Date: 8 December 1980 1309-EST (Monday) From: Guy.Steele at CMU-10A To: McKeeman.PA at PARC-MAXC Subject: Re: That 28 move Plummer Cross CC: cube-lovers at MIT-MC In-Reply-To: McKeeman.PA@PARC-MAXC's message of 6 Dec 80 19:42-EST Message-Id: <08Dec80 130910 GS70@CMU-10A> A QTW cannot take you between two positions of equal distance, I believe -- is there not some parity quantity obeyed by QTW's (net twist of the six center cubies)? If so, then there cannot be two positions of equal distance separated by a QTW, for then there would be an odd length identity transformation, which would violate parity. (In the example you gave, there are *not* two positions of equal distance, but only one -- the halfway point.)