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Every Rubik’s Cube can be solved in 20 moves or less

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A team of math whizzes and programmers did some major number crunching and determined that every varying position of a Rubik’s Cube, all 43,252,003,274,489,856,000 of them, can be solved within 20 moves. Aided by 35 CPU-years of idle computer time donated by the algorithm-loving folks at Google, the team solved all possible Rubik’s Cube positions to find the so-called God Number.

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.

Full story at Neatorama.

Tons of math news.


Comments (2)

Aug 11, 2010
Satwinder Singh said...
Wow, just amazing.. :)
Aug 14, 2010
Lorne Marr said...
What bothers me is how they counted the total number of positions in the first place. If you think about it, the cube can only be in positions which you can achieve by turning it - so that you can turn it back if you want to solve it. If you just re-stick the colourful stickers, the cube will become unsolvable.
Therefore, if they came up with the number of the possible states that way, then they MUST have realized they won't need more than 20 moves to arrive at a state that had not been recorded before.
If they found that number by calculating combinations, then it must be the wrong figure IMHO.

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