The Number of Gods in Magic Cube

Hello everyone, today we will talk about the number of gods in the Magic Cube:

Magic Cube is a popular puzzle toy that has been popular since the 1980s. Previously, we talked about the standard color scheme of Magic Cube and the combinations in Magic Cube groups. We learned that restoring Magic Cube is a skill that requires players to master the relevant gameplay skills in order to restore it.

However, the time required to restore a Magic Cube varies among different Magic Cubes. Some friends can restore the Magic Cube in a short period of time, which means that as long as they master the restoration techniques, the number of rotations required to restore the Magic Cube can be reduced.

How many times do we need to rotate to restore the Magic Cube? This question has made many Magic Cube enthusiasts curious from the beginning, and even attracted the interest of some mathematicians, because it is a quite difficult mathematical problem. Mathematicians even gave this minimum number of rotations a grand name, called "God's Number.".

Since the 1990s, mathematicians have been searching for this mysterious "number of gods". The most direct way to find the "number of gods" is to calculate the minimum number of rotations for each color combination, and the largest one is obviously the minimum number of rotations that can ensure that any color combination is restored, that is, the "number of gods". Unfortunately, such calculations cannot even be performed by a computer, as there are too many color combinations in the Magic Cube.

Until 1992, a German mathematician named Kosenba proposed a two-step new approach. It is to first transform any color combination into one of the special color combinations selected by him through mathematical means, and then restore it. The advantage of this is that the computational cost of each step is much smaller than directly calculating the number of gods.

Using this new approach, it was proven in 2007 that the number of gods could not exceed 26. This means that with only 26 rotations, any color combination of Magic Cube can be restored. But this number is not yet the "number of gods". Although Cosimba's new approach reduces the calculation of two numbers, the restoration method found may not necessarily have the least number of rotations.

In 2008, computer expert Rocky used a compromise to compress his estimate of the number of gods to 22. But the number 22 is still not the "number of gods", and an obvious sign of this is that people have never found that any color combination requires more than 20 rotations to recover, which leads people to speculate that the "number of gods" should be 20. In July 2010, this speculation was finally proven by Cosimba himself and several collaborators.