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

Graph theory

In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

 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 41,472 arrangements of the four cubes only two of which are solutions. A generalized version of the puzzle with more than four cubes is NP-complete

NP-complete

In computational complexity theory, the complexity class NP-complete is a class of decision problems. A decision problem L is NP-complete if it is in the set of NP problems so that any given solution to the decision problem can be verified in polynomial time, and also in the set of NP-hard...

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The puzzle was created by Franz Owen Armbruster, also known as Frank Armbruster and published by Parker Brothers

Parker Brothers

Parker Brothers is a toy and game manufacturer and brand. Since 1883, the company has published more than 1,800 games; among their best known products are Monopoly, Cluedo , Sorry, Risk, Trivial Pursuit, Ouija, Aggravation, and Probe...

 in 1967. Over 12 million puzzles were sold. The puzzle has similarities to a much older puzzle known as The Great Tantalizer and derives from a set of 30 cubes devised by Percy Alexander MacMahon

Percy Alexander MacMahon

Percy Alexander MacMahon was a mathematician, especially noted in connection with the partitions of numbers and enumerative combinatorics.-Early life:...

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External links

• http://www.dean.usma.edu/math/people/rickey/hm/Teaching%20Instant%20Insanity.htm
• http://www.maa.org/mathland/mathtrek_8_9_99.html