Question 11
(BUL 1) Let $f(n)$ be the least number of distinct points in the plane such that for each $k=1,2,\ldots,n$ there exists a straight line containing exactly $k$ of these points. Find an explicit expression for $f(n)$.
Simplified version. Show that $f(n)=\left[\frac{n+1}2\right]\left[\frac{n+2}2\right]$ ($[x]$ denoting the greatest integer not exceeding $x$).
Simplified version. Show that $f(n)=\left[\frac{n+1}2\right]\left[\frac{n+2}2\right]$ ($[x]$ denoting the greatest integer not exceeding $x$).