Rubik's Conundrum

July 7, 2011

Brit Trogen



Of all the people who write for this blog, there is at least one who is able to solve a Rubik's cube. I'm not going to say who it is... Maybe it's me. Maybe it's not. But for everyone out there who doesn't have this impressive party trick, an international team of researchers recently came out with some news that should now make you feel even more inferior: no matter how scrambled the cube may be, it will never take more than 20 moves to solve it. Assuming you never mess up, of course.


For a three-square-per-row cube, this discovery came at the cost of evaluating all 43 quintillion possible start positions that a cube might possibly originate in, and used more than a little fancy math-work. But as with all math riddles, the simplest version is never enough. What about a cube with four squares per row? Or five? And as a side note, if you already knew that five-sided Rubik's cubes existed, you've just earned yourself 43 quintillion nerd points.


Initially, there was concern that calculating the starting positions of such cubes might be beyond the computational abilities of all the computers on earth. But researchers at MIT (where else?) have solved the Rubik's cube riddle. The number of moves required to solve a cube with N squares per row is proportional to: N2/log N (for details of how they came up with the algorithm, click here).


While solving the Rubik's cube sounds awesome, this is also a classic example of a configuration problem, like the kind used to determine the most efficient way to stack boxes in a warehouse. With tweaking, the researchers believe their algorithms could be adapted to solve other such problems... though in all reality that's really much less awesome than the study itself. Now when these guys go to parties where someone whips out a cube, they can say that they've already solved it. 



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