Puzzles
Four coloured cubes, one tower, and 41,472 ways to get it wrong
You have four cubes, each face painted in one of four colours differently arranged on every cube. Stack all four into a tower so that all four colours appear exactly once on each of the tower's four vertical sides.
Reveal the answer
The puzzle yields to a trick: draw a graph connecting each cube's opposite-face colour pairs, and the two paths needed for a solution reveal themselves without brute-force trial and error. A version dates to an 1900 puzzle called the 'Katzenjammer Puzzle'; it was reworked and sold as 'Instant Insanity' by Parker Brothers in 1967, selling over 12 million copies, and its graph-theory solution remains a favourite teaching example.