IMO Shortlist 2008 problem C3

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Dodao/la: arhiva
2. travnja 2012.
In the coordinate plane consider the set S of all points with integer coordinates. For a positive integer k, two distinct points a, B\in S will be called k-friends if there is a point C\in S such that the area of the triangle ABC is equal to k. A set T\subset S will be called k-clique if every two points in T are k-friends. Find the least positive integer k for which there exits a k-clique with more than 200 elements.

Proposed by Jorge Tipe, Peru
Izvor: Međunarodna matematička olimpijada, shortlist 2008