Intelligent Machines

Rubik's Cube Math

Solving a cube won’t take more than N2/log N moves

In 2010, an international team of researchers proved that no matter how scrambled a Rubik’s cube got, it would require no more than 20 moves to solve it. Their proof, however, relied on the equivalent of 35 years’ worth of number crunching on a good modern computer.

For cubes bigger than the standard Rubik’s cube, adequately canvassing starting positions may well be beyond the computational capacity of all the computers in the world. But in September, Erik Demaine (right), an associate professor of computer science and engineering, led a team including his father, CSAIL visiting professor Martin Demaine (left), that demonstrated the mathematical relationship between the number of squares in a cube and the number of moves in the shortest solution to its most scrambled state.

The standard way to solve a Rubik’s cube is to find a square that’s out of position and move it into place while leaving the rest of the cube as little changed as possible. That yields a worst-case solution whose number of moves is proportional to N2, where N is the number of squares per row. But the team saw that under some circumstances, a single sequence of twists could move multiple squares into place.

Describing those circumstances mathematically was no easy task. “In the first hour, we saw that it had to be at least N2/log N,” Erik Demaine says. “But then it was many months before we could prove that N2/log N was enough moves.”

Want to go ad free? No ad blockers needed.

Become an Insider
Already an Insider? Log in.

Uh oh–you've read all of your free articles for this month.

Insider Premium
$179.95/yr US PRICE

More from Intelligent Machines

Artificial intelligence and robots are transforming how we work and live.

Want more award-winning journalism? Subscribe to Insider Plus.
  • Insider Plus {! insider.prices.plus !}*

    {! insider.display.menuOptionsLabel !}

    Everything included in Insider Basic, plus ad-free web experience, select discounts to partner offerings and MIT Technology Review events

    See details+

    What's Included

    Bimonthly magazine delivery and unlimited 24/7 access to MIT Technology Review’s website

    The Download: our daily newsletter of what's important in technology and innovation

    Access to the magazine PDF archive—thousands of articles going back to 1899 at your fingertips

    Special discounts to select partner offerings

    Discount to MIT Technology Review events

    Ad-free web experience

/
You've read all of your free articles this month. This is your last free article this month. You've read of free articles this month. or  for unlimited online access.