I use Google Maps for driving directions a lot. I do sometimes laugh about the “alternate routes” that show up as I drive. For instance, if I turn off the freeway at the next exit, it will only add 10 minutes to my route. Or something like that. Notice I don’t mean reroutes for traffic, just the alternate suggestions.
What got in my head today, though, was what if each time one of these alternate, longer routes came up, I took it? Then I took the next one, and the next one? Would I ever actually get to my destination? It would be interesting to run this as some sort of simulation, because it sure would take a while in real life.
Two conditions: (1) you never traverse the same road twice and (2) alternate routes available are guaranteed to reach the destination without violating the first rule.
Then there’s a finite number of such sets of paths and you will reach the destination.
If rule 1 is violated, then you can just drive in circles.
If rule 2 is violated but not rule 1, then you run out of options to reach the destination.