Only small tidbits of math remain unresolved for Rubik’s Cube. While God’s number is 20, it’s unknown exactly how many of the 43,252,003,274,489,856,000 combinations require a whole 20 moves to be solved.

The first major insight on God’s Number was by Dr. Morwen Thistlethwaite in 1981, who proved it was at most 52. That means he proved every scrambled cube can be solved in 52 moves or less.Progress continued through the 1990s and 2000s. Finally, in June 2010, a team of four scientists proved that God’s number is 20.

Instrumental to this era of speed cubing was Dr. Jessica Fridrich, who in 1997 developed a method for solving the cube faster than ever. Most of the fastest cube solvers nowadays use some version of the Fridrich method.

Dr. David Singmaster, who wrote the famous guide “Notes on Rubik’s ‘Magic Cube’” and developed a writing method for describing turns of the cube’s faces. That notation has become the standard, and is now known as Singmaster notation.

the total number of ways you can scramble a Rubik’s cube: 43,252,003,274,489,856,000. Written in a more mathematical way, that number is (388!)(21212!)/12.

no algorithm can flip a single edge in place

There aren’t any algorithms that can swap only a pair of corners, nor only a pair of edges.

swapping a pair of edges and a pair of corners cancel each other out, since there’s an algorithm to undo that.

If you break it apart and reassemble the cubies randomly, there’s actually only a 1 in 12 chance that it’s solvable.