Problems
Geometry
Plane geometry
Area
Finding the area by rearrangment
Set theory and logic
Set theory
Inclusion-exclusion principle
Methods
Pigeonhole principle
Pigeonhole principle (area and volume)
Proof by contradiction

a) A square of area 6 contains three polygons, each of area 3. Prove that among them there are two polygons that have an overlap of area no less than 1.

b) A square of area 5 contains nine polygons of area 1. Prove that among them there are two polygons that have an overlap of area no less than \(\frac{1}{9}\).

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