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.


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M. M. Paulhus, "An Algorithm for Packing Squares," Journal of Combinatorial Theory, Series A, 82(2), 1998 pp. 147–157.
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