A boy, a girl and a dog are standing together on a long, straight road. Simultaneously, they all start walking in the same direction: The boy at 4 mph, the girl at 3 mph, and the dog trots back and forth between them at 10 mph. Assume all reversals of direction instantaneous.

In one hour, where is the dog and in which direction is he facing?

(In reply to Question by Penny)

This is an exercise in the pure mathematics of a situation. The problem says to ignore certain real-world complications. Unfortunately ignoring those complications means either abandoning all common sense or divorcing the mathematics of the puzzle from the situation used to set it up.

In the first few moments, the situation makes no sense in the real world where the dog can't turn instantaneously nor move back and forth in infinitesimal increments in infinitesimal time units. It is hard to picture in the forward direction at all.

The problem is much better conceptualized as a variant on the bee problem played backward. The infinite number of instantaneous switchbacks in infinitesimal increments still don't make any real-world sense, but at least they are easier to imagine.

Posted by TomM on 2004-01-24 20:51:54