You could actually solve the problem by showing the intended amount of rotations for solving the level.
"I guess we might have overdone that a bit"
Probably. I just gave the game another shot and gotta admit, its quite addictive. I spent like 20 minutes on it and was pretty good at it this time :D (can't believe how many levels there are). But on the other hand, it doesnt progress at all. Its quite cool how you managed design so many levels with simple rotations of the cube, but I guess it also confuses a bit.
I really believe that this game has a huge potential and wish you best of luck :D