Researchers from Northeastern University in the US have managed to prove that the Rubik’s cube can be solved in just 26 moves. Sadly, it appears that they were unaware that people stopped trying to solve the Rubik’s cube about the same time digital watches and ET dolls went out of fashion.
If you happen to have been born in the past twenty or so years, you may be fortunate enough to have never have encountered a Rubik’s cube (except maybe at a garage sale). For your benefit, the Rubik’s cube was a mechanical puzzle cube invented by a Hungarian professor Ernő Rubik in 1974. Each face of the cube had nine colored panels. The idea was that you would twist the colored panels so that they were out of sequence (as pictured), and then try to get them to match up again. More then 300,000,000 Rubik’s cubes and imitations were sold.
You have to remember that this was before the age of computers, when people where amused by simple things.
Previously it had been proven that the Rubik’s cube could be solved in 27 moves. Now computer science professor Gene Cooperman and graduate student Dan Kunkle have proven that only 26 moves are needed to solve any configuration of a Rubik’s cube.
Cooperman and Kunkle were able to accomplish this new record through two primary techniques. They used 7 terabytes of distributed disk as an extension to RAM, in order to hold some large tables and developed a new, “faster faster” way of computing moves, and even whole groups of moves, by using mathematical group theory.
Cooperman and Kunkle put all of the configurations of a Rubik’s cube in a family of sets of configurations (called a family of cosets in mathematical group theory). They then looked at the result of applying a single move to all of the configurations of a coset at once. They simulated this on a computer at a rate of 100,000,000 times per second, using a new technique in mathematical group theory.
Cooperman and Kunkle are not the first researchers to apply themselves to the pursuit of a faster solution of the Rubik’s cube.
In May 1997, UCLA computer science Professor Richard Korf announced that he had found the first optimal solutions to Rubik’s cube. His research showed that the median optimal solution was 18 moves, and he believed any cube could be solved in no more than 20 moves. However, he was unable to prove this, and no one has ever been able to prove that it could be solved in less than 27 moves.
“Korf had written a program that spends a long time to find optimal solutions for single states of the Rubik’s cube,” says Kunkle.
“Our program first does a large pre-computation and then it very quickly – in about a second – finds a solution in 26 moves or less for any state of Rubik’s cube.
Cooperman and Kunkle used computers at Teragrid and at Northeastern, part of the first node from a $200,000 grant Cooperman and colleagues received from the National Science Foundation in 2006 to obtain 20 terabytes of storage.
At this point, I do have admit I have been a little flippant, and in order to avoid death threats and hate mail from Rubik’s cube aficionados (not to mention from scientists at Northeastern University), I should point out that there is a serious side to this achievement.
According to Cooperman, the Rubik’s cube is a testing ground for problems of search and enumeration.
“Search and enumeration is a large research area encompassing many researchers working in different disciplines – from artificial intelligence to operations,” he said.
“The Rubik’s cube allows researchers from different disciplines to compare their methods on a single, well-known problem.”