We wanted to find the minimum number of police officers to capture a target. Remember that all units and the target are points with constant speed, perfect logic, and instant reaction time. Consider the lines perpendicular to those through the target and officers. Clearly, the target cannot cross any of these lines, the officers would always block it off. Furthermore, the target cannot delay all the officers in this way at once. The inactive ones can close in. It follows that a closed shape can catch the target. The smallest 2D shape is a triangle. We realize that we can generalize this. In higher dimensions, we use perpendicular planes and such. But the smallest figure is always the simplex! The simplex has n+1 vertices. Therefore, our answer is that 3 constables are needed to catch the target in 2 dimensions.