NL-NWO 2000 Problem 4
Fifteen boys are standing on a field, and each of them has a ball. No two distances between two of the boys are equal. Each boy throws his ball to the boy standing closest to him.
(a) Show that one of the boys does not get any ball. (b) Prove that none of the boys gets more than five balls.
Dataset text AI-MO AoPS. Quoted with source.
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