15 boys are throwing balls to each other
Source: Dutch NMO 2000
October 22, 2005
pigeonhole principletrigonometry
Problem Statement
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.