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?

This is the same as the Bee problem in reverse (here and here). In the bee problem, the two travelers bounding the area in which the bee shuttles back and forth approach from being apart. Here the two travelers bounding the area in which the dog is free to shuttle start together and move apart.

The problem is that the bee problem can start from either of the two travelers or anywhere in between and still it happens that there are infinitely many reversals at the end. Here the infinitely many reversals come at the beginning, so there is no defined direction in which the dog is facing at the beginning, and infinitely many reversals, so that's neither odd nor even.

Since the bee problem could have begun with the shuttler anywhere in between the outliers, this can end up with the dog anywhere between the boy and the girl.

Posted by Charlie on 2004-01-24 14:34:48