Problem #PRU-35149

Problems Geometry Plane geometry Geometric inequalities Area inequalities Methods Algebraic methods Partitions into pairs and groups; bijections Pigeonhole principle Pigeonhole principle (area and volume)
 13–15  3.0

Problem

In a square which has sides of length 1 there are 100 figures, the total area of which sums to more than 99. Prove that in the square there is a point which belongs to all of these figures.