RU-ALLRUSSIAN 1975 Problem 9
Three flies crawl along the perimeter of a triangle. At least one fly makes a complete circuit of the perimeter. For the entire period the center of mass of the flies remains fixed. Show that it must be at the centroid of the triangle. [You may not assume, without proof, that the flies have the same mass, or that they crawl at the same speed, or that any fly crawls at a constant speed.]
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
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