Did you solve it? Are you smart enough to work for Elon Musk?

theguardian.com:

Earlier today I set you the following problem, which was Elon Musk’s favourite interview question for engineers applying to work at SpaceX (according to his biographer Ashlee Vance).

You’re standing on the surface of the Earth. You walk one mile south, one mile west and one mile north. You end up exactly where you started. Where are you?

A correct answer is the North Pole. Musk would then ask: “Where else could it be?”

Today’s first puzzle was that one: where else could it be?

Solution

There are an infinite number of places near the South Pole where walking a mile south, west and north returns you to exactly where you started. Consider the circle of latitude near the South Pole that has a circumference of 1 mile. From any point on this circle, walking one mile west along this circle will take you back to that same point. Thus any point a mile north of this circle of latitude is a solution to the problem. But there are more points too: Consider the circle of latitude that has a circumference of 0.5 miles. Any point a mile north of this circle is also a solution. Indeed, the solutions are any point one mile north of a circle whose circumference is (1/n) miles for all n.

I also set three more problems, which also involve the shape of the Earth.

1. One direction

You are standing on the surface of the Earth. You head north and travel for ten miles in a straight line. After a quick stop, you again head north and travel another ten miles in a straight line. You end up exactly where you started. Where are you?

Solution

You are anywhere north of the line of latitude that is ten miles south of the North Pole. If you start heading north, you will pop over the pole before you finish the ten miles, and so when you head north again you are