Packing a Square Lattice with a Rectangle-Free Set of Points
N. S. Mendelsohn · Mathematics Magazine · 1987
This paper originated when I was perusing the book Mathematical Gems III [2] by Ross Honsberger. Honsberger has an engaging way of writing, but even better than this, he has excellent taste in his choice of problems. I have had a long-term interest in the construction of problems for undergraduate and high school mathematical contests. One of the techniques that I and many others have used is to take some topic of modem mathematics and to construct a sufficiently simple example so that a solution can be found which does not require the solver to have a knowledge of the theory on which the problem is based. As a corollary, when I look at problems composed by others, I have a dual interest, namely: first to solve the problem and second, to try and find out what led the composer to the problem. With this in mind, I looked at two problems which appeared in Mathematical Gems III. These problems and their solutions appear on pages 2-6. They are both problems that appeared in the 1974 USSR National Olympiad (high school).