MathDB

Let

f(n)

be the least number of distinct points in the plane such that for each

k = 1, 2, \cdots, n

there exists a straight line containing exactly

k

of these points. Find an explicit expression for

f(n).

Simplified version.
Show that

f(n)=\left[\frac{n+1}{2}\right]\left[\frac{n+2}{2}\right].

Where

[x]

denoting the greatest integer not exceeding

x.

Problem Statement