Shulou(Shulou.com)11/24 Report--

Rubik's cube is a kind of educational toy that people like very much. Since the early 1980s, this toy has become popular all over the world.

Rubik's cube has racing, blind twist, single twist and other ways of playing, the popularity has not declined for a long time, large and small events will be held every year, is one of the most popular intelligence games.

The Rubik's cube in the general sense refers to the third-order Rubik's cube in a narrow sense. The shape of the third-order Rubik's cube is usually a cube, made of elastic hard plastic. The regular racing game is to disrupt the Rubik's cube and then recover in the shortest possible time. In a broad sense, Rubik's cube refers to all kinds of geometry that can be disturbed and recovered by rotation.

Rubik's cube and Huarong Road, French singles (independent diamond chess) are known as the three miracles of the intellectual game world.

Photo Source: the pexls Cube was invented by Ernoe Rubik, a professor of architecture at the Institute of Applied Arts in Budapest, Hungary, also known as Rubik's cube.

What Rubik originally wanted to invent was not an educational toy, but a teaching tool that could demonstrate the rotation of space and help students understand the geometry of space intuitively. After a period of consideration, he decided to make a cube of 3 × 3 × 3 structure which is composed of small squares and each surface can rotate at will.

But how can we make the sides of the cube rotate at will without falling apart? This question left Rubik thinking hard. One summer afternoon in 1974, he was enjoying the cool on the banks of the Danube. When his eyes fell inadvertently on the pebbles on the banks of the river, inspiration flashed, and he came up with a solution to the difficulty, that is, to deal with the internal structure of the cube with a circular surface similar to pebbles. Thus he completed the design of the Rubik's cube.

Why is the Rubik's cube so charming? That's because it has an almost endless combination of colors. The standard Rubik's cube is a 3 × 3 × 3 cube, with each face initially having a definite color.

But after many random turns, those colors will be disturbed. At this point, if you want to restore it (that is, restore each face to its original color), it will not be so easy. Because the total number of color combinations of the Rubik's cube is astronomical: about 43 252 003 274 489 856 000.

How far can we go if we make all these color combinations into a Rubik's cube and line them up? Can I go from Beijing to Shanghai? More than that. Can you row from the earth to the moon? More than that. Can you row from the sun to Neptune? More than that. Can it be arranged from the solar system to Proxima? It's more than that! In fact, it is 250 light-years long!

The Rubik's cube has so many color combinations that it takes skill to restore the Rubik's cube. However, skilled players are often able to recover the Rubik's cube in an amazing short time, which shows that as long as you master the skill, it does not take too many turns to restore the Rubik's cube.

Photo Source: pexls since 1981, Rubik's cube enthusiasts began to hold worldwide Rubik's cube competitions. In this kind of competition, players continue to set a world record for the shortest recovery time.

However, players do not use the least number of turns to recover the Rubik's cube in theory (that is, not the "number of God"), because they use a method that is easy for the human brain to master and pursue the shortest recovery time.

It takes a little longer to turn a few more times, but it's still much faster than finding the theoretically minimum number of turns-in fact, the latter is often not what the human brain can do at all.

Image source: network, at least how many times does it take to make the Rubik's cube recover? Or, more precisely, how many turns does it take to ensure that a Rubik's cube of any color combination is restored? This question not only makes Rubik's cube enthusiasts curious, but also arouses the interest of some mathematicians because it is a difficult mathematical problem. Mathematicians even give this minimum number of turns a magnificent nickname, "the number of God".

Mathematicians have been looking for this mysterious "number of God" since the 1990s.

One of the most direct ways to find the "number of God" is to calculate the minimum number of turns for all color combinations one by one, and the largest of them is obviously the minimum number of turns that can ensure that any color combination is restored, that is, the "number of God". Unfortunately, that kind of calculation is incompetent even by the most powerful computer in the world, because there are so many color combinations of Rubik's cube.

What should I do? Mathematicians have to resort to their old profession-mathematics.

In 1992, a German mathematician named Herbert Kociemba put forward a new idea.

He found that some of the basic rotation of the Rubik's cube can form its own series, through which nearly 20 billion color combinations can be formed. Using these 20 billion combinations, Koxianba decomposes the recovery problem of the Rubik's cube into two steps: the first step is to transform any color combination into one of those 20 billion combinations, and the second step is to restore the 20 billion combinations. If we compare Rubik's cube recovery to sailing a boat in the ocean to a fixed destination, then the 20 billion color combinations proposed by Kochanba are like a special body of water-a special body of water 20 billion times larger than that fixed location. The two steps he proposed were like letting the boat sail first to that particular area of water and then from there to that fixed destination. It is obviously much easier to find a huge special area of water in the ocean than to find that small destination directly, which is the advantage of Kexianba's new idea. But even so, it is not easy to estimate the "number of God" using Cosamba's method. In particular, for fast calculation, it is best to store the minimum number of turns that restore the 20 billion color combinations (which is equivalent to a map of "special waters") in the computer's memory, which requires about 300MB of memory.

