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: another twist by Mindrod)

Yes, if he has no max velocity, then he can travel faster than light.

So let me rephrase. Charlie has no given maximum velocity. One can assume that his maximum velocity is then the maximum feasible velocity of a boat. (I do not know what this is.) However, if Stan goes, for example, 1 mph, then Charlie could probably utilize the spiral technique. So the spiral technique would work, but this depends on conditions which aren't stated. Simply put, it would work in some occasions but not in others.

And frankly, nothing is stated in the problem that Charlie can't go faster than the speed of light. You only say this because it's impossible. But what if it becomes possible later (I'm sure that in 1000 AD they said that cars were impossible.)? The problem didn't specify the time, planet, universe, etc.

The easy way to exploit that is just to say that Charlie thought about it and poof, it happened. It is not stated in the problem that that couldn't be the answer. But it's not a very mathematical answer, so we discard it without thinking, although, its technically possible.

Posted by Joe on 2005-11-03 16:26:57