Shouldn’t the answer always start with: “Assume a spherical cow…”
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Smacks of “How Would You Move Mt. Fuji?” - one shovel at a time, duh.
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Or, actually, an infinite sequence of places, because if you’re even closer and the circumference becomes one-half mile, or one-third mile or one-fourth mile or …, your walk to the west simply circles the Pole multiple times and you still return to your starting point.
Oh, @Bemopolis beat me to it. And each of those answers also has an infinite number of solutions since you can start anywhere on the circle.
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This reminds me of Elon Musk’s iPod Submarine. It’s a simple game where you must provide stupid solutions to serious problems.
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Any answer other than “north pole” violates one of the conditions. In the ‘circles near the south pole’ case, you don’t “walk one mile west”. You may start walking west but you travel in many other directions as you go around the circle. I win! Job, please.
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I would not call it a scam though.
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Infinity plus one, no? (to include the North Pole) 
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Pedant alert: The video ends with: there are an infinite number of an infinite number solutions, technically there are a countably infinite (C(1/n) for all natural numbers n) number of uncountably infinite (points on a real line segment, in this case a circle), or just an uncountably infinite number of solutions.
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Indicate a point on that circle at which you are not walking due west. I’ll wait.
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The correct answer is “working for Elon Musk” because that’s the sort of job where you can walk three miles and get nowhere.
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Someone check my math, but none of the above. There are two poles, magnetic and geographic. Since “South” is a definition of the reaction of a compass to the magnetic pole, being at a true geographic pole would mean that moving South is a vector moving away from the magnetic pole. Once you move “West” the vector for North/South would change, making it impossible to return to the exact same location.
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Yep. You win.
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Questions I liked were: “How do hotels keep their water hot when you turn on the spigot?” (mainly just looking to see how many ideas could be brainstormed by the interviewee, and how they broke down where the variables were in the problem to be solved).
My favorite, though, was my interviewer gesturing to a CPU trace diagram poster on the wall and saying “You’re writing a game for this architecture. What are your considerations?” I did allright. 
It ended up being the modified multicore Xenon used in the Xbox 360.
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And everyone wonders why “Full Self Driving”* keeps killing people.
* not even slighly self driving.
Anyway, when we say directions, are we basing them off of magnetic north or true north?
Hardly matters, though, as the next riddle is “Are you white and male?”
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Another solution: On a mountain one mile north from where the circumference of the mountain is one mile around.
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Came here to say this.
My dream job is at the South Pole MAPO lab as the manual machinist.
Well my actual dream job is working for myself but if I have to work for any boss that’s the only job left I actually want to do.
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My answer: Am I an African or European swallow?
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Your direction is only west for the whole mile if your circumnavigating the Earth. If you’re walking around a mountain you can’t keep going west all the way around
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The answer is that they have no good process for picking job applicants, so they throw cheap stuff like this at them to weed out a lot of people before sending them on to people who know what they’re talking about.
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