# The Rubik's Cube and combinatorial optimization

I doubt it's possible to find a person who hasn't heard about the Rubik's Cube, so I'm not going to repeat the Wikipedia description (https://en.wikipedia.org/wiki/Rubik%27s_Cube) of this puzzle, but rather focus on the connections it has to mathematics and computer science. If it's not explicitly stated, by "cube" I mean the 3×3 classic Rubik's Cube. There are lots of variations based on the original 3×3 puzzle, but they are still far less popular than the classic invention.

Despite being quite simple in terms of mechanics and the task at hand, the cube is quite a tricky object in terms of all the transformations we can make by possible rotations of its sides. It was calculated that in total, the cube has ~4.33 × 10^{19} distinct states reachable by rotating it. That's only the states that are reachable without disassembling the cube; by taking it apart and then assembling...