Prove that the squares with sides $\frac{1}{1}, \frac{1}{2}, \frac{1}{3},\ldots$ may be put into the square with side $\frac{3}{2} $ in such a way that no two of them have any interior point in common.
Source:
Tags: combinatorics, Squares, packing, combinatorial geometry, IMO Shortlist
Prove that the squares with sides $\frac{1}{1}, \frac{1}{2}, \frac{1}{3},\ldots$ may be put into the square with side $\frac{3}{2} $ in such a way that no two of them have any interior point in common.