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1999 HMMT Team #10 combo geo with 5 points at lattice points

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March 8, 2024
geometrycombinatoricscombinatorial geometry

Problem Statement

If 55 points are placed in the plane at lattice points (i.e. points (x,y)(x,y) where xx and yy are both integers) such that no three are collinear, then there are 1010 triangles whose vertices are among these points. What is the minimum possible number of these triangles that have area greater than 1/21/2?
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