300 megabytes is not a large number today, but in the year when Kexianba came up with new ideas, the average machine had far less than 1/10 of its memory. Therefore, it was not until three years later that the first estimate was given by using Kexianba's method. The man's name is M. Reid, an American mathematician.

In 1995, Reid calculated that any color combination of the Rubik's cube could be transformed into one of the 20 billion combinations of Cosemba after up to 12 turns, and any of those 20 billion combinations could be restored after up to 18 turns. This shows that any color combination of the Rubik's cube can be restored after up to 12-18-30 turns.

Using this line of thinking, in 2007, it was proved that the number of God could not be greater than 26. In other words, it only takes 26 turns to ensure that the Rubik's cube of any color combination is restored.

But this number is not "the number of God", because Kosamba's new idea has an obvious limitation, that is, it must first go through one of the special color combinations he has chosen.

In fact, some of the restoration methods with the least number of turns do not go through those special color combinations. Therefore, although Kexianba's new idea reduces the amount of calculation, the restoration method found is not necessarily the one with the least number of turns.

Image source: pexls to break through this limitation, mathematicians have adopted a compromise, that is, to appropriately increase the number of special color combinations, because the larger the number, the more likely it is that the restoration method with the least number of rotation will pass through those special color combinations. Of course, this will undoubtedly increase the amount of computation. However, the rapid development of computer technology soon offset the increase in the amount of computation.

In 2008, computer guru Tom Rocky (TomRokicki) used this compromise to reduce the estimate of "number of God" to 22. In other words, it only takes 22 turns to ensure that the Rubik's cube of any color combination is restored.

So, is the number 22 "the number of God"? The answer is no. An obvious sign of this is that people have never found that any color combination needs to be rotated more than 20 times to recover.

This leads people to guess that the "number of God" should be 20 (it cannot be less than 20, because many color combinations have been proved to require 20 turns to recover). In July 2010, this guess was finally proved by Kexianba himself and several collaborators.

Therefore, we can now use mathematical certainty to answer, "at least how many times does it take for the Rubik's cube to recover?" The answer is: 20 times.

Comprehensive since: the book "Pauli's mistake: flowers and grass in the temple of science", "the number of God" Baidu encyclopedia part of the image source network copyright belongs to the original author all ★ book introduction ★

Pauli's mistakes: flowers and Grass in the Hall of Science by Lu Changhai Tsinghua University Press this is the third popular science book in the same series after Little House and Master: people and things in the Hall of Science and because the Stars are there: bricks and tiles in the Hall of Science. What important mistakes did Pauli make in his life? Inconclusive frontier explorations such as the cosmological constant and the quantum theory of gravity may be twists and turns and tidbits relative to the main line. But it may be the source of the future main line. The history of science also proves this point. Therefore, the seemingly tidbits of this book contain more scientific possibilities, which is of great benefit to the supplement of the reader's knowledge structure. In terms of scientific thinking, after reading this book, you may have a better understanding of this passage. "Science has always made mistakes and has been constantly correcting them. Never being right is by no means a feature of science-- on the contrary, if there is something that claims to be always right, it is the brightest indicator that it is by no means science." The scientific spirit of questioning and criticism is also the driving force of scientific development. A brief introduction to ★ authors ★

Lu Changhai, born in Hangzhou, studied in the Physics Department of Fudan University. After graduation, he went to study in the United States. He received his Ph. D. in Physics from Columbia University in 2000 and currently lives in New York. The author of "that Star is not on the Star Map: looking for the boundaries of the Solar system", "the Story of the Sun", "Riemann conjecture" (won the 7th Wu Dayou original Science Popularization work Gold Award), "from Strange to Wormhole: selected lectures on General Relativity", "Xiaolou and Masters: people and things in the Hall of Science" (selected "2014 good Books of China") He has published more than 100 popular science and professional science works in newspapers and magazines such as Southern weekend, Science Illustrated, Modern Physics knowledge, Mathematical Culture (any special contributor), etc. This article comes from the official account of Wechat: Origin Reading (ID:tupydread), author: Lu Changhai, Editor: Zhang Runxin

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