Vietnam TST 2017 Problem 1
Source: Vietnam TST 2017
March 26, 2017
combinatorics
Problem Statement
There are distinct holes in a line and ants. Each ant comes out of a hole and crawls along the line with a constant speed into another hole, then comes in. Let be the set of moments for which the ant comes in or out of the holes. Given that and the speeds of the ants are distinct. Prove that there exists two ants that don't collide.