Problem #PRU-79322

Problems Geometry Solid geometry Spheres Circle on a sphere Methods Pigeonhole principle Pigeonhole principle (area and volume) Extremal principle Smallest or largest distance (length)

Problem

A spherical sun is observed to have a finite number of circular sunspots, each of which covers less than half of the sun’s surface. These sunspots are said to be enclosed, that is no two sunspots can touch, and they do not overlap with one another. Prove that the sun will have two diametrically opposite points that are not covered by sunspots.