Stack four coloured cubes so every side of the tower shows all four colours, no repeats
Each of four cubes has its six faces painted in some arrangement of four colours. The challenge, sold commercially as 'Instant Insanity' in the 1960s, is to stack them into a tower so that all four colours appear exactly once on each of the tower's four long sides. With over 41,000 possible stackings, trial and error rarely gets there.
Reveal the answer
The puzzle can be solved systematically using graph theory: each cube's colour arrangement is turned into a small graph, and a solution corresponds to finding two edge-disjoint paths through a combined graph of all four cubes. Treated as brute-force guessing it looks nearly hopeless, which is exactly where the puzzle's name comes from.
— devised by Frank Armbruster; marketed by Parker Brothers, Instant Insanity — 1966/1967