Puzzles
Euler's 36 officers who could never be arranged in a square
Take 6 army regiments, each sending 6 officers of 6 different ranks. Can all 36 officers be arranged in a 6x6 square so that every row and column contains one officer of each rank and one from each regiment, with no repeats? Euler guessed the answer in 1782, long before anyone could prove it.
Reveal the answer
No — it's impossible for a 6x6 grid specifically. Euler correctly conjectured this could not be done, though the full proof came only in 1901 (Gaston Tarry) and the deeper pattern — for which sizes it's impossible — wasn't settled until 1959. The puzzle founded the mathematics of orthogonal Latin squares, the structure behind Sudoku and modern experimental design.
— Leonhard Euler, Recherches sur une nouvelle espèce de quarrés magiques — 1782