There is no guarantee that the route is static. If, for example, you are a ping host halfway around the world, one ping can travel one route, and the next ping can go on a completely different route. Even if you like traceroute (start at TTL 0 and increment by one for each answer), there is no guarantee that the route will not change from one packet to another.
The reason is because you cannot know what is happening with the exchange of data between the two routers from you to your destination. The router may answer once, but after a second there may be a power outage, or the cable may be disconnected, or for some other reason the network may be disconnected (my favorite is to clean the eject plugs because they need an outlet for their vacuum )
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