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max cardinality of set of lattice point with lines no parallel to given triangle

Source: Danube 2014 p4

July 22, 2019
lattice pointsparallelogramMaximalcardinalitycombinatoricsgeometrycombinatorial geometry

Problem Statement

Let nn be a positive integer and let △\triangle be the closed triangular domain with vertices at the lattice points (0,0),(n,0)(0, 0), (n, 0) and (0,n)(0, n). Determine the maximal cardinality a set SS of lattice points in △\triangle may have, if the line through every pair of distinct points in SS is parallel to no side of △\triangle.
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