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
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.))