5

Part of 1997 German National Olympiad

Problems(1)

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

Source: Germany 1997 p5

n

discs in a plane, possibly overlapping, whose union has the area

1

. Prove that we can choose some of them which are mutually disjoint and have the total area greater than

1/9

geometrycombinatoricsareacombinatorial geometry