Math in the News
Any Rubik's Cube Configuration Can Be Solved in 33 1 (Wrist) Moves
June 11, 2007
Computer scientist Gene Cooperman and graduate student Dan Kunkle of Northeastern University used group theory and a lot of computer memory to answer one of life's riddles about Rubik's cube, perhaps the most famous combinatorial puzzle of all time: Optimally if one were a genius what number of wrist twists suffice to solve any of the many billions of configurations of the puzzle that Erno Rubik invented in the 1970s?
The answer is a meager 33 1 times. Their solution easily shatters the old record of 33 moves.
The two researchers arrived at the answer the easy way via computers, naturally by putting all of the possible configurations of a Rubik's cube into a family of sets of configurations, which in group theory is called a family of cosets. After analyzing the results of applying a single move all at once to all of the configurations of a coset, they used their 7 terabytes of distributed disk (as an extension to RAM) to compute moves at 100,000,000 times per second.
Their program, they said, does a precomputation and then in about a second voila! Out pops no more than 33 1 moves to solve any Rubik's cube configuration.
But there is a serious side to all this. "Search and enumeration," Cooperman said, "is a large research area encompassing many researchers working in different disciplines from artificial intelligence to operations. The Rubik's cube allows researchers from different disciplines to compare methods on a single, well-known problem."
Source: Northeastern University, May 31, 2007