I will look into collecting all of the relevant messages on God's
number into one place. If you want to poke around in the archives
yourself (please be carefull, and don't delete them again) I will
remind you all that old cube-lovers mail is archived in the following
MC:ALAN;CUBE MAIL0 ;oldest mail in foward order
MC:ALAN;CUBE MAIL1 ;next oldest mail in foward order
MC:ALAN;CUBE MAIL2 ;more of same
MC:ALAN;CUBE MAIL ;recent mail in reverse order
(I someone else wants to attempt the compilation, there is a better
chance it will get done. Let me know and I will be happy to lend a
Some of the seeming inconsistencies in the message included by Isaacs
in his message are a result of the usual half versus quarter twist
screw. The reason the writer can see 9 configurations after a single twist
is because he has a different definition of a "single twist".
I also am not sure, but I also think that the counting argument given
here suffers from the some confusion Singmaster had when he computed a
lower bound of 17 htw. I think, in fact, that a lower bound of 19 htw
results if the argument is executed correctly (Singmaster corrected
himself about this by the fourth edition, I think). Someone with a
copy of Singmaster handy should look this up.
The 41 move count for Thistlethwaite's algorithm is probably a half
twist count given that it was reported by Singmaster.