Date: 18 Aug 1982 2226-PDT From: ISAACS at SRI-KL Subject: KERI's Article To: CUBE-LOVERS at MIT-MC 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 -------