MathDB

Let

n

be a positive integer. Let

S

be a subset of points on the plane with these conditions:

i)

There does not exist

n

lines in the plane such that every element of

S

be on at least one of them.

ii)

for all

X \in S

there exists

n

lines in the plane such that every element of

S - {X}

be on at least one of them.
Find maximum of

\mid S\mid

.
Proposed by Erfan Salavati

Problem Statement