In addition, since the cube’s six faces can rotate, these rotations can be considered operations or permutations. Therefore, the 3x3x3 Rubik’s Cube is a permutation group as it can be represented as an ordered list of 54 elements (six different colours, repeated nine times on individual cubes). In other words, a permutation group is a set whose elements consist of different orderings of a finite list and whose group operation is the permutations which reorder the set in a different way. In mathematics, a group consists of a set of objects and a binary operator which satisfy a certain mathematical conditions.Ī permutation group is a finite group G whose elements are permutations of a given set and whose group operation is composition of permutations in G. When using group theory, mathematicians have shown that solving the Rubik’s Cube is almost trivial. Solving the 3x3x3 Rubik’s Cube mathematically primarily relies on a branch of algebra called group theory. This number is commonly referred to as God’s Number. It’s far from impossible to solve, however: It is currently estimated that the smallest number of moves needed to solve the cube from any starting position is as low as 20 moves. This makes solving the cube solely by making random moves unreasonable. In fact, there are 43,252,003,274,489,856,000 (43 quintillion) possible orientations, or permutations, for a 3x3x3 cube. “This means that there is only one completed situation, where all the sides have one color each.” “The cube is not easily solved because it does not hve a definite scrambled point,” Tran wrote. Raymond Tran, a Computer Science graduate at UBC, explained the challenges of solving the puzzle in a mathematical essay paper. Originally called the ‘Magic Cube’ by its Hungarian inventor Erno Rubik, over 350 million have been sold since 1974.Īccording to the New York Post, Rubik himself originally could not solve his eponymous cube, although he was eventually able to complete it. The puzzle’s main objective is to recreate the original positioning (one color per side) by rotating the cube’s six faces. Although at first glance just a colorful and simple game, the Rubik’s Cube has been used in both competitions and mathematical research.
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