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How many distinct midpoints

Source: Moldova TST 2014, Second Day, Problem 4

March 30, 2014
combinatorics proposedcombinatorics

Problem Statement

Consider n≥2n \geq 2 distinct points in the plane A1,A2,...,AnA_1,A_2,...,A_n . Color the midpoints of the segments determined by each pair of points in red. What is the minimum number of distinct red points?
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