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All Rubik’s cube variations solvable in 25 moves

By Adam Myers ⋅ March 27, 2008 ⋅ Tags: algorithm, intel, math, rubiks

The childhood toy, the Rubik’s cube, has been proven to be solvable from any initial configuration set in 25 moves, one less than the 26 proven last year by a group at Northeastern University. Tomas Rokicki, a mathematician by school, uses a rather nifty piece of computer science. Rokicki’s proof is a neat piece of computer science. He’s used the symmetry of the cube to study transformations of the cube in sets, rather than as individual moves. 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.

1500 computing hours later on a quad core Intel CPU, 25 became the magic number. Optimism exists that as few as 20 moves are possible, from start to finish. No official word on whether Intel is sponsoring his work in an effort to prove the necessity of their Quad Core CPU’s for us common folks.

In all seriousness, this is a great example of how an inefficient method – many Rubik’s cube geniuses can solve in ~60 moves – is much faster in terms of time. No doubt, the 25 move solution is elegant and genius in it’s own right but just not worth it in terms of computation time. Granted, that isn’t really the point I realize.

Me, I find the hammer solution both quick and elegant.

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