Posers and Puzzles

Posers and Puzzles

  1. Joined
    06 Apr '08
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    1871
    07 Apr '08 13:27
    How many places are there on Earth, so that if you go 1km north, 1km west and 1km south, you'll end up at exactly the same place

    hint: there are more than one ... 😀
  2. Joined
    15 Nov '07
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    1554
    07 Apr '08 13:441 edit
    An infinite amount, assuming a set distance can be broken down into infinite smaller distances.

    EDIT:spelling
  3. Joined
    06 Apr '08
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    1871
    07 Apr '08 13:50
    nope, you can't break it ... you have to walk 1km north THEN 1km west and THEN 1km sourth. Also, if you think there are infinitely many such places, can you described them (e.g. how to find them)
  4. Standard memberPBE6
    Bananarama
    False berry
    Joined
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    07 Apr '08 14:06
    Originally posted by 3v1l5w1n
    nope, you can't break it ... you have to walk 1km north THEN 1km west and THEN 1km sourth. Also, if you think there are infinitely many such places, can you described them (e.g. how to find them)
    Aha! This is an oldie but a goodie, just remembered the answer.

    The first point people think of is the South Pole. The second set of points is a bit trickier, but I'm sure most people can "wrap" their heads "around" it. 😉
  5. Joined
    11 Nov '05
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    43938
    07 Apr '08 14:18
    One classic puzzle of the same category is something like this:
    "I am a hunter. I went 1 mile south, didn't find anything. Went 1 mile west, shot a bear. Went home again, having to carry the bear over my shoulder one whole mile."
    Question, what colour had the bear?
  6. Pale Blue Dot
    Joined
    22 Jul '07
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    21637
    07 Apr '08 14:411 edit
    The equator?
  7. Joined
    06 Apr '08
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    1871
    07 Apr '08 15:10
    definitely not
  8. Joined
    07 Sep '05
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    35068
    07 Apr '08 15:22
    Originally posted by PBE6
    Aha! This is an oldie but a goodie, just remembered the answer.
    Yes, quite neat, isn't it?
  9. Joined
    06 Apr '08
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    1871
    07 Apr '08 15:40
    here is a hint:

    there are basically two possibilities:

    1.) You end up going in a equilateral triangle with all right angles (yes, it is possible and quite common on a sufrace of a sphere that inner angles of a triangle sum up to more than 180 degrees) - this is if you start from the South Pole.

    2.) In this option you definitely won't be going in a triangle ... so what else can you do to come back to the same place (while changing the direction twice)
  10. Joined
    12 Mar '03
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    37858
    07 Apr '08 15:42
    1 = southhpole

    every point on every parallel near the north pole with a perimeter of 1/1, 1/2, 1/3, ... km
  11. Pale Blue Dot
    Joined
    22 Jul '07
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    21637
    07 Apr '08 16:062 edits
    Travel by air from the equator for 23 hours 59 minutes 58 seconds.
  12. Pale Blue Dot
    Joined
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    07 Apr '08 16:331 edit
    1.159 km from the North Pole?

    Walk north towards the North Pole for 1 km, turn west and walk for 1 km (360 degrees), turn south and walk back 1 km to your point of departure.
  13. Joined
    06 Apr '08
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    1871
    07 Apr '08 17:01
    Originally posted by Mephisto2
    1 = southhpole

    every point on every parallel near the north pole with a perimeter of 1/1, 1/2, 1/3, ... km
    quite close, actually i think you just forgot to devide by pi ... so

    all the solutions can be described as this:

    1.) the South Pole
    2.) the union of concentric circles with the center at the North Pole and the radius r = ( 1 / 2 * pi * n ) + 1 where n is 1, 2, 3, ...
  14. Joined
    12 Mar '03
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    37858
    07 Apr '08 17:33
    Originally posted by 3v1l5w1n
    quite close, actually i think you just forgot to devide by pi ... so

    all the solutions can be described as this:

    1.) the South Pole
    2.) the union of concentric circles with the center at the North Pole and the radius r = ( 1 / 2 * pi * n ) + 1 where n is 1, 2, 3, ...
    Why would I have to divide the perimeter by pi to find the perimeter?
  15. Joined
    15 Feb '07
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    667
    07 Apr '08 21:29
    If the circumference at the longitude 1 km to the north from your starting point is of the form 1/k km, where k is an integer, then taking the path of 1 km North, 1 km West, and 1 km South will bring you back to your starting point. (You'll be in the same place bofore and after the second km travelled.)

    I'm sure someone has given the formula for finding these longitudes.
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