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The Rubik's Cube is constructed by labeling each of the 48 non-center facets with the integers 1 to 48. Each configuration of the cube can be represented as a permutation of the labels 1 to 48, depending on the position of each facet. Using this representation, the solved cube is the identity permutation which leaves the cube unchanged, while ...
Mechanically identical to the standard 3×3×3 cube. However, the numbers on the centre pieces force the solver to become aware that each one can be in one of four orientations, thus hugely increasing the total number of combinations. The number of combinations of centre face orientations is 4 6. However, odd combinations (overall odd number of ...
Three main properties affect that number: Cube size: The number of cubies to be placed is a quadratic (second order polynomial) function of cube size and therefore has a major influence on cube solving complexity. Odd or even size: Even size cubes have an additional effect to just cube size that adds complexity relative to odd size cubes.
The centered cube number for a pattern with n concentric layers around the central point is given by the formula [1] + (+) = (+) (+ +). The same number can also be expressed as a trapezoidal number (difference of two triangular numbers), or a sum of consecutive numbers, as [2]
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The maximal number of face turns needed to solve any instance of the Rubik's Cube is 20, [2] and the maximal number of quarter turns is 26. [3] These numbers are also the diameters of the corresponding Cayley graphs of the Rubik's Cube group. In STM (slice turn metric) the minimal number of turns is unknown, lower bound being 18 and upper bound ...
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