Cop and Robber on a Number Line
game
At time t = 0, a robber is at some point x on the number line. Over time, the robber moves at some uniform speed s to the left or the right from its starting position. There is a cop who can choose to be anywhere on the number line at any point of time. The cop cannot see the robber and does not know the initial location of the robber. The cop also knows nothing about the speed s and direction of movement.
If the cop and the robber occupy the same location at the same time instant, then the robber is said to be captured. Does the cop have a strategy to capture the robber in finite time?
