Problem #PRU-22000

Problems Algebra and arithmetic Number theory. Divisibility Divisibility of a number. General properties Methods Algebraic methods Partitions into pairs and groups; bijections Pigeonhole principle Pigeonhole principle (other)
 12–13  3.0

Problem

You are given 11 different natural numbers that are less than or equal to 20. Prove that it is always possible to choose two numbers where one is divisible by the other.