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 exactly 20 moves. However, the majority of solutions take between 15 and 19 moves to solve.
