Interview Questions And Answers 
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How many points are there on the globe where by walking one mile south, one mile east and one mile north you reach the place where you started.
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At the north pole. The south pole wouldn’t
quite work, since you can only go north from the south pole.
I would rather say an infinite number of places. If take the place quite close to the southpole where the circumference of the earth is exactly 1km it will mean that after walking for 1 km you end up on the same spot as you started. So your starting point for this quest is 1km north of any point on this circle.
Thats an interesting point, but once you walk 1km to get to the south pole, which way do you turn to go east? There is no East/West once you get to the pole!
Like the last line says: You start at any point 1 km North of the latitude which is of circumference 1 km, so you start 2 km north of the South Pole. So after going south, you go one km east (make a full circle) and walk back up north. Great solution! Hats off!!
vrouwe, There will be no such place available on south pole even if the globe is perfect round.
There is only one point on the globe. The North Pole. The circumference 1 mile north of the south pole sounds good, but is wrong. If you walk south from this circle and reach the south pole, you cannot move east as is required by the question, thus this is not a point at which you can walk 1 mile east, so you didn’t do what the question asks.
- 1 point
Notice that geometry on a *GLOBE* is non-euclidean! In eucliden geometry, all shapes are drawn on a flat plane; but a globe is not flat!
In euclidean geometry, the sum of the angles of a triange is always 180 degrees…but on a globe, the angles of a triangle sum to 360 degrees! Thus, you can move as described (in a triangle) and wind up at the same point ANYWHERE on the globe.
Therefore, there are an infinite number of points where this can be done.
I think drchaz is almost right there are infinite points, but if globe is meant to be earth then 1 mile is a very small distance to reach the same point after following the directions.
So i think there is no such point on earch.
An interesting problem would be to find out the distance that if travelled on EARTH with these instructions would bring you back to the starting point.
Both answers (North Pole, and all points on the circle 1 mile north of the circle having circumference of 1 mile around the South pole) are right.
I agree with aashishg. “Both answers (North Pole, and all points on the circle 1 mile north of the circle having circumference of 1 mile around the South pole) are right.”
MrStrype
I would like to complete aashishg’s answer (”North Pole, and all points on the circle 1 mile north of the circle having circumference of 1 mile around the South pole) are right.”) - also there are points 1 mile north of the circles having circumference of 1/n miles, where n is positive non-zero integer number (the idea is that when going 1 mile east you can circle twice or more around the south pole).
In that case, there’s also a ring 1/n miles in circumference south of the north pole.
Eya: Yes there is a ring 1/n miles in circumeference south of the north pole, but so what? Where would you start from — from a point on this ring or from 1 mile north of this ring? There is no point one mile north of this ring.
drchaz: Your solution is incorrect. Both the south and north traversals that are required would have to be along a longitude. These could be two different longitudes if our starting point is the north pole, or the same longitude if the solution is to start from any point one mile north of the ring with circumference 1/n miles (where n is a positive integer).
The primary consideration is the perception of north/south and east/west.
Since the north/south connected by longitudes are not parallel but converge at the poles, the only chance for a person to get back to the same point when he started, he needs to traverse along the longitudes and latitudes and that too at the points where the assymetry is the least.
Accordingly, the points on the latitude half mile north of equator present the best shot.
Anywhere else, the “curvature” of earth and the convergence of the longitudes will put him either short or long of his start point…
This also assumes that the measurement system used to determine “North” takes into account the disalignment between the true north and the geomagnetic north of Earth.
This problem is actually discussed in Yakov Perelman’s “Mathematics can be Fun”
there can not be any such place…we may be at any point but if we go 1 mile south then 1 mile east then 1 mile north…we will still be 1 mile to the east of starting point…so to return to the starting point we will hav to again go 1 mile west
there is only one such point and that is the north pole.
There are, as others have said, infinitely many such places:
One is the north pole.
The rest are points exactly one mile north of points on the circle (just north of the south pole) that marks where the circumference is exactly one mile. First, you’d walk south and end up on the circle. Then, you’d walk west a mile, circling the globe. Then, you’d walk north again–same spot.
It’s not true that all points satisfy the riddle, but it is true that there’s an infinite number of points that do.
Think out of the box..
To reach from the same point according to the question, consider a triangle with three points.
u will reach to the same point.
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