This is partly the result of an unfortunate exchange on Worldbuilding Meta:
@HDE226868 hahahaha. No math allowed. – James yesterday
I shall find a way! – HDE 226868 yesterday
I think I have.
This is sort of based off of the travelling salesman problem, where the object is to find the shortest distance between a given number of points. This is, as mathematicians quickly found out, much harder than it seems.
In a Middle-Earth-esque world, a wizard is responsible for patrolling a network of small villages to keep the people in the area from harm. The villagers don't know about his abilities, simply that he's an eccentric old man who wanders around. They also don't want to interact with him, because they fear him - as a whole, they're pretty xenophobic.
One day, though, the wizard suffers an attack of amnesia. He remembers much of who he is, but he forgets how to get between villages the fastest way possible. He quickly realizes that there are multiple paths from one village to another, but only one is the shortest.
How can he figure out what route to travel through? He's using an approximation: Travel to the closest village he hasn't already been to.
- He has to travel by foot.
- He has forgotten how to use his powers, except for one: The ability to hover ten feet in the air for approximately seven seconds.
Note: I did not intend for magic to be allowed. That said, I originally didn't specify that, so I'll consider Cort Ammon's answer as perfectly fine, especially as it's quite clever. Future answers: Please don't use magic! Thank you.