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At least how many gangsters will be killed?

Source: IMO Shortlist 2000, G7

August 10, 2008
geometryPythagorean TheoremIMO Shortlist

Problem Statement

Ten gangsters are standing on a flat surface, and the distances between them are all distinct. At twelve o’clock, when the church bells start chiming, each of them fatally shoots the one among the other nine gangsters who is the nearest. At least how many gangsters will be killed?
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