# Imagine that $k$ runners on a $1$ mile long circular running track startrunning with different constant speeds. Pick one of the runners. Willthere be a time when this runner is $1/k$ miles away from all otherrunners?

Does there exist a rectangular box such that all of its side lengths, all of the lengths of the diagonals of the faces, and the length of the long diagonals, are all whole numbers (integers)?