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Puzzle: The mystery point on globe


Suppose you stand at a point on globe where, by walking 1 mile South, then 1 mile East and then again 1 mile North you reach to the same point from where you had started. The question is how many such points exists on this globe.

The answer may be theoretical but should be with valid logic and calculations.

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By  Roshan

Shaan Shaan   5 years ago

The trivial answer to this question is one point, namely, the North Pole. But if you think that answer should suffice, you might want to think again!
Let’s think this through methodically. If we consider the southern hemisphere, there is a ring near the South Pole that has a circumference of one mile. So what if we were standing at any point one mile north of this ring? If we walked one mile south, we would be on the ring. Then one mile east would bring us back to same point on the ring (since it’s circumference is one mile). One mile north from that point would bring us back to the point were we started from. If we count, there would be an infinite number of points north of this one mile ring.
So what’s our running total of possible points? We have 1 + infinite points. But we’re not done yet!
Consider a ring that is half a mile in circumference near the South Pole. Walking a mile along this ring would cause us to circle twice, but still bring us to back to the point we started from. As a result, starting from a point that is one mile north of a half mile ring would also be valid. Similarly, for any positive integer n, there is a circle with radius
r = 1 / (2 * pi * n)
centered at the South Pole. Walking one mile along these rings would cause us to circle n times and return to the same point as we started. There are infinite possible values for n. Furthermore, there are infinite ways of determining a starting point that is one mile north of these n rings, thus giving us (infinity * infinity) possible points that satisfy the required condition.
So the real answer to this question is 1 + infinity * infinity = infinite possible points!

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Rajat Kumar Rajat Kumar   5 years ago

In reference of universe the point at which you start will always be fixed,now since the earth rotates and you are moving in the opposite direction in east we just have to move at the speed so that by the time that the movement of 1 km south 1 km east 1km north is completed the point at which we essentially arrive is at the same place from universe point of view where we started intitally.It would essentially mean that every point on earth would have the same property and thus there are infinite such points.The trick is to just move at the speed so that by the time we complete the journey the point we end at is at the same universal point from where we started.

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