
Since he is a mathematician, he naturally considers how to use mathematical methods to solve this problem.
Simplifying a complex problem is the work of mathematics.
Take the current problem as an example. From a mathematical point of view, although the color combinations of the Rubik’s Cube are ever-changing, they are actually produced by a series of basic operations, and those operations have several very simple characteristics: any operation is There is a reverse operation.
For example, the operation opposite to clockwise rotation is counterclockwise rotation.
For such operations, there is a very effective tool in the arsenal of mathematicians to deal with it. This tool is called group theory.
Group theory has a great effect on solving various problems in Rubik's Cube. For the study of Rubik's Cube, group theory has a very important advantage, that is, it can make full use of the symmetry of Rubik's Cube.
When using the knowledge of group theory to look at the huge number of 432.5 billion, it is very easy to find an omission, that is, the symmetry of the Rubik's Cube as a cube is not considered. The result of this is that many of the 432.5 billion color combinations are actually the same, just viewed from different angles.
Therefore, the group theory symmetry alone can easily reduce the color combination of the Rubik's Cube by two orders of magnitude.
However, the number of 432.5 billion is too large, even if it is reduced by two orders of magnitude, it cannot be calculated by human resources.
So at this time, Cheng Nuo had to use a new tool.
The name of this new tool is the Sisleswaite algorithm, which can be used to calculate the shortest path or shortest step.
The Sislswaite algorithm establishes multiple identical calculation paths through the expansion of edges, turning the originally complex calculations into simple repetitive calculations.
Cheng Nuo held the "group theory" in his left hand and the "Sisserswaite Algorithm" in his right hand, and solved the problem easily.
The amount of computing that originally required more than 20 supercomputers to run for an hour was easily reduced by Cheng Nuo to the level that an ordinary computer can handle in five minutes.
Creak-creak-
Cheng Nuo's turning sound was not loud, so it didn't attract too many people's attention. But Edward, who was sitting in front of Cheng Nuo, couldn't help but notice this classmate who was impatiently starting to spin as soon as he got the Rubik's Cube.
Edward's face was suspicious at first. The other classmate didn't get the Rubik's Cube and thought about it for a long time before actually turning it, but this one was good, and the Rubik's Cube was not hot in his hands, so he started to operate in a hurry.
This game is not a racing game, no matter how fast it is, it is not as important as turning steps.
But no matter how he guessed in his mind, Mr. Edward kept his sight on the Rubik's Cube that was turning in Cheng Nuo's hands, and he was still meditating on the number of turns.
He also wanted to know how many rotations could this student need to restore the Rubik's Cube during the first operation.
30 times? Or 40 times?
As for 20 times, UU Reading www.uukanshu.com Edward really doesn't believe that Cheng Nuo can find the one-four hundred billionths like a dead mouse.
1, 2, 3,...... 8, 9, 10......
Edward counted the numbers silently. As the numbers tended to 20, the six-sided colors of the Rubik's Cube in his sight became more and more regular from the previous chaos.
Creak-creak-
In the quiet classroom, many people gradually began to look towards Cheng Nuo, who was standing in front.
Since Cheng Nuo was standing with her back to them, she didn't understand what was going on. He just saw Mr. Edward's widening eyes.
Cheng Nuo turned the Rubik's Cube extremely fast, and there was a specific turning process in his mind, and there was no need to pause too much.
Therefore, Edward did not leave too much time for thinking.
A few seconds later, with a click, Cheng Nuo put the restored Rubik's Cube on the table in front of Edward, smiled and said, "20 steps, the restoration is complete!"