# Lattice Midpoints

$$n$$ lattice points are drawn on the coordinate plane. These points' pairwise midpoints are then drawn. What is the smallest possible value of $$n$$ such that one is guaranteed to have at least $$2014$$ of the midpoints also be lattice points?

Details and Assumptions

This problem is inspired by a classic proof problem.

If two pairs of points happen to have a common midpoint, both midpoints should be counted.

×