A graph-colouring theorem
R. C. Walker · The Mathematical Gazette · 1976
Imagine six drawing pins stuck in the wall. If we stretch threads, either red or blue, between every pair of pins, we inevitably create at least one triangle all of one colour. This we shall call Theorem 1: the proof follows. Consider any pin. From this emanate five threads (since there are five other pins), of which three must be of one colour. We may without loss of generality assume that they are three red threads.