How many ways can I make six moves on a Rubik's cube? I am writing a program to solve a Rubik's cube, and would like to know the answer to this question.
There are 12 ways to make one move on a Rubik's cube. How many ways are there to make a sequence of six moves?
From my project's specification: up to six moves may be used to scramble the cube. My job is to write a program that can return the cube to the solved state. I am allowed to use up to 90 moves to solve it. Currently, I can solve the cube, but it takes me over 100 moves (which fails the objective)... so I ask this question to figure out if a brute force method is applicable to this situation.
If the number of ways to make six moves is not overly excessive, I can just make six random moves, then check to see if the cube is solved. Repeat if necessary.

12^6 is just under 3 million.  So it would probably not work to randomly try six unscrambles.  But it wouldn't be too hard to make a data file of all the positions and their unscramble twists if you can find a reasonable way to search it, like some hash function on a description of the position.
