Following on some wild claims that Shav made about Rubik's cubes at the London Meet-Up, I woke up at the crack of 3 pm and braved a serious hangover to determine whether or not he was talking rubbish. I haven't reached a conclusive result quite yet, but I'm mostly convinced he's an honest man:
Can anyone finish the proof? Can someone tell me if I'm on the right track?
Originally posted by adramforall http://www.speedcubing.com/chris/
Do you know of any bounds on how many moves are needed? My analysis was good enough to prove that at least 18 moves are required however you start (although it doesn't give a configuration which can be done in 18 moves, so the actual number may be much higher), but I didn't manage to prove that it can always be done in 54 (although I'm almost certain it can). On a second glance, I don't think the approach I started there will work.