# It took 36 years to find 20 steps to solve any rubik's cube

The creator of the Rubik’s Cube, Ernő Rubik, took a month to solve the challenge himself.

In 1974, in addition to Stephen Hawking’s prediction of the existence of Hawking radiation, science determined the location of the supermassive black hole Sagittarius A in the middle of the Milky Way, the first time the United States used barcodes to sell goods. , mankind also witnessed another special event:

Hungarian professor of architecture and design Ernő Rubik invents a toy ahead of its time, a rubik’s cube.

Ernő Rubik – the inventor of the rubik.

It is a cube, assembled from 27 smaller cubes, area 3x3x3 with small cube faces of different colors. You can rotate the Rubik’s Cube however you like, to bring the little cubes to any face. The gameplay is also simple: facing a Rubik’s cube in a scrambled state, each face has all kinds of colors, you have to rotate the cube so that each of its 3×3 faces has the same color.

Since that day, players have spawned many different solutions and strategies to successfully play the Rubik’s Cube. These “cubers” (nickname of rubik players) with proficient puzzle fingers can complete a rubik’s cube in just a few seconds. The current world record is 3.47 seconds.

The ways of inverting the rubik’s cube have an unpredictable nature, each with a different solution that has captivated mathematicians. Rubik’s cube with each different rotation produces other puzzles that are extremely mathematical, like lemon leaves with chicken.

Rubik is a cube, assembled from 27 smaller cubes, area 3x3x3 with small cube faces of different colors.

A normal rubik’s cube will have 3×3 faces showing a single color, the puzzle begins when we mix the faces together, to create a colorful block. There are a total of 18 basic moves, rotate one face forward, backward, left, right and then clockwise, counterclockwise or 180 degrees. It can be seen that the process of solving a rubik’s cube, in any state, is the above 18 steps arranged in different order.

The million dollar question for the cuber community here: what is the smallest number of moves to solve a rubik’s cube? And a further question, what is the smallest number of moves to solve ANY Rubik’s Cube arrangement? This almighty number is still called God’s Number by rubik players.

As Ernő Rubik pointed out in an interview with Business Insider, this big question ” is closely related to the math problems surrounding the rubik’s cube “.

Math finally found the answer: it was 20 moves. But it took 36 years of research, mathematicians and programmers to find the final answer. In 2010, a group of mathematicians and computer programmers proved that 20 is the divine number.

Why took so many years? Because the rubik’s cube itself is too complicated, more complicated than you think. The analysis shows that the number of puzzles hidden in the colorful cube, the number of ways to arrange the color arrays on the rubik’s cube, is 43,000,000,000,000,000,000,000 ways – 43 billion billion ways.

In the years following 1974, the technology was not modern enough to find the solution that required the fewest moves for all 43 billion billion puzzles. The most important key in the journey is to find the smallest number of moves to successfully solve any disordered state. Having that number, mathematicians will be able to take advantage of the relationship between the different states of inversion.

In 1995, mathematician Michael Reid discovered an inverted state called “superflip” , he proved that it only takes at least 20 steps to solve the superflip state. Thanks to Mr. Reid, we were able to set a lower limit for the number of Gods. The remaining question is whether there are any perverted states that require more than 20 steps to solve?

The process of solving a rubik’s cube, in any state, is the above 18 steps arranged in different order.

In the following decades, there were continuously appearing upper limits of the number of steps required to solve a rubik’s cube. One of the first mathematical analyzes of the Rubik’s Cube, performed by Morwen Thistlethwaite, proved that solving any cube requires only 52 steps at most.

Programmer Tomas Rokicki built an analysis that found the shortest possible solutions to a rubik’s cube, based on one of the first mathematical studies involving the colorful cube, work by Herbert Kociemba. The mathematician has divided the process of solving the rubik’s cube into two parts, based on a combination of 19.5 billion rubik’s cubes that have been partially solved. All of the flipped states in the other 19.5 billion combination have a relatively small number of solving steps.

Step one would be to return the cube to one of the other 19.5 billion states. The second step is to apply the solution.

Older rubik projects all show a maximum number of steps of 30, for any rubik’s inversion. Among them, the solution only needs up to 18 steps, putting the rubik in a special state to solve it takes 12 steps.

Mr. Rokicki improved on the above solution by combining the other 19.5 billion combinations into a special combination, and then trying to solve all of those 19.5 billion rubik’s inversions at once. So in total, they “only” have to solve 2,217,093,120 combinations, each of which has “each” 19,508,428,800 ways of inverting the rubik’s cube.

So you only need to solve 2.2 billion times, not do all 43 billion billion ways of inversion. This method still requires a powerful supercomputer, but technology has finally caught up with the human need to solve math problems. In 2010, Rokicki and colleagues used Google’s supercomputer to find the Divine number, we got the result 20.

It took researchers over three decades, using both deep mathematics and supercomputers to solve the rubik puzzle; No “popular” cuber is as dedicated as they are. But each person has different conditions for their own pleasure. Perhaps for us “ordinary people”, blindly spinning the rubik’s cube in our hands is already a joy.