Instant Insanity!

The puzzle consists of four cubes with faces colored with four colors (commonly red, blue, green, and white). The objective of the puzzle is to stack these cubes in a column so that each side of the stack (front, back, left, and right) shows each of the four colors. The distribution of colors on each cube is unique, and the order in which the four cubes are stacked is irrelevant as long as each side shows every color. This problem has a graph-theoretic solution in which a graph with four vertices labeled B, G, R, W (for blue, green, red, and white) can be used to represent each cube; there is an edge between two vertices if the two colors are on the opposite sides of the cube, and a loop at a vertex if the opposite sides have the same color. Each individual cube can be placed in one of 24 positions, by placing any one of the six faces upward and then giving the cube up to three quarter-turns. Once the stack is formed, it can be rotated up to three quarter-turns without altering the orientation of any cube relative to the others. Ignoring the order in which the cubes are stacked, the total possible number of arrangements is therefore 3,456 (24 * 24 * 24 * 24 / (4 * 4!)). The puzzle is studied by D. E. Knuth in an article on estimating the running time of exhaustive search procedures with backtracking. Every position of the puzzle can be solved in eight moves or less. The first known patented version of the puzzle was created by Frederick Alvin Schossow in 1900, and marketed as the Katzenjammer puzzle. The puzzle was recreated by Franz Owen Armbruster, also known as Frank Armbruster, and independently published by Parker Brothers and Pressman, in 1967. Over 12 million puzzles were sold by Parker Brothers alone. The puzzle is similar or identical to numerous other puzzles (e.g., The Great Tantalizer, circa 1940, and the most popular name prior to Instant Insanity). One version of the puzzle is currently being marketed by Winning Moves Games USA.