To be precise, there are 43,252,003,274,489,856,000 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.
But using one of Google's supercomputers, an international team of geeks found the puzzle need not take any time at all.
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.
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.
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 out but 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.