In July 2008, many of the best Rubik's Cube players from all over the world gathered in Dubis, central Czech Republic, to participate in the important Rubik's Cube event: Czech Open. In this competition, Dutch player E. Akkersdijk set an amazing record: it only takes 7.08 seconds to restore a Rubik's cube with completely disturbed colors. Coincidentally, in August this year, people also made important progress in the research on the mathematical problems behind the Rubik's Cube. In this article, we will introduce the Rubik's Cube and the mathematical problems behind it.

1. Toys that are popular all over the world

1974 In the spring, E. Rubik, a professor of architecture at Budapest Institute of Applied Arts, had an interesting idea. He wants to design a teaching tool to help students intuitively understand the various rotations of space geometry. After thinking, he decided to make a 3×3×3 cube with small squares, and each side can rotate at will.

Although this idea is good, it faces a thorny problem in practice, that is, how to make all sides of such a cube rotate at will? Rubik tried many ways, such as connecting small squares with magnets or rubber bands, but all failed. One afternoon that summer, he was enjoying the cool air by the Danube, and his eyes inadvertently fell on the pebbles by the river. Suddenly, a new idea flashed through his mind: treating the internal structure of a cube with a round surface similar to a cobblestone surface. The new idea succeeded, and rubik quickly finished his own design. And applied for a patent with the Hungarian Patent Office. This design is the familiar Rubik's Cube (also called Rubik's Cube) [Note 1].

Six years later, rubik's Rubik's Cube, led by a Hungarian businessman and amateur mathematician, entered the western European and American markets and became a fashionable toy all over the world at an alarming rate. In the next 25 years, the sales of Rubik's Cube exceeded 300 million. Among the players of Rubik's Cube, there are both babbling children and bosses of multinational companies. Although the Rubik's Cube didn't become a teaching tool of space geometry as rubik imagined, it became the best-selling toy in history.

The biggest magic power of the best-selling Rubik's Cube lies in its amazing number of color combinations. When a Rubik's cube leaves the factory, there are six colors on each side, but after these colors are disrupted, the number of combinations that can be formed is as high as 432.5 billion [Note 2]. If we make each of these combinations into a Rubik's cube, these Rubik's cubes will be arranged together. It can be discharged from the earth to the distant starry sky 250 light years away. In other words, if we put a lamp at one end of such a row of Rubik's cubes, it will take 250 years for the light to shine on the other end. If a diligent player wants to try all the combinations, even if he doesn't eat, drink or sleep, he will find ten different combinations every second. It takes150 billion years to get it (in contrast, our universe is less than14 billion years at present). Compared with such combined figures, the adjectives of "thousands", "hundreds of millions" and "billions" commonly used by advertisers on weekdays have become rare modesty. We can be modest. If you don't know how to turn around at will, even if a person has been playing the Rubik's Cube since BIGBANG, there is almost no hope to restore a Rubik's Cube with its colors disrupted.