Final answer:
The puzzle involves figuring out how the girl can cross the bridge from a city where a pass is needed to another where it's not, without getting caught. She uses the guard's 5-minute break to start crossing and, walking at her top speed, reaches the other side just as the guard returns to the middle.
Step-by-step explanation:
The question presents a riddle involving two cities and a bridge connecting them. It's a logic puzzle rather than a mathematical problem. To solve it, one must determine how a girl can cross the bridge from the second city to the first city, which does not require a pass, without getting caught by the guard. She starts crossing when the guard takes his 5-minute break. If she walks at her top speed, she would be halfway across the bridge when the guard returns from his break. If she continues at the same speed, by the time the guard gets to the middle, she would have reached the end of the bridge. Therefore, the guard would not have enough time to catch her as she reaches the city where no pass is required. This riddle teaches critical thinking and problem-solving skills.