Problem: Let A and B be two cities, with two different roads connecting them. Suppose that two cars can travel from A to B on different roads, keeping a distance that does not exceed 1 mile between them. Is it possible for two cars to travel one from A to B, the other from B to A such that the distance between them is always greater than one mile?
Update: (23 January 2011)
Solution: Posted by Gaurav Sinha (chera) (CSE IITK 1996 Graduate, Now working at Indian Revenue Service) in comments! A more general solution with clear explanation posted by Ameya Ranade (Microsoft Software Engineer, CSE IITB 2009 Graduate)