Official: just 20 moves needed to solve a Rubik's Cube

To be precise: there are 43,252,003,274,489,856,000 different possible configurations of the coloured squares on any Rubik's Cube. Yet now researchers have calculated that you're never more than 20 moves away from solving the famous puzzle.

That might seem startling to anyone who has owned one of the classic toys for decades without being able to solve it just once – or has even resorted to peeling off the stickers and placing them back on in the correct pattern to pretend to their friends they have cracked it.

But using one of Google's supercomputers, an international team of square-eyed enthusiasts in California have confirmed that the puzzle need not take any time at all, no matter what its starting position. In fact, only 300 million arrangements – a small fraction of the total number – require a full 20 moves, with the majority of solutions taking between 15 and 19. It had already been thought that 20 was the maximum number of moves needed, after a previous estimate of 18 was disproved upon the 1995 discovery of a configuration that needed two more.

Announcing definitively that 20 was the "magic number", Professor Morley Davidson, a mathematician from Ohio's Kent State University, said: "We were secretly hoping in our tests that there would be one that required 21."

Despite Google's state-of-the-art technology, Professor Davidson said it would have been "completely hopeless" to try testing all of the combinations individually, and so the team studied duplicate and symmetrical patterns to reduce the number that required analysing.

They began by splitting the configurations into 2.2 billion groups of 20 billion positions, which they were eventually able to whittle down to the 56 million groups of 20 billion combinations they analysed. Even then, their calculations would have taken a good desktop PC 35 years to work its way through them, but with Google's equipment it took just a few weeks.

More than 400 million Rubik's Cubes have been sold since it was invented in 1974 by the Hungarian architect Erno Rubik, and Professor Davidson told the BBC his devotion to the project was because the puzzle had inspired his whole career.

"It's come full circle for me," he said. "Rubik's Cube was an icon of the Eighties when I was growing up and was the reason I went into mathematics. It's the universal popularity of the puzzle – it's probably the most popular puzzle in human history."

Professor Davidson carried out the work with John Dethridge, an engineer at Google, Herbert Kociemba, a maths teacher and Tomas Rokicki, a computer programmer from California. With the preliminary results now available online, the quartet are submitting their evidence to peer-reviewed journals for final confirmation among the mathematical community. Beyond that, they are considering looking at the Cube's other mathematical mysteries or working on the four-layered version.

Start your day with The Independent, sign up for daily news emails
PROMOTED VIDEO
ebooks
ebooksA year of political gossip, levity and intrigue from the sharpest pen in Westminster
Latest stories from i100
Have you tried new the Independent Digital Edition apps?
Independent Dating
and  

By clicking 'Search' you
are agreeing to our
Terms of Use.

iJobs Job Widget
iJobs General

Ashdown Group: Junior Web Developer - Kent - £40,000

£30000 - £40000 per annum + benefits: Ashdown Group: Junior Web Developer - ne...

Recruitment Genius: Production Team Leader / Chargehand

Negotiable: Recruitment Genius: A vacancy has arisen for a Chargehand to join ...

Ashdown Group: Client Services Manager - Relationship Management - London

£30000 - £32000 per annum + benefits : Ashdown Group: A highly successful, int...

Recruitment Genius: Credit Controller / Customer Service

£18000 - £20000 per annum: Recruitment Genius: This rapidly expanding business...

Day In a Page

Syria crisis: Celebrities call on David Cameron to take more refugees as one young mother tells of torture by Assad regime

Celebrities call on David Cameron to take more Syrian refugees

One young mother tells of torture by Assad regime
The enemy within: People who hear voices in their heads are being encouraged to talk back – with promising results

The enemy within

People who hear voices in their heads are being encouraged to talk back
'In Auschwitz you got used to anything'

'In Auschwitz you got used to anything'

Survivors of the Nazi concentration camp remember its horror, 70 years on
Autumn/winter menswear 2015: The uniforms that make up modern life come to the fore

Autumn/winter menswear 2015

The uniforms that make up modern life come to the fore
'I'm gay, and plan to fight military homophobia'

'I'm gay, and plan to fight military homophobia'

Army general planning to come out
Iraq invasion 2003: The bloody warnings six wise men gave to Tony Blair as he prepared to launch poorly planned campaign

What the six wise men told Tony Blair

Months before the invasion of Iraq in 2003, experts sought to warn the PM about his plans. Here, four of them recall that day
25 years of The Independent on Sunday: The stories, the writers and the changes over the last quarter of a century

25 years of The Independent on Sunday

The stories, the writers and the changes over the last quarter of a century
Homeless Veterans appeal: 'Really caring is a dangerous emotion in this kind of work'

Homeless Veterans appeal

As head of The Soldiers' Charity, Martin Rutledge has to temper compassion with realism. He tells Chris Green how his Army career prepared him
Wu-Tang Clan and The Sexual Objects offer fans a chance to own the only copies of their latest albums

Smash hit go under the hammer

It's nice to pick up a new record once in a while, but the purchasers of two latest releases can go a step further - by buying the only copy
Geeks who rocked the world: Documentary looks back at origins of the computer-games industry

The geeks who rocked the world

A new documentary looks back at origins of the computer-games industry
Belle & Sebastian interview: Stuart Murdoch reveals how the band is taking a new direction

Belle & Sebastian is taking a new direction

Twenty years ago, Belle & Sebastian was a fey indie band from Glasgow. It still is – except today, as prime mover Stuart Murdoch admits, it has a global cult following, from Hollywood to South Korea
America: Land of the free, home of the political dynasty

America: Land of the free, home of the political dynasty

These days in the US things are pretty much stuck where they are, both in politics and society at large, says Rupert Cornwell
A graphic history of US civil rights – in comic book form

A graphic history of US civil rights – in comic book form

A veteran of the Fifties campaigns is inspiring a new generation of activists
Winston Churchill: the enigma of a British hero

Winston Churchill: the enigma of a British hero

A C Benson called him 'a horrid little fellow', George Orwell would have shot him, but what a giant he seems now, says DJ Taylor
Growing mussels: Precious freshwater shellfish are thriving in a unique green project

Growing mussels

Precious freshwater shellfish are thriving in a unique green project