Proof You Can Solve the Rubik's Cube W/In 20 Moves!

As a kid, I got one for Christmas and within an hour of my cousin joining us for the big family celebration, she'd messed it up (I was kind of OCD about not ruining its perfect pattern) and I never did manage to solve it. I was mad at her for quite a while about that, although if she hadn't messed it up, I never would've played with it so she ended up sort of doing me a favor.

Did anyone else ever not manage to solve theirs?

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The math of the Rubik's cube
by Larry Hardesty
June 29, 2011

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.

The standard way to solve a Rubik’s cube, Demaine explains, is to find a square that’s out of position and move it into the right place while leaving the rest of the cube as little changed as possible. That approach will indeed yield a worst-case solution that’s proportional to N2. Demaine and his colleagues recognized that under some circumstances, a single sequence of twists could move multiple squares into their proper places, cutting down the total number of moves.

Cheaters!