Not all cube configurations are achievable by cube moves. That is, if you pull off one corner of a cube, rotate it, and stick it on again you get a cube which c

Not all cube configurations are achievable by cube moves. That is, if you pull off one corner of a cube, rotate it, and stick it on again you get a cube which cannot be solved (except by disassembling it again). I think it actually is possible to infer the sixth side of a cube if you can see the other 5, because only only one configuration of the remaining side is actually acheivable.