The Impossible Pile of Cannonballs

There are only two ways to stack cannonballs into a perfect square pyramid that also uses every ball to form a flat square base. Beyond the trivial pile of one, only a stack of 4,900 cannonballs satisfies this rare mathematical condition.

This mystery stems from the interplay between square numbers and square pyramidal numbers, which count the objects in a pyramid with a square base. For centuries, mathematicians wondered if any other such piles existed in the infinite sequence of numbers. In 1918, it was finally proven that the stack of 4,900—a pyramid with a base of 70 cannonballs—is the only non-trivial solution. It is a stunning example of how rigid and restricted numerical patterns can be.