Puzzles
A box with whole-number edges and face diagonals can't get its space diagonal to work
An Euler brick is a rectangular box where every edge and every diagonal drawn across each face is a whole number — the smallest known example has edges 44, 117 and 240. Can you also find one where the diagonal running through the very middle of the box, corner to opposite corner, is a whole number too?
Reveal the answer
Nobody has ever found one — such a box, called a 'perfect cuboid,' remains an open problem in number theory, studied since Leonhard Euler examined these bricks in the 18th century. Exhaustive computer searches have ruled out any perfect cuboid with a smallest edge below roughly 500 billion, but no one has proven it's impossible either.