MathDB

3

Part of 1983 Austrian-Polish Competition

Problems(1)

F contains a subfamily consisting of pairwise disjoint discs, joint area >=S/9

Source: Austrian Polish 1983 APMC

4/30/2020
A bounded planar region of area SS is covered by a finite family FF of closed discs. Prove that FF contains a subfamily consisting of pairwise disjoint discs, of joint area not less than S/9S/9.
areageometrydiscscovering