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Lattice Points for Endpoints and Midpoints

Source: 2006 SMT Advanced Topics Test Problem 7

March 20, 2010
analytic geometry

Problem Statement

A lattice point in the plane is a point whose coordinates are both integers. Given a set of 100 distinct lattice points in the plane, find the smallest number of line segments AB‾ \overline{AB} for which A A and B B are distinct lattice points in this set and the midpoint of AB‾ \overline{AB} is also a lattice point (not necessarily in the set).
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