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Possibility question; isn't the answer 2?

  1. Oct 3, 2013 #1
    So I'm doing some math stuff on this internet website for fun, aplusclick. Anyway, there was this question on the site:

    "A boy begins walking from his starting point. Each hour, he either walks one kilometer to the east or one kilometer to the north, but he never walks in the same direction.

    In how many different ways can he get to a point that is 8 kilometers to the north and 8 kilometers to the east of his starting point?"

    The answer is 2^8, or 256. But shouldn't it be 2?

    He can either start by going east, then north, then east - until his displacement is 8 km N, 8 km E
    or he can start by going north, then east, then north, etc

    So shouldn't it be 2? Can someone break this down for me if I am wrong?
  2. jcsd
  3. Oct 4, 2013 #2

    Simon Bridge

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    You are correct - the question is poorly worded: what question does the answer belong to?
  4. Oct 4, 2013 #3


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    Yeah, for the answer to be 256, you have to remove the restriction that he never walks the same way for two consecutive 1KM legs.
  5. Oct 4, 2013 #4
    But then the answer is 16!/(8!8!) =12870
  6. Oct 4, 2013 #5


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    To get 256, he has to walk for 8 hours, without a restriction on walking directions.

    An alternative interpretation: He never deviates more than 1km north or east from the direct (diagonal) path, so the difference between "hours moved north" and "hours moved east" is at least -1 and at most 1. That would give 256 as well.
  7. Oct 10, 2013 #6

    Simon Bridge

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    You know, most people would have responded to the question as x86 did and leave it at that.
    I sometimes wonder if we, who go explore things like which question the answer belongs to are just plain weird.
    Mind you - it more fun this way :)
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