An enemy submarine is somewhere on the number line (consider only integers for this problem). It is moving at some rate (again, integral units per minute). You know neither its position nor its velocity.
You can launch a torpedo each minute at any integer on the number line. If the the submarine is there, you hit it and it sinks. You have all the time and torpedoes you want. You must sink this enemy sub - devise a strategy that is guaranteed to eventually hit the enemy sub.
A similar problem we solved some time back was "Finding a Hermit"
Posted by Aaditya Ramdas (CSE, IITB Alumnus working at Tower Research) in comments!!