Elon Musk is known as the cofounder of PayPal and Tesla Motors. He’s often called the real life version of the comic book character “Iron Man.” A new authorized biography of him, Elon Musk is already listed as a best-seller on Amazon in pre-sales.
“You’re standing on the surface of the Earth, ” Musk begins, according to the book. “You walk one mile south, one mile west, and one mile north. You end up exactly where you started. Where are you?”
The post is titled “How to survive a job interview with Elon Musk.” It then ironically gets the answer WRONG, stating “There are two answers to the riddle.”
CLOSE, BUT NOT QUITE!
It is more accurate to say there are two SETS of answers. Let me take a moment to explain the complete solution of this fascinating brain teaser.
Answer in Video Form
For those that prefer, you can watch a video I made explaining the solution.
Microsoft Interview Question
So this puzzle has a history in the tech industry. It is famously one of the brain teasers that Microsoft would ask in their culture of crazy interview questions. You can read about these interesting problems in William Poundstone’s How Would You Move Mount Fuji?, which is where I first learned about this puzzle.
(Note: you can go “one mile east” or “one mile west” and the puzzle does not change).
A more complete answer is there are “one plus infinity times infinity” locations.
Well let’s tackle the “one” first.
The North Pole
This is the answer most people think about.
Because you are at the North Pole, you end up walking in a triangle when you go one mile south, one mile west, and then one mile north.
So that’s one solution.
Infinity solutions near the South Pole
Think about a circle that is one mile in circumference, and just north of the South Pole. We’ll call that C(1).
If you are one mile north of this circle, then you will also end up back at the same spot. You will travel one mile south, then you’ll travel one mile around the circle, and then you’ll go north and end up back at the same spot as you started.
Actually this is true for any point on the circle that is one mile north of C(1). So this is an infinite number of solutions.
Infinity times infinity!
Now think about a circle that is one-half mile in circumference and also just north of the South Pole. We’ll call that C(1/2).
If you are one mile north of this circle, then you will also end up back at the same spot. You will travel one mile south, then you’ll travel the circle TWICE, and then you’ll go north and end up back at the same spot.
Similarly, if you are one mile north of the circle C(1/3)–a circumference of 1/3 near the South Pole–then you will also end up back at the same spot. You will travel around C(1/3) a total of 3 times.
We can use the same argument for C(1/4), C(1/5), and so on for any C(1/n), where each circle has a circumference of 1/n. If you go one mile west in any of these circles, you will travel around the circle times and end up back at the same point.
Therefore, you will always end up at the same spot if you are one mile north of any circle C(1), C(1/2), C(1/3), etc.
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