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House visitors go to neighbor

Source: UMD 2023 Part II Problem 2

November 30, 2023
combinatoricsinductionUMD

Problem Statement

Let n≥2n \ge 2 be an integer. There are nn houses in a town. All distances between pairs of houses are different. Every house sends a visitor to the house closest to it. Find all possible values of nn (with full justification) for which we can design a town with nn houses where every house is visited.
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