MathDB

Let

M

be a set of 999 points in the plane with the property: For any 3 distinct points in

M

we can choose two of them, such that the distance between them is less than

1

. a)Prove that there exists a disc of radius not greater than 1 that covers at least 500 points in

M

. b)Is it true that there always exists a disc of radius not greater than 1 that covers at least 501 points in

M

Problem Statement