## Pirates!

A ship in the plane has integer coordinates. It also has integer velocity (again in \(\mathbb{Z} \times \mathbb{Z}\)). Each turn the ship advances according to its velocity. So, for example, if the ship was at (2, 4) and its velocity is (6, 4) its new position will be (8, 8), and the position after that will be (14, 12):

You, as a pirate, obviously want to blow the ship up! You do not know the original position of the ship nor its velocity. You can only shoot one bomb per turn, which blows up exactly one point in the plane. What strategy should you employ in order to be sure you will eventually hit the ship?

It is recommended to watch to this video while solving the riddle. It provides great inspiration!

Thanks to Nadav Sherman for giving me this riddle.