Geek Challenge: Eccentric Traveler

This month's geek challenge focuses on some strange sightseeing aspirations of an eccentric traveler. Our eccentric traveler's odd expedition begins by considering the following riddle:

You walk one mile South, then one mile East, then one mile North. When you finish walking you are at your original location. Where are you?

After initially deducing the solution to be the North Pole, our eccentric traveler realized there were other starting locations in the world where one could walk this path and quickly became preoccupied with traveling to all of them. Our traveler charted out what he thought to be the most efficient path in order to pass by all of these locations (including the North Pole) and immediately began ironing out logistics for the trip.

He will be traveling in his special hover car capable of going 100 mph over land and water without stopping for fuel or even slowing down for turns. He has also convinced an up-and-coming energy drink company to sponsor his trip. They will drop him off at his starting position, film the journey, and supply him with food and drink on the go. Since he is very confident in his assessment that his charted locations satisfy the riddle, he will not be traveling the described 3 mile path from any of the starting locations to check that he's right, only passing by to see them up-close before traveling to the next one.

The solution to this challenge has two steps:

1. What are all the starting locations that satisfy this riddle?
2. What path should our eccentric traveler take to see all of them and how long will it take?

The solution with the most complete analysis will be this months Geek Challenge winner!

Submit responses to geekchallenge@dmcinfo.com by March 6, 2017.