The shape of a military base is an equilateral triangle of side $10$ kilometers. Security constraints make cellular phone communication possible only within $2.5$ kilometers. Each of $17$ soldiers patrols the base randomly and tries to contact all others. Prove that at each moment at least two soldiers can communicate.
Problem
Source: 2011 Saudi Arabia Pre-TST November 2.1
Tags: combinatorics, combinatorial geometry, Equilateral