From:

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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

ivory-like material.

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

closure(F,B,R,L,U^2,D^2)

13 moves to a cube reachable by

closure(F,B,R^2,L^2,U^2,D^2)

15 moves to a cube reachable by

closure(F^2,B^2,R^2,L^2,U^2,D^2)

17 moves to a cube reachable by

the identity

----

52 moves total. Singmaster expects the 17 to be 15 by the time he returns to

London.

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?

Bill