I love Rubik's cubes. There are all sizes, shapes, colors ... But in this post, I will tell you three curiosities of the normal cube, the one of the whole life, the original. The 3 rows cube, the 3x3x3.
1) Rubik's cube has 43 quintillion possible combinations. If we put a cube for each of the possible combinations of states followed by each other in a straight line, they would occupy hundreds of light years. A light year, is the distance that travels light in a year, and that is equivalent to 9.5 trillion kilometers. A distance, unimaginable. In another post I show you where the 43 quintillion possible combinations come from.
2) God's Number: The maximum number of movements required to solve the cube regardless of its state. No matter what the state of the cube, you need at most 20 movement to reach the final state. It all started in the 80's, proving that the cube could be solved in only 53 movements. It was in 2010 when it was shown that the cube could be solved with only 20 moves.
3) Rubik's cube responds to group theory: A group consists of a set and any operations you can do on it with their respective properties, such as associative property. An example would be as set as integers and the sum operation. This would form a group. Applied to Rubik's cubes, if as a set we take the possible movements that we can make with the cube, and as an operation the composition of movements, that is, make a movement and then make another, we can get all possible states of the cube.