ARO 2011 11-4
Source:
April 26, 2011
combinatorics proposedcombinatorics
Problem Statement
Ten cars are moving at the road. There are some cities at the road. Each car is moving with some constant speed through cities and with some different constant speed outside the cities (different cars may move with different speed). There are 2011 points at the road. Cars don't overtake at the points. Prove that there are 2 points such that cars pass through these points in the same order.S. Berlov