David talked at ICME (Int. Conf. Math. Ed.) in Berkeley on 8/11 about using the
cube to teach group theory. He talked to some Rubniks at Stanford this noon.
Among the tidbits:
Notes on Rubik's 'Magic Cube', Fifth Edition, Preliminary Version, 75 pgs., $5.
Including: A Detailed Step-By-Step Solution, Thistlewaite's Best Algorithm (52
moves), Conway's Monoswop, Rubik's Duotwist and much more. Write:
David Singmaster, Polytechnic of the South Bank, London, SE1 0AA, UK.
He brought a 3x3x2 domino version, and a 2x2x2 Stanford homebrew which is
apparently nearly identical to a Japanese patent showed up. The 2x2x2 is
conceptually just a pasting of big overlapping corners on the standard 3x3x3
version although the one we saw was nicely machined in brass and some kind of
Singmaster counts double twists, e.g., R^2, as single moves. He doesn't see much
use for the IJK whole-cube moves.
The Thistlewaite algorithm goes from subgroup to subgroup as follows:
Starting with a random cube, reachable by
closure(F,B,R,L,U,D) = the full group
7 moves to a cube reachable by
13 moves to a cube reachable by
15 moves to a cube reachable by
17 moves to a cube reachable by
52 moves total. Singmaster expects the 17 to be 15 by the time he returns to
The Hungarians have cube races. A contestant take his/her cube out of its box
and unscrambles the judges' randomizing in about 50 seconds. Apparently they
file and lubricate their cubes with loving care to reach such speeds.
The U.S. made white cubes violate no patents because Rubik never applied for
foreign rights. Hmmmm. Is that ethical?