Chapter 438

Chapter 441

in order to recover the magic cube successfully with the least steps, we must first understand the concept of the number of God!

The so-called number of gods refers to the minimum number of steps required to restore a randomly disordered cube.

Since the Rubik's cube was invented and used by mathematicians as a concise teaching tool, mathematicians have been engaged in the research of Rubik's cube. The search for the number of God is the most important.

From 30 to 26 to 22, they never stop.

It was not until 2010 that the mysterious "number of God" interwoven with the game and mathematics was finally revealed: the "number of God" research "veteran" koshiba "," rookie "rocic, and two other collaborators announced the proof that the" number of God "was 20.

The amount of computing required for this proof process is almost the same as that of Intel's four core processors for 35 years without stopping computing. This number is certainly quite frightening.

The disordered state of the Rubik's cube used in the game has been seen. The positions of each magic block in six colors are relative, and each edge block is reversed. In the so-called "most chaotic state.". The least reduction step is the number of God.

If you know the number of gods, you will undoubtedly know the standard answer. Dear Mr. dewar, what he wants to see is the process, not the result. There is a big difference between the two.

In order to recover a disordered cube in 20 steps, although the amount of calculation is not as large as the search for the number of gods, it is also a great 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 deduce the process through the results, and to verify one by one by using the change combination of position color after each rotation.

But this idea was just a thought, and soon they shook their heads and gave up.

If there are dozens of computers nearby, people may try it a little. It is estimated that one hour can barely deduce the rotation steps. But at this time, people do not have any computing equipment to use except a mobile phone, which is just a dream.

Therefore, this relatively impractical approach is not reliable, and the reckless method of 432.5 billion possibilities to try again is even more inappropriate.

People can only hold their chin, a time into trouble.

Different from the others, Cheng Nuo got the Rubik's cube and stood in front of Mr. Edward with confidence and began to turn.

In fact, after Mr. Edward explained the rules of the game, Cheng Nuo had a solution in mind, and when people were fighting for me to grab the Rubik's cube, he had already deduced the rotation process in his mind.

Cheng Nuo's natural method is not to use the color arrangement for backward deduction. Even though his computing power is more than ten times that of ordinary people, he can't compare with more than a dozen supercomputers.

Since he is a mathematician, it is natural to consider how to use mathematical methods to solve this problem.

Simplifying a complex problem is the work of mathematics.

Take the current problem for example, from a mathematical point of view, although the color combination of Rubik's cube is ever-changing, it is actually generated by a series of basic operations, and those operations also have several very simple characteristics: any operation has an opposite operation.

For example, the operation opposite to clockwise rotation is counter clockwise rotation.

And for this kind of operation, mathematicians have a very effective tool in their arsenal to deal with it. This tool is called group theory.

Group theory plays an important role in 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 we use the knowledge of group theory to look at the huge number of 432.5 billion, it is easy to find an omission, that is, the symmetry of Rubik's cube as a cube is not taken into account. As a result, many of the 432.5 billion color combinations are actually identical, just from different perspectives.

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

However, the figure of 432.5 billion is too large. Even if it is reduced by two orders of magnitude, it can not be calculated by manpower.

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

The new tool, called sissylvester algorithm, can be used to calculate the shortest path or the shortest step.

Sissylvester algorithm through the expansion of the edge, the establishment of a number of the same calculation path, the original complex calculation into a simple repeated calculation.

Cheng Nuo holds "group theory" in his left hand and "sissylvester algorithm" in his right hand, and solves the problem easily.

It used to take more than 20 supercomputers to run for an hour, but Cheng Nuo easily reduced the amount of computation to an ordinary computer in five minutes.

Creak - creak-The sound of Cheng Nuo's rotation was not big, so it didn't attract too many people's attention. But Edward, sitting in front of Cheng Nuo, couldn't help noticing the student who just got the Rubik's cube and began to turn.

Edward's face was suspicious at first. Which of the other students did not get the Rubik's cube and pondered for a long time before actually turning, but this one was good. The Rubik's cube was not hot enough to start the operation impatiently.

This game is not a race game. Even if it is fast, it is not as important as turning steps.

However, no matter how he guessed in his heart, Mr. Edward still put his eyes on Cheng Nuo's magic cube, and recited the number of turns in his heart.

He also wanted to know that in the quiet classroom, many people began to look at Cheng Nuo who was standing in front of him.

As Cheng Nuo was standing with his back to them, he did not understand what was going on. He only saw Mr. Edward's eyes opening wider and wider.

Cheng Nuo turns Rubik's cube very fast. He already has a specific rotation process in his mind, so there is no need for too many pauses.

As a result, Edward was not given too much time to think.

A few seconds later, with a click, Cheng Nuo put the restored magic cube on the table in front of Edward, and said with a smile, "20 steps, the restoration is finished!"

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