A 30-year quest to find the minimum number of moves needed to solve every one of the billions of configurations for a Rubik's Cube may have ended.
Any scrambled cube can be solved in 20 moves or fewer, researchers claim.
The international team used a bank of computers at Google to help crank through the solutions.
The figure is known as "God's number" because an all-knowing entity would know the optimal number of steps needed to solve the puzzle.
"We now know for certain that the magic number is 20," Professor Morley Davidson, a mathematician from Kent State University, told BBC News.
The results suggest that there are more than 100,000 starting positions - of a possible 43 billion billion - that can be solved in 20 moves or less.
However, the majority of solutions take between 15 and 19 moves to solve.
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