Points on globe – Interview puzzle

How many points are there on the globe, so that if you walk 1km south, then 1km east and then 1km north, you reach the place where you started.
Solution:

We have to find special point, On the Globe, the first step is to think about special points on the globe:

1. North Pole
2. South pole
3. Points on equator
4. Points on arctic circle
5. Points on antarctic circle

Knowledge of geography is not expected in IT interview, so point 4 and point 5 are less likely.

North pole is a clear answer. If a person is at North pole and he moves 1km South, then 1km East and then 1 km North, he will reach the North pole again.

So North pole is 1 such point.

Now, you can verify that points on equator will not satisfy such thing. Similarly any point on arctic or antarctic circle also does not fit in the question.

South pole is not such a point, because we cannot move southwards from south pole.

But if you move northwards from the south pole, you will come to a point where the circumference of earth is just one km (i.e if you move 1km east (or west) you will complete one circle and reach the same point. Let us call this ‘Circle-A’ (as shown in the diagram).

Now move 1km North of Circle-A, and you will reach a point in Circle-B.

From any point in Circle-B, If you move 1km south (reach a point in Circle-A), then 1km East (reach the same point in Circle-A by moving the complete circle) and then 1km North, you will reach the same point where you started from.

Hence all the points on Circle-B satisfy the condition given in the question.

Answer: There are infinite such points.