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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. 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 can be constructed in such a way that the two boats will intersect before a complete turn is made.
References
Ogilvy, C. S. Excursions in Mathematics. New York: Dover, pp. 84 and 148, 1994.