Packing Squares with Side 1/n

A finite volume of potatoes will fit in a finite sack. This seemingly simple statement leads to a family of very difficult questions, sometimes called potato sack problems.

Consider squares with sides , ,, …, . What is the smallest rectangle that can contain the squares as ? One bound is , but no one has found a packing for a rectangle of that area. In 1968, Meir and Moser showed that a square of size was enough. The current record is held by Marc Paulhus, who developed the packing algorithm used for this Demonstration.