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## Homework Statement

Arnoldo Téllez walked one mile to the south, then one mile to the east, and then one mile to the north, getting back to the point where he started. He could have started in the north pole, but he didn't. Where did he start?

(Taken from ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY: A PROBLEM-SOLVING APPROACH, by Varberg and Fleming.)

## Homework Equations

## The Attempt at a Solution

He could have started at several different points:

- At any of the points that are one mile to the north from the parallel whose length is one mile (if that parallel exists).

- At any of the points that are one mile to the north from the parallel whose length is one half of a mile (if that parallel exists), thus walking twice over that parallel.

- At any of the points that are one mile to the north from the parallel whose length is one third of a mile (if that parallel exists), thus walking three times over that parallel.

- and so on...

Is the answer correct?