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A(n) =[(n+1)/2] [(n+2)/2} , distinct points in the plane

Source: Germany Federal - Bundeswettbewerb Mathematik 1990, round 2, p2

February 21, 2020
combinatorial geometrycombinatorics

Problem Statement

Let A(n)A(n) be the least possible number of distinct points in the plane with the following property: For every k=1,2,...,nk = 1,2,...,n there is a line containing precisely kk of these points. Show that A(n)=[n+12][n+22]A(n) =\left[\frac{n+1}{2}\right] \left[\frac{n+2}{2}\right]
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