samsloan wrote:

Even that is not obvious. There are 21 possible rolls of the dice (6!
= 21) and three possible positions of the doubling cube plus 24
possible slots for each checker.

I haven't been following this thread so maybe I've missed something...
BUT
from what I read above: What do you mean by "possible rolls of the
dice"?
Combinations or Permutations? There are 21 of the former but 36 of
the
latter. Also 6! (6 factorial) is 720 not 21. Now, where did I go
wrong???

LRB