Instant Insanity

This puzzle consists of four cubes with four colours in different combinations. The aim of the game is to stack them into a 1x1x4 column so that each side always displays all four colours. No statement is made about the concealed faces.   

History

Although the company Parker Brothers launched the game on the market as "Instant Insanity" in 1967, the puzzle is actually older and previously went by the name "The Great Tantalizer" or the "Katzenjammer Puzzle". The names allude to the difficulty of finding a solution by trying out the wealth of combinations via trial and error. With the monumental success of the Rubik’s Cube, however, the game soon faded into obscurity.  

Mathematics

There is essentially only one solution, which can be found with the aid of graph theory: numbering the cubes. Study a graph where the points correspond to the four colours. Two points are connected by an edge if the corresponding colours face each other on a cube. Label the edges with the number of the respective cube. Then look for two sub-graphs, which contain all four points and in which the four cubes occur exactly once. One sub-graph indicates how the colours need to look from above and below, the other determines the colours that need to appear on the front and back.