A man walks 1 mile south, 1 mile east, and 1 mile north. He ends up exactly where he started....?

Question

where on earth could he be?

the north pole is one place. i need some more places. and south pole doesnt work. challenging, isnt this?

my teacher says there are more than 1 place.....

Answer 1

1, The north pole as a starting point
and
2, at any point at a distance of 1mile + 1/(2π) [in miles] ...( approx = 1.159 miles) from the South pole

The north pole reasoning is obvious, here is the reasoning for ANS#2 ...
the north and south parts of the question cancel out 1 mile South + one mile north = same point ... ONLY if the 1 mile east is in a full circle
so, assuming the circumference of the circle (2πr) = 1 mile
we know the starting point is 1 mile away to the north (B'Coz you start walking south for a mile before you go "eastwards" in a circle)
r = C/(2π) = 1mile/(2π) or 1/2 π miles (read that as "half Pi miles")
so start point = Any point 1 mile + (1/2) π miles in a straight line from the South pole.

Answer 2

He could be starting off a little north of the south pole, so that when whe walks 1 mile east he travels in a complete circle around the south pole. So somewhere in Antarctica, let's say he's at point A. He travels 1 mile south to point B (though still not arriving at the south pole). Then he walks 1 mile east, during which time he circles the pole, winding up at point B again. (Think of a latitude ring that's 1 mile in circumference.) From there, going 1 mile north just brings him back to point A.

Answer 3

1 Mile North

Answer 4

I come in the discussion too late, Geezah, mathguru and David already answered correctly, the latter explained in best manner, but their answers are incomplete, that's why I decided to enter. They all have overlooked the possibilities of MORE THAN 1 COMPLETE TURNS around the South Pole on circles with circumferences 1/2 mile (2 turns), 1/3 mile (3 turns), etc., which, along with the set of points at 1+ 1/(2π) miles from the South Pole, produces all solutions:
all points on the parallel at 1 + 1/(2π) miles from the Pole;
all points on the parallel at 1 + 1/(2*2π) miles;
all points on the parallel at 1 + 1/(3*2π) miles, etc.
finally, one more single point - the North Pole.

Answer 5

Just outside the south pole, where if he goes 1 mile south, he is at a point where the circumference of that latitude is = 1 mile, so 1 mile east would put him full circle, so 1 mile north puts him back where he was. I forget how to calculate that.

Answer 6

The North Pole or in case you have been on good of Mount Everest or any large mountain with a top as once you bypass down one mile then bypass around one mile and bypass back up one mile you will possibly nevertheless finally end up back on the top.

Answer 7

The North Pole is the only place where this is possible.

Answer 8

He can only be on a North pole.

Answer 9

Yes, on a mountain that has a one mile circumference.

Answer 10

North pole is the only place. It won't work at any other place.