How many places?
Logic
Level
2
How many places are there on earth where if you walk a mile north, a mile east, and then a mile south, you end at the same spot you began your 3-mile journey?
2
Infinite
0
6
1
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1 solution
Walking north/south means travelling up or down a line of constant longitude (a semicircle connecting the poles). Likewise, walking east/west means traveling along a circle of constant latitude (a circle parallel to the equator). The equator is a very big circle, but as you approach the poles these circles become smaller, eventually disappearing at the poles. So, there is a longitude circle C near the north pole with circumference equal to one mile. So, to go on a journey as described above, pick any point p on this circle, of which there are infinitely many, and start one mile south of p . Travel north one mile to p . Going east for a mile equates to traveling once around C , ending up back at p . Finally, travel a mile south to your starting point.