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Question: In the context of Rubik's Cube, what is God's number?
In the context of the Rubik's Cube, **God’s number** is the maximum number of moves required to solve the cube from any possible scrambled position, if you always use the shortest possible solution. In 2010, it was determined that God’s number is **20** in the standard “face-turn” metric (where turning any face by 90° or 180° counts as one move). This means that **no matter how scrambled a Rubik’s Cube is, it can always be solved in 20 moves or fewer** using optimal moves.
God's number is the term used to describe the minimum number of moves required to solve a Rubik's Cube from any arbitrary starting position. For the standard 3x3x3 Rubik's Cube, God's number has been proven to be 20. This means that no matter how scrambled the cube is, it can be solved in 20 moves or fewer. This result was definitively reached by computer scientists and mathematicians using extensive computational resources and has been verified through exhaustive search algorithms.
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Has the optimal solve been computed for every possible Rubik's cube scramble?
The Internet
March 2, 2025, 12:07 p.m.
The optimal solve has not been computed for every possible Rubik's cube scramble. While the God's number has been determined for certain sizes of the Rubik's Cube, such as 20 moves for the 3x3x3 cube and 11 moves for the 2x2x2 cube, the exact optimal solves for every conceivable scramble of larger cubes like the 4x4x4 and 5x5x5 remain unproven. Calculating God's Number for the 3x3x3 cube was confirmed in 2010 by a team of researchers, including Tomas Rokicki and Google's computational resources. The 3x3x3 cube has 43 quintillion possible positions, and no position requires more than 20 moves to solve. However, the 4x4x4 cube, known as "Rubik's Revenge," presents increased complexity with center pieces and edge pairing. Its God's Number is estimated to be 26 but has not been definitively proven. As computational power continues to increase, it's possible that God's Numbers for more complex cubes, such as the 5x5x5, 6x6x6, and beyond, may eventually be calculated. These calculations require enormous resources due to the exponentially growing number of possible positions as the layers of the cubes increase. In summary, while God's Numbers for smaller cubes like the 2x2x2 and 3x3x3 have been determined, the optimal solves for every possible scramble of larger cubes, including the 4x4x4 and 5x5x5, are still open questions in the world of Rubik's Cube theory.
WebBot via The Internet
March 2, 2025, 12:08 p.m.