Consider a finite set S of points in the two-dimensional plane. A point p of S is called a covidiot, if p is within two meters of some other point of S. Let R be a rectangle whose horizontal sides have a length of 20 meters and whose vertical sides have a length of 30 meters. Assume that all points of S are contained in R and that S contains at least 601 points. • Use the Pigeonhole Principle to prove that S contains at least two covidiots.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.