My Rubix Cube Solutions manual says there are 43 quintillion
combinations. Also it says the world’s record is 22.95 seconds in
solving the cube. And the most fascinating is, “Theoretically the
shortest path to solving Rubik’s Cube from any scrambled position is
as few as 22 twists. So far no one has succeeded in demonstrating this
method.”

Does anyone know how they calculate this ‘theoretical’ number of
moves? Also, I’ve been toying with the idea of having the computer
figure out how to solve the cube in the least possible moves.

It’s not easy. Could someone give me some suggestions on how this
could be done? I was thinking that the computer would have to
‘remember’ certain patterns, and ‘get smarter’ based upon these
patterns. Sound like a neural net problem?

Anyway, has anyone already done this? Is there any code out there
involving the Rubix Cube?  Please point me in the right direction.