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n discs in plane, possibly overlapping, whose union has the area 1

Source: Germany 1997 p5

February 22, 2020
geometrycombinatoricsareacombinatorial geometry

Problem Statement

We are given nn discs in a plane, possibly overlapping, whose union has the area 11. Prove that we can choose some of them which are mutually disjoint and have the total area greater than 1/91/9.
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