This is another one puzzle asked from Micrsoft. How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started? Answer for this puzzle is given below.
Answer:
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!
Visitors can write your comments and different answers as you think..
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