Reversing moves game

[shelley]

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.

 

[Meep]

An approach could be looking at the edges and corners separately, as each would require <= the movecount to solve the entire cube. Could look at other features like orientations too.

 

[qqwref]

I have a feeling there isn't an easy way to do this. My reasoning is that there are many positions that look like they should be solvable in few moves, since they are full of obvious blocks, but that still take 10+ optimally.