IMO 2008 Shortlist C3
In the coordinate plane consider the set S of all points with integer coordinates. For a positive integer k, two distinc...
Category: Combinatorics
Problem
In the coordinate plane consider the set S of all points with integer coordinates. For a positive integer k, two distinct points A,B ∈ S will be called k-friends if there is a point C ∈ S such that the area of the triangle ABC is equal to k. A set T ⊂ S will be called a k-clique if every two points in T are k-friends. Find the least positive integer k for which there exists a k-clique with more than 200 elements.