20 Moves Or Less Will Solve Rubik's Cube

For nearly 30 years, mathematicians have been puzzling over the question: What's the lowest number of moves needed to solve a Rubik's Cube? An international team says it has finally found the answer.


And now for a less explosive form of entertainment: the Rubik's Cube. You may have seen those people who can solve the cube in seconds flat. Thirty years ago, Kristin Looney was one of them.

Ms. KRISTIN LOONEY (CEO, Looney Labs): When I was 16, I placed fifth in the nation on the television show "That's Incredible," solving the Rubik's Cube in 35 seconds.


But for most of us, it takes a bit more time - like hours, weeks, months, years.

Ms. LOONEY: Oh, it's actually a very complex puzzle. I mean, it is for anybody. It looks like it should be simple, but it isn't.

MONTAGNE: In fact, the cube has more than 43 quintillion potential starting positions.

Professor MORLEY DAVIDSON (Department of Mathematical Sciences, Kent State University): A quintillion is a billion billion. So it's a ridiculously large number.

INSKEEP: I would've said it was a made-up number, but Morley Davidson says it's real. He's from Kent State University, and he is a mathematician. For decades, he and his colleagues have been trying to answer this question about the Rubik's Cube: No matter how scrambled up it is, how many twists and turns should you ever need to solve it?

This week, Davidson says that question has been put to rest.

Prof. DAVIDSON: The team I was working with proved that every position a Rubik's Cube can be solved in, at most, 20 moves.

MONTAGNE: Twenty moves. That's it. Rubik's Cube fans call it God's number. Davidson says it could have taken many lifetimes to prove this, even with a desktop computer. What his team needed was something a bit more powerful to run its simulation.

Prof. DAVIDSON: We originally wrote a proposal to run it at the Ohio Supercomputer Center in Columbus, and we haven't heard back from them yet.

INSKEEP: But fortunately, Google stepped in and offered to run the cube-solving simulation on its machines. For a few weeks, their computers solved thousands of virtual Rubik's Cubes every second, churning through every possible combination.

MONTAGNE: And, of course, that leads us to the question: Is there a point to any of this?

Prof. DAVIDSON: Yeah. I would say this falls into category of recreational math, because while it's obviously not all that useful to engineering problems and the usual sort of applications, say in medicine and whatnot, it's a math question that really comes from the heart.

MONTAGNE: Though without a supercomputer nearby, even Rubik's Cube experts like Kristin Looney generally need a few more turns to solve the puzzle.

(Soundbite of clicking)

Ms. LOONEY: All right. This is going to be a lot more than 20 moves here.

(Soundbite of laughter)

(Soundbite of music)


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