There are 43,252,003,274,489,856,000 possible varying positions for the Rubik's Cube. A team of mathematicians and programmers determined that all of them can be solved within 20 moves:
Link via Popular Science | Photo by Flickr user huangjiahui used under Creative Commons license
With about 35 CPU-years of idle computer time donated by Google, a team of researchers has essentially solved every position of the Rubik's Cube™, and shown that no position requires more than twenty moves.
Every solver of the Cube uses an algorithm, which is a sequence of steps for solving the Cube. One algorithm might use a sequence of moves to solve the top face, then another sequence of moves to position the middle edges, and so on. There are many different algorithms, varying in complexity and number of moves required, but those that can be memorized by a mortal typically require more than forty moves.
Link via Popular Science | Photo by Flickr user huangjiahui used under Creative Commons license
You can only arrive at states which you can achieve by turning it - so that you can turn it back if you want to solve it.
Therefore, if they came up with the number of the possible states that way, then they MUST have realized that they will not need more than 20 moves to arrive at a state that has not been recorded before.
If they found that number by calculating combinations, then it must be wrong.
You can try it yourself with your own cube. It isn't always 20 moves since it is limited by being web based, but its never over 25. It uses a version of the algorithm outlined in the article above.
Who says girls aren't good at math!
For years, Google has been boasting about the genius of its employees.
This mathematical "solution" appears to this layperson to be a non-winner. I have recently been engrossed by the story of the those who created the paradigms behind quantum mechanics.
They did not use computers. The formulae of Einstein, Heidinger, Schrodinger and Dirac could be stated in a single line.
WTF is working for Google? I wonder what Wolfgang Pauli would have said about them.
Give the human race a problem, challenge, puzzle or anything and somebody, somewhere is going to manage it eventually, no matter how difficult or how trivial. It may take years, it might take massive collaboration, but d*** it we're going to do it.