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God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, [1] but which can also be applied to other combinatorial puzzles and mathematical games. [2] It refers to any algorithm which produces a solution having the fewest possible moves (i.e., the solver should not require any more than this number).
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 ...
For instance, the corner cubies of a Rubik's cube are a single piece but each has three stickers. The stickers in higher-dimensional puzzles will have a dimensionality greater than two. For instance, in the 4-cube, the stickers are three-dimensional solids. For comparison purposes, the data relating to the standard 3 3 Rubik's cube is as follows;
Each of the six faces is a different colour, but each of the nine pieces on a face is identical in colour in the solved condition. In the unsolved condition, colours are distributed amongst the pieces of the cube. Puzzles like the Rubik's Cube which are manipulated by rotating a section of pieces are popularly called twisty puzzles. They are ...
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 ...
In October 1979, he self-published his Notes on the "Magic Cube". [16] The booklet contained his mathematical analysis of Rubik's Cube, allowing a solution to be constructed using basic group theory. [17] In August 1980 he published an expanded 5th edition of the book retitled as Notes on Rubik's "Magic Cube". [16]
computer graphic of the superflip pattern. The superflip or 12-flip is a special configuration on a Rubik's Cube, in which all the edge and corner pieces are in the correct permutation, and the eight corners are correctly oriented, but all twelve edges are oriented incorrectly ("flipped").
The Rubik's Cube was inducted into the US National Toy Hall of Fame in 2014. [14] On the original, classic Rubik's Cube, each of the six faces was covered by nine stickers, with each face in one of six solid colours: white, red, blue, orange, green, and yellow. Some later versions of the cube have been updated to use coloured plastic panels ...