A boy, a girl and a dog start at the same point facing in the same direction. The boy and girl start walking forward, the boy at 4 mph, the girl at 3 mph. The dog runs at 10 mph backwards and forwards between the boy and girl - when it meets one of them, it turns around and runs towards the other. After half an hour, where is the dog and which way is it facing?

Answer 1: The dog can be at any point between the boy and the girl, facing either way. Proof: if you put the boy and girl at their final positions, with the dog anywhere between them, and run the procedure backwards, all three will return at the same instant to the starting point.

Answer 2: This scenario is impossible, because as soon as they start moving, the dog will either leap ahead of the boy and girl or run the opposite way, thereby ceasing to be between the boy and girl.