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Submission + - Rubik's cube proof cut to 25 moves (

KentuckyFC writes: "A scrambled Rubik's cube can be solved in just 25 moves, regardless of the starting configuration. Tomas Rosicki, a Stanford-trained mathematician, has proven the new limit (down from 26 which was proved last year) using a neat piece of computer science. Rather than study individual moves, he's used the symmetry of the cube to study its transformations in sets. This allows him to separate the "cube space" into 2 billion sets each containing 20 billion elements. He then shows that a large number of these sets are essentially equivalent to other sets and so can be ignored (abstract on the physics arxiv). Even then, to crunch through the remaining sets, he needed a workstation with 8GB of memory and around 1500 hours of time on a Q6600 CPU running at 1.6GHz. Next up, 24 moves."
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Rubik's cube proof cut to 25 moves

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I have a theory that it's impossible to prove anything, but I can't prove it.