How To Solve Elon Musk's Favorite Riddle - 1 Mile South, 1 Mile West, 1 Mile North

I'm somewhere on earth. I walk one mile south, one mile west, and one mile north. I end up exactly where I started. Where could I have started?

This puzzle is a classic brain teaser that was asked at Microsoft. It is also one of the favorites of Elon Musk, co-founder of PayPal and Tesla Motors.

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[vestrocity]

My answer: In debt.
If you're in debt, and you walk 1 mile South, 1 mile West, and 1 mile North, you're still in debt

[CaseyBrick]

Your gym is exactly 1 mile south of your house. You walk 1 mile south to the gym. Hop on a treadmill and walk one mile to the west. Then walk home 1 mile north.

[ieatbananaswiththepeel]

“Only geniuses can solve this!”

Me, who just finished Numberphile’s video on geometry on non Euclidean planes: *maybe I am a genius*

[FilamentFriday]

My thought before the solution: On a treadmill.

[TheGreyfoo]

Suppose I go to the effort of adopting three dogs, and naming them "One Mile North", "One Mile West" and "One Mile South".
Thus, if I were to WALK my dogs, I could say that I walked "One Mile North, One Mile West and One Mile South".
And yes, I would most definitely be back where I started: Forever Alone.

[cameronlindo]

'I end up exactly back where I started'
Where am I?
Where you started hehe

[johnrowley]

To start with, he said he is somewhere on earth, he eventually says, “Where am I?” So, naturally I answered, “You’re on earth!” Made sense to me!! 😁👍

[littleretroship]

I saw a video similar to this a while ago. It was to go in a straight line, turn 90° go in a straight line, turn 90°, go in a straight line and you are where you started because you are on a globe
So it can be several locations. Two of the easiest examples are the north and South Pole at any angle. I’d also assume the equator and maybe (not sure) the rest of the world

[subzeroelectronics]

When I read this, I immediately thought, “oh, that’s just the non-Euclidian spherical geometry that Code Parade is always talking about.”
I’m a genius, guys.

[SaintNine]

It's always struck me as obvious. You're at the north pole. I hadn't thought about the other solutions though. They're are then an infinite number of circles that are fractions of 1 mile in circumference that you can start one mile north of.

[alexdotdash]

I am actually really happy that I got this correct. I am currently looking into hyperbolic geometry, and understanding spherical geometry is important, especially knowing how geodesics work. Love this.

[killerellik]

You end up where you started, directly above the center of the earth! Exactly where we all are!👍!

[edic]

*I'm exactly back where I started. Where am I? *
Me: you are where you started, jimbo.

[patrickingalls]

No closer to a bathroom when you really really have to go! 😁

[jimmykitty]

Hey Presh Talwalker, ❤
That's Awesome! I saw this problem firstly on a math book named "Neuron-e Onuronon" when I saw in class 2. I was able to solve this when I was in class 8 but I wasn't sure. Thanks for sharing the solution ❤

[parkchanyeol]

No matter where I go, I end up on YouTube.

[ravenlord]

The 677 downvotes are from the people of the Flat Earth Society.

[SteveHeller]

I've always liked this puzzle. I especially like that there is a countably infinite family of uncountably infinite sets of solutions. The two infinities are different!!

[dangerxcom]

My thought was that it took you long enough to walk 3 miles for the earth to have rotated 1 mile to the east and I guess this could be anywhere
And this would sort of leave you where you started (in the universe I guess), just not with the same land around you

[rinzler]

I'm not kidding, north pole came straight to mind.