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# Matlab: Rubik’s Cube Simulator and Solver

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This program allows you to generate a randomly scramble cube of arbitrary dimension which can then be manipulated manually or solved by the computer. You can also input your own state using a webcam (3x3x3), or simply enter the colors of each facelet (2,3,4x.x.).

There are several built-in solving mechanisms available:
– God’s Algorithm for the 2x2x2: this is the optimal solution for the given state (in half-turn metric).
– Thistlethwaite 45 (T45) for the 3x3x3: this algorithm will always find a solution of 45 moves or less, averaging at 31.
– Layer-by-Layer (Beginners’) Solution: this is the method commonly used by beginners to solve the cube. More intuitive than T45, but also more extensive and less effective.
– 423T45 for the 4x4x4 (read 4 to 3, T45): this algorithm brings the cube to a state which can be handled like it was a 3x3x3 cube. When this is achieved, T45 can be applied to solve it (~180 moves on avg).
– Inverse Scramble for all cubes: it is like cheating, but when the scramble is known, each cube can be solved by inversing the sequence.

All of the above methods (with exception of the inverse scramble, which is trivial) are explained extensively in the included PDF. The PDF also contains a vast theoretical description of the cube.

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