Question 17
The streets in a city are on a rectangular grid with $m$ east-west streets and $n$ north-south streets. It is known that a car will leave some (unknown) junction and move along the streets at an unknown and possibly variable speed, eventually returning to its starting point without ever moving along the same block twice. Detectors can be positioned anywhere except at a junction to record the time at which the car passes and its direction of travel. What is the minimum number of detectors needed to ensure that the car's route can be reconstructed?