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finite set of points, different distances

Source: Polish MO Second Round 1971 p4

September 8, 2024
geometrycombinatorial geometrycombinatorics

Problem Statement

On the plane there is a finite set of points ZZ with the property that no two distances of the points of the set ZZ are equal. We connect the points A,B A, B belonging to Z Z if and only if A A is the point closest to B B or B B is the point closest to A A . Prove that no point in the set ZZ will be connected to more than five others.
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