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Math Help - Walk 1 mi South, 1 mi West, 1 mi North, end up where you started

  1. #1
    Member Last_Singularity's Avatar
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    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!
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  2. #2
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    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.

    *
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  3. #3
    Member Last_Singularity's Avatar
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    Soroban got it =)
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  4. #4
    Super Member craig's Avatar
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    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
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  5. #5
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    Quote Originally Posted by Last_Singularity View Post
    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.
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  6. #6
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    Quote Originally Posted by earboth View Post
    Beside Sorobans solution:
    .
    That does not change Soroban's solution

    (the question asks for the number not a list)

    .
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  7. #7
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    A non-Euclidean puzzle.
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