MathDB

Subsets of points lying in disks

Source: Romania TST 2023 Day 2 P4

April 7, 2024

geometrycombinatoricscombinatorial geometry

Problem Statement

Fix a positive integer

n.{}

Consider an

n{}

-point set

S{}

in the plane. An eligible set is a non-empty set of the form

S\cap D,{}

where

D

is a closed disk in the plane. In terms of

n,

determine the smallest possible number of eligible subsets

S{}

may contain.
Proposed by Cristi Săvescu