Puzzle, Rubik's Cube

This Rubik’s Cube, purchased about 1980, is an early example of a puzzle that was developed in 1974 by a Hungarian professor of architecture, Erno Rubik. It was originally called a Magic Cube but was renamed after the Ideal Toy Company took over distribution in 1980.

The puzzle is shaped as a 3 X 3 X 3 cube and looks as if it is made up of twenty six visible 1 X 1 X 1 cubes, called cubies, together with another cubie at the center of the cube that is not visible. The puzzle was sold with each face of the cube (a 3 X 3 square) showing the 1 X 1 square faces of nine cubies that are all of the same color. The squares are white, blue, red, yellow, green, and orange. The background plastic of the cube is black.

There are three different types of cubies that are visible: corner pieces have three visible faces displaying three different colors; edge pieces that lie between two corner pieces have two visible faces displaying two different colors; and center pieces display only one face. The twenty six visible pieces on the cube include eight corner pieces, twelve edge pieces, and six center pieces. The space at the center of the cube is taken up by a mechanism that allows the puzzle solver to rotate any face of the 3 X 3 X 3 cube. These rotations scramble the cubies so more than one color can appear on the faces of the puzzle. There are more than 42 quintillion (42 followed by 18 zeros) possible arrangements of the cubies that can be reached by this type of rotation. The object of the puzzle is to get the cube back to its original position after the faces have been scrambled so they no longer display only one color.

While a rotation of a face of the puzzle scrambles the puzzle it cannot change the type of any cubie. That fact is important in the mathematical analysis of the solution of this puzzle, which involves permutations and permutation groups. Starting around 1980 many variants of this Rubik’s cube, including 2006.0061.01-15 and 2012.0091.03, have been manufactured. There are many books, articles, and websites about the Rubik’s Cube and other twisting puzzles that use the same or similar mechanisms.

References:

Douglas R. Hofstadter, “METAMAGICAL THEMAS: The Magic Cube’s cubies are twiddled by cubists and solved by cubemeisters,” Scientific American, vol. 244, #3, March, 1981, pp. 20-39.

Douglas R. Hofstadter, “METAMAGICAL THEMAS: Beyond Rubik’s Cube: spheres, pyramids, dodecahedrons and God knows what else,” Scientific American, vol. 247, #1, July, 1982, pp. 16-31.

RubikZone [Number of Combinations] website.

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