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

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.

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