Question 5
Larry and Rob are two robots travelling in one car from Argovia to Zillis. Both robots have control over the steering and steer according to the following algorithm: Larry makes a $90^\circ$ left turn after every $\ell$ kilometer driving from start; Rob makes a $90^\circ$ right turn after every $r$ kilometer driving from start, where $\ell$ and $r$ are relatively prime positive integers. If both turns occur simultaneously, the car keeps going without changing direction. Assume that the ground is flat and the car can move in any direction.
The car starts from Argovia facing towards Zillis. For which pairs $(\ell,r)$ is the car guaranteed to reach Zillis, regardless of how far it is from Argovia?
The car starts from Argovia facing towards Zillis. For which pairs $(\ell,r)$ is the car guaranteed to reach Zillis, regardless of how far it is from Argovia?