From:

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The "Games and Mathematics" article in "Rubik's" Magazine (mentioned

yesterday) asks an interestion question: how can you characterize the

random coloring on a cube in order to determine if the cube is 1) solvable

by twisting, or 2) solvable by dismantling and reassembling.

The obvious criteria are 6 colors, 9 of each, 4 on edges, 4 on corners, 1

on a center, no 2 facies of a cubie the same color. For case 2, Keri

claims you need 4 more tests. For instance, he gives test 1: Given 1

corner with colors A, B, and C, let the other 3 colors be a, b, and c.

Then you can't have a capital and small of the same letter on one corner,

and the 8 corners are exactly the 8 combinations. What are the other

tests? Are 4 really necessary? What are the tests for case 1?

By the way, he (from some other article) classifies the 3 unscrambling

methods as follows:

1) Chemical unscrambling: repaint the sides.

2) Physical unscrambling: dismantle and reassemble

3) Mechanical (or mathematical): normal way, by twisting.

--- Stan -------