Tile a square with smaller squares, no two the same size, none left over
Can a square be divided into a finite number of smaller squares, using every size only once, with no gaps or overlaps? For decades mathematicians weren't even sure it was possible.
Reveal the answer
Yes: a team at Cambridge (Brooks, Smith, Stone and Tutte) cracked it in the late 1930s by treating the tiling as an electrical circuit and applying Kirchhoff's laws. The smallest known 'perfect squared square' uses just 21 differently-sized squares, found by A. J. W. Duijvestijn in 1978 and later proven to be the minimum possible.