Date: 31 July 1980 13:06-EDT From: Alan Bawden To: RP at MIT-MC cc: CUBE-HACKERS at MIT-MC Date: 31 JUL 1980 1006-EDT From: RP at MIT-MC (Richard Pavelle) IS IT POSSIBLE? The Singmaster notes claim that Thistlethwaite had an 85 twist algorithm in an addenda dated November 30, 1979. I presume that since then Thistlethwaite has continued to cube-hack, so why not 50 (or even 41)? It should be noted that Singmaster insists on counting a 180 twist as ONE twist, so I presume that the 85 number is measured that way. How is Gardner counting? It is certainly possible. If you count twists Singmaster's way, you can show that there are positions at least 18 twists away from home. There is nothing to suggest that this might not in fact be the maximum. So there might be room for Thistlethwaite to lower his number all the way to 18! (If you count 180 twists as TWO twists, then a similar proof shows that there are positions 21 twists away from home. In a past message I reported that some of us had proved the existence of positions as far away from home as around 30. I believe that the reasoning that led to such a high number was incorrect. (Although I cannot prove that there AREN'T positions that far away, I now believe that I have never seen a proof that there ARE.))