Computational problems in graph theory | NP-complete problems | Combination puzzles
Instant Insanity
Instant Insanity is the name given by Parker Brothers to their 1967 version of a puzzle which has existed since antiquity, and which has been marketed by many toy and puzzle makers under a variety of names, including: Devil's Dice (Pressman); DamBlocks (Schaper); Logi-Qubes (Schaeffer); Logi Cubes (ThinkinGames); Daffy Dots (Reiss); Those Blocks (Austin); PsykoNosis (A to Z Ideas), and many others. 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. 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. Trial and error is a slow way to solve this problem, as there are 331,776 possible arrangements of the four cubes (6 faces, 4 turns = 24 positions of each cube, times four cubes, totalling 331,776). And the solution is symmetrical 8 ways (if you have a solution, and you flip all of the four cubes forward, you have another valid solution. You can do that move 4 times multiplied by the rotation of every cube 180 degrees around its vertical axe, which gives 8 symmetries in total), so therefore the odds are 331,776 divided by 8 equals 41,472 chance of randomly tossing the cubes into a solution. 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 A. Schossow in 1900, and marketed as the Katzenjammer puzzle. The puzzle was recreated by Franz Owen Armbruster, also known as , 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. (Wikipedia).
