Monkeys and Coconuts
Source: https://www.mathe-wettbewerbe.de/bwm/aufgaben/aufgaben-1999/aufgaben_99_1.pdf
December 8, 2015
number theoryalgebracombinatoricspigeonhole principle
Problem Statement
Exactly 1600 Coconuts are distributed on exactly 100 monkeys, where some monkeys also can have 0 coconuts.
Prove that, no matter how you distribute the coconuts, at least 4 monkeys will always have the same amount of coconuts.(The original problem is written in German. So, I apologize when I've changed the original problem or something has become unclear while translating.)