# Rubik’s Cube

The Rubik’s Cube is a 3D combination puzzle. It is the brainchild of the Hungarian professor of architecture Ernő Rubik, who invented in it 1974. Since then, over 300 million Rubik’s Cubes have been sold worldwide. If they were stacked on top of each other, they would reach the top of Mount Everest, twice.

It is estimated that in the mid-eighties about a fifth of the world’s population had, at some point, handled a Rubik’s Cube. And because of its simple design, people continue to be astounded by its devilish complexity. The percentage of people that has ever solved the Cube, is more somewhat more difficult to ascertain.

Obviously, there is only one solution in which all six sides of the Cube have the same colour; as for all the different unsolved states, the original 3x3x3 Cube has 43252003274489856000 (that is to say, over 43 quintillion) possible Cubes. If there was a Cube for every permutation, they would cover the Earth with 273 layers – a sea of Cubes 15,5 meters (50 foot) deep. If there was a cube scrambled for every permutation and they were laid end to end then they would stretch approximately 261 light years – from Earth to Alpha Columbae.

Because of the vast amount different Cubes, algorithms (a sequence of moves that has a desired effect) are used to solve the Cube. Without algorithms to solve the Cube, it could take ages: if you made a single turn of one of the Cube’s faces every second, it would take you 1371,51 billion years to go through all the possible configurations. The universe is only 13,82 billion years old. If you had started this project during the Big Bang, you still would not be done yet.

Amazingly, the best speed cubers (people who take part in speed cubing – a sport where competitors try and solve the cube as quickly as possible) can solve the cube in under six seconds. At the time of writing, the world record is 4,90 seconds; the record for blindfolded solving (including memorization beforehand) is 21,05 seconds.

Mike: Look I don’t know, ok; it’s like a fucking Rubik’s Cube! I mean, it’s impossible at this point.
Selina: What? Mike, a Rubik’s cube is not impossible to solve.
Gary: Yeah, I saw an Asian kid do it in like ten seconds.
Selina: Ten seconds Mike.
– Veep (2012) Season 1, Episode 3; “Catherine” [No. 3]

## 2 thoughts on “Rubik’s Cube”

1. ‘Each corner piece has 8 possible locations in space, hence there are 8! possible placements for the corners.

Furthermore, each corner can be oriented in three possible ways (if the colors on the corner are red, white, and blue, there is exactly one orientation of the corner piece with red up, one with white up, and a third one with blue up). Seven corner pieces can be oriented in any way, but the orientation of the last corner is determined by the orientations of the other 7.

Similarly, there are exactly 12 locations in space where one can place the 12 edge pieces hence 12! ways. There is a small subtlety though, stemming from the fact that the corners placement of the corners influences the possible placement of the edges. The permutation which gives the placement of the 8 corner pieces must have the same parity as the permutation that gives the placement of the 12 edges. Hence, once we choose one of the 8! ways to place the corner pieces, and, once the corners are placed, there are “only” 12!/2 distinct ways of placing the edges.

One can see that each edge piece has two orientations and 11 of them can be oriented in any way we want.

Hence we can conclude that the number of possible configurations is 8! x 3^7 x 12!/2 x 2^11, which is equal to 43252003274489856000.’

Courtesy of http://math.williams.edu/.