How can a Rubik's Cube with 43 quintillion positions always be solved in 20 moves?

Because researchers proved it with the help of a lot of computers. A standard Rubik's Cube can be twisted into 43,252,003,274,489,856,000 arrangements, about 43 quintillion. Yet in July 2010 a team of researchers including Tomas Rokicki, using computers provided by Google, proved that every single one can be solved in 20 moves or fewer. Puzzle fans call that limit God's number.

The giant number comes from counting the pieces. The cube has eight corners that can be arranged 40,320 ways, and seven of them can be twisted freely, giving 2,187 more options. Its twelve edges add hundreds of millions of arrangements, and eleven of them can be flipped. Multiply it all and you get 43 quintillion. One cube for each position would cover Earth's surface 275 times.

The human story is charming. The cube was invented in 1974 by Ernő Rubik, a Hungarian sculptor and architecture professor, who was really trying to build a structure whose small parts could move independently without falling apart. Only after scrambling it did he realise he had made a puzzle, and it took him about a month to solve his own creation.

In practice nobody needs 20 moves very often. A random scramble most likely needs 18, and only about one scramble in 90 billion needs the full 20. Most people, however, never found the short path: when the cube became a craze, most people could solve only one or two sides.