Instant Insanity
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The "Instant Insanity" puzzle consists of four cubes with faces colored with four colors (red, blue, green, and white commonly). The object of the puzzle is to stack these cubes in a column so that each side (front, back, left, and right) of the stack 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 doesn't lead us anywhere in solving this problem, for there are 41,472 arrangements of the four cubes.
The image at right shows the puzzle in the 'solved' configuration. The colors (from left to right) on the rear of the cubes are Blue,Red,Green, White. On the bottom, (L-R) WGBR.
[edit] External links
http://www.dean.usma.edu/math/people/rickey/hm/Teaching%20Instant%20Insanity.htm
