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Ten miles south, east, north and west

Puzzling Asked on August 20, 2021

I’m standing on the surface of the Earth. I walk ten miles south, ten miles east, ten miles north and ten miles west. I end up exactly where I started.
Where on earth am I?

3 Answers

I think there are three(ish) choices. The simplest one is

To find the other solutions, we have to notice that

This means we can also start

and then we can, of course, start

Correct answer by Bass on August 20, 2021

I think the answer is:

Reasoning:

Update: Based on @Bass's answer, I was curious about the actual calculation. Turns out it's really not that hard.

Answered by Jeremy Dover on August 20, 2021

I think the answer depends on what "going east/west" means. That is:

Under this definition, suppose you start from P1, walk south to P2, east to P3, north to P4 and west to P5. (Each walk is 10 miles long.) I check the following three cases.

Case 1:

Case 2:

Case 3:

Answered by sj2tpgk on August 20, 2021

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