Somewhere on the high seas smuggler Stan is attempting, without much luck, to outspeed coast guard Charlie, whose boat can go faster than Stan's. Charlie is one mile east of Stan when a heavy fog descends. It's so heavy that nobody can see or hear anything further than a few feet. Immediately after the fog descends, Stan changes course and attempts to escape at constant speed under a new, fixed course. Meanwhile, Charlie has lost track of Stan. But Charlie happens to know Stan's speed, that it is constant, and that Stan is sticking to some fixed heading, unknown to Charlie.

How does Charlie catch Stan?

Charlie may change course and speed at will. He knows his own speed and course at all times. There is no wind, Charlie does not have radio or radar, there is enough space for maneuvering, etc.

(In reply to re(2): new twist by Mindrod)

Stan is proceeding away from his starting point at some constant velocity and heading.  By spiraling out, Charlie can cover the full 360 degrees of Stan's possible headings, while at each moment, also being the same distance from that starting point as Stan.  Eventually he and Stan will both arrive at the same "heading" and distance from the starting point.

I hope that was clear enough.

Posted by Bob Smith on 2005-11-03 08:35:53