Most of you have probably played this game, where you have someone do some moves on a solved cube and you try to reverse them. 4-7 moves can usually be reversed pretty easily, though I've done 8 and even 9 on one occasion. It just took me 15 minutes.
Of course, every time I play this game, my opponent eventually gets bored and gives me a fully scrambled cube and "conveniently forgets" how many moves he did, prompting me to stare at the cube for way too long before giving up.
Is there a way to easily determine if a cube is within a certain small number (say seven) of moves away from solved? The most obvious strategy in this game is to look for existing blocks, but your opponent can be clever and scramble in such a way to break up as many blocks as possible, or fully scramble a cube and then make some blocks to trick you.