I am aware of God's number and how there is a lower bound of 26 quarter turns on such algorithms. However, I wished to know if there is a certain algorithm that can look at the faces of the cube and give a set of moves to solve the cube even if it does not do it in 26 moves and takes more time?
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1Sure. Almost every newspaper or magazine published one in the 80's – Hagen von Eitzen Apr 20 '20 at 18:35
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1An algorithm is merely a series of steps to follow. It's clearly possible for a person to look at the faces of the cube, and produce a sequence of moves that will solve the cube. That sequence of steps is an algorithm. You could even write down a sequence of moves that would solve every possible configuration, which is also an algorithm. Asking "is there an algorithm to solve a particular Rubik's cube configuration" is equivalent to asking "is there a series of steps I can take to solve this Rubik's cube", to which the answer is clearly yes. – Nuclear Hoagie Apr 20 '20 at 18:37
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Thistlewaite's algorithm, while far from optimal, is fairly approachable. https://math.stackexchange.com/questions/1362471/rubiks-cube-thistlethwaite-four-phase-algorithm – Josh B. Apr 21 '20 at 01:25
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There are ~43 quintillion possible configurations of the Rubik's cube, any one of which can be reached from any other by specific series of moves. A very naive algorithm for solving any cube is to simply have a series of steps that visits every single configuration, including the solved one. It doesn't matter what the cube looks like when you start, since you'll be visiting every possible configuration of the cube, regardless of what color stickers are on the surface. At some point, you'll arrive at the solved configuration. It'll take awhile, but you're guaranteed to get a solved cube, and you don't even need to look at it before you start!
To get a sense of the practicality of this method, see this question.
Nuclear Hoagie
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