Let's say you a Rubik's cube that can be solved using a sequences of the 12 standard moves. Can it be solved if you are required to alternate between clockwise and counter-clockwise moves? If not, which positions can you solve a Rubik's cube using these moves?
One way to solve this problem would be to show that regular clockwise quarter turn on a Rubick's cube can be simulated by an even number of these alternating moves, since then you could string these plays together for every clockwise quarter turn required to solve the rubik's cube the regular way (we only need to consider clockwise quarter turns since any normally solvable rubik's cube can be solved using only clockwise quarter turns). I'm not sure if this is the only way though.