Can a square be sliced into smaller squares, no two the same size, with none left over?
Cut a large square into smaller squares — every piece a square, no two the same size, and no wasted space. Mathematicians call this 'squaring the square,' and for decades no one could produce a single valid example.
Reveal the answer
It's possible, but only just — the smallest known 'perfect' squared square uses 21 distinct squares, found by A.J.W. Duijvestijn in 1978 using a computer search. The first solution of any kind came in the 1930s from four Cambridge students — Roland Brooks, Cedric Smith, Arthur Stone and William Tutte — who represented the problem as an electrical circuit and solved it with Kirchhoff's laws. Martin Gardner popularized their work in Scientific American.