MathDB

A finite set

S

of points in the coordinate plane is called overdetermined if

|S|\ge 2

and there exists a nonzero polynomial

P(t)

, with real coefficients and of degree at most

|S|-2

, satisfying

P(x)=y

for every point

(x,y)\in S

. For each integer

n\ge 2

, find the largest integer

k

(in terms of

n

) such that there exists a set of

n

distinct points that is not overdetermined, but has

k

overdetermined subsets.
Proposed by Carl Schildkraut

Problem Statement