# Walk 1 mi South, 1 mi West, 1 mi North, end up where you started

• Jan 6th 2009, 06:03 AM
Last_Singularity
Walk 1 mi South, 1 mi West, 1 mi North, end up where you started
How many places on Earth can you walk: 1 mile South, 1 mile West, and then 1 mile North, and end up in the same place where you started from?

For simplicity, assume that the Earth is a perfectly smooth sphere - so no one complains about hitting mountains or icebergs on their trip. And all the conventional properties of directions count, i.e. - moving South & North means parallel to longitude lines and West parallels a latitude line, etc.

For all you physicists, this means zero displacement, but a distance of 3 miles traveled.

If anyone has already seen this riddle, don't spoil it for the others!
• Jan 6th 2009, 07:07 AM
Soroban

Highlight between the asterisks . . .

*
Actually, there is an infinite number of such places.

Consider a circle of latitude near the South Pole which is one mile in circumference.
Select any point on this circle and walk one mile north.

From this starting point, we can walk one mile south,
one mile west (going "around the earth"),
then one mile north to our starting point.

Moreover, we can select a starting point so that we can walk one mile south,
and when we walk one mile west, we go twice "around the earth"
. . . and so on.

*
• Jan 6th 2009, 07:17 AM
Last_Singularity
Soroban got it =)
• Jan 6th 2009, 08:57 AM
craig
Took me a minute to visualise the solution but got there in the end.

good one, the hard part now is trying to remember it when telling it again ;)
• Jan 9th 2009, 03:35 AM
earboth
Quote:

Originally Posted by Last_Singularity
How many places on Earth can you walk: 1 mile South, 1 mile West, and then 1 mile North, and end up in the same place where you started from?

For simplicity, assume that the Earth is a perfectly smooth sphere - so no one complains about hitting mountains or icebergs on their trip. And all the conventional properties of directions count, i.e. - moving South & North means parallel to longitude lines and West parallels a latitude line, etc.

For all you physicists, this means zero displacement, but a distance of 3 miles traveled.

If anyone has already seen this riddle, don't spoil it for the others!

Beside Sorobans solution:

Start at the Nort pole: Any direction from the North pole is South. After 1 mile make a right turn, walk 1 mile, make another right turn, walk 1 mile and you are at the North pole again.
• Jan 9th 2009, 03:38 AM
Constatine11
Quote:

Originally Posted by earboth
Beside Sorobans solution:
.

That does not change Soroban's solution(Cool)

(the question asks for the number not a list)

.
• Jan 11th 2009, 11:33 AM
Cifrocco
A non-Euclidean puzzle.