The math of the Rubik’s cube
Last August, 30 years after the Rubik’s cube first appeared, an international team of researchers proved that no matter how scrambled a cube got, it could be solved in no more than 20 moves. Although the researchers used some clever tricks to avoid evaluating all 43 quintillion of the cube’s possible starting positions, their proof still relied on the equivalent of 35 years’ worth of number crunching on a good modern computer. Erik Demaine's collection of Rubik's-cube-type puzzles includes cubes with five, six, and seven squares to a row, as well as one of the original cubes, signed by its inventor (close-up below).Photo: Dominick Reuter Unfortunately, for cubes bigger than the standard Rubik’s cube — with, say, four or five squares to a row, rather than three — adequately canvassing starting positions may well be beyond the computational capacity of all the computers in the world. But in a paper to be...