A fast boat is overtaking a slower one when fog suddenly sets in. At this point, the boat being pursued changes course, but not speed, and proceeds straight in a new direction which is not known to the fast boat. How should the pursuing vessel proceed in order to be sure of catching the other boat?
The amazing answer is that the pursuing boat should continue to the point where the slow boat would be if it had set its course directly for the pursuing boat when the
fog set in. If the boat is not there, it should proceed in a spiral
whose origin is the point where the slow boat was when the fog set in. The spiral
must be constructed in such a way that, while circling the origin, the fast boat's
distance from it increases at the same rate as the boat being pursued. The two courses
must therefore intersect before the fast boat has completed one 
circuit. In order to make the problem reasonably
practical, the fast boat should be capable of maintaining a speed four or five times
as fast as the slow boat. Also, if the fast boat's speed remains constant, the spiral
must be logarithmic.
The Season 3 episode "Spree, Part 2" (2007) of the television crime drama NUMB3RS featured an urban permutation of the trawler problem.
