universal data

Chapter 438 God's Number
441 chapter

If you want to restore the Rubik's Cube smoothly with the least number of steps, you must first understand a concept - the number of God!
The so-called God's number refers to the minimum number of steps required to restore an arbitrarily scrambled Rubik's Cube.

Since the Rubik's Cube was invented and used as a concise teaching tool by mathematicians, mathematicians have continued to invest in the study of the Rubik's Cube.And the search for the number of God is the most important among them.

From 30, to 26, and then to 22, their footsteps never stopped.

It wasn't until 2010 that the mysterious "Number of God" intertwined with mathematics finally came to light: the "veteran" Kosenba, the "rookie" Rokic, who studied the "Number of God", and two other collaborators announced that Proof 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 Google's quad-core processor for 35 years of non-stop calculation.This number is undoubtedly quite scary.

Everyone has seen the scrambled state of the Rubik's Cube used in the game. The position of each magic block of the six colors is relative, and each edge block is reversed.In the so-called "most chaotic state".Its minimum reduction step is the numerical value of the number of God.

Knowing the number of gods is undoubtedly knowing the standard answer.What Mr. Edouard looks at is the process, not the result. There is a big difference between the two.

To recover a shuffled Rubik's Cube in 20 steps, although the amount of calculation involved is not as huge as the search for the number of God, it is still a considerable challenge for a group of doctoral students.

The first idea that popped into my mind was to use the arrangement of the six colors to perform inverse deductions, deduce the process through the results, and use the combination of changes in position and color after each rotation to verify one by one.

But everyone just thought about this idea, and soon shook their heads and gave up.

If dozens of computers are placed here, everyone may try a little bit, and it is estimated that one hour can barely deduce the rotation steps.But at this time, everyone doesn't have any computing devices that can be used except a mobile phone. This kind of thinking is tantamount to wishful thinking.

Therefore, this relatively unrealistic approach is unreliable, and the brute force method of trying 4325 billion possibilities 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, stood in front of Mr. Edward with confidence and began to spin it.

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

Naturally, Cheng Nuo didn't use the method of reverse derivation by color arrangement.Even if his computing power is more than ten times that of ordinary people, it is still not as good as 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 puzzle 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 can There is a reverse operation.

For example, the opposite operation of turning clockwise is turning counterclockwise.

And for such operations, mathematicians have a very effective tool in their arsenal against it called group theory.

Group theory plays a great role in solving various problems in Rubik's Cube.For Rubik's cube research, 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 4325 billion billion, it is easy to find an omission, that is, the symmetry of the Rubik's Cube as a cube is not considered.The upshot of this is that many of those 4325 billion color combinations are actually the same, just viewed from different angles.

Therefore, the color combination of the Rubik's Cube can be easily reduced by two orders of magnitude based on the symmetry of group theory alone.

However, the number of 4325 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 new tool, called Heatherswaite's algorithm, can be used to calculate the shortest path or shortest steps.

The Sithlethwaite algorithm establishes multiple identical calculation paths through the expansion of the sides, turning the original extremely complex calculations into simple repeated calculations.

Cheng Nuo held "Group Theory" in his left hand and "Heatherswaite Algorithm" in his right hand, and easily solved this problem.

The amount of computation 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 could do it in 5 minutes.

Crack-crack-
Cheng Nuo's turning 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 student who impatiently began to spin the Rubik's Cube as soon as he got it.

Edward's face was suspicious at first.Which of the other students did not start to actually rotate the Rubik's Cube after pondering for a long time after getting it, but this one is lucky, the Rubik's Cube has not warmed up in his hands, and he can't wait to start operating.

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 still focused on the Rubik's Cube that kept turning in Cheng Nuo's hand, and he was still thinking about the number of turns in his heart.

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

30 times?Or 40 times?
As for the 20 times, Edward really didn't believe that Cheng Nuo could find the 4000/[-] billion like a dead mouse.

1, 2, 3, ... 8, 9, 10 ...

Edward counted the numbers one by one, and as the numbers approached 20, the colors of the six sides of the Rubik's Cube in his sight became more and more regular from the chaotic ones before.

Crack-crack-
In the quiet classroom, many people gradually began to cast their eyes on 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 going on. He just saw Mr. Edward's widening eyeballs.

Cheng Nuo turned the Rubik's Cube extremely fast, and he already had the specific turning process in his mind, so there was no need for too many pauses.

Therefore, there was not much time left for Edward to think.

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

(End of this chapter)