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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.

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