Can you cut a square into smaller squares, all different sizes, none repeated?
A 'perfect squared square' divides one large square into smaller squares, no two of which are the same size, with no leftover space. For decades after the problem was posed, nobody knew whether such a dissection was even possible.
Reveal the answer
Yes — four Cambridge mathematicians (R.L. Brooks, C.A.B. Smith, A.H. Stone, and W.T. Tutte, publishing jointly as 'Blanche Descartes') found the first examples between 1936 and 1938, using an ingenious trick: they modeled the squares as an electrical circuit of resistors and used Kirchhoff's circuit laws to find a valid arrangement. Their first solutions used 69 smaller squares.