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Number of ways to go to the opposite corner.

  1. Jun 20, 2011 #1

    ssd

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    # of ways to go to the opposite corner.

    Suppose m+1 parallel (laid N-S)roads cross n+1 parallel (laid E-W) roads. In how many different ways one can move from North- East corner (of crossing) to South- West corner heading either West or South? What the simplest / attractive way (explanation) to make students of age 17yr understand while teaching in class. I observed, students really do not get the logic.
     
    Last edited: Jun 20, 2011
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  3. Jun 20, 2011 #2

    Hurkyl

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    Re: # of ways to go to the opposite corner.

    The usual way to do this is to write paths as words in the letters "S" and "W", and count how many of those words correspond to a path from one corner to another, right?

    I imagine the best way would be to make them understand the bijection. Exercises converting from words to paths and back. Have them think about which words correspond to a path from corner to corner.
     
  4. Jun 21, 2011 #3

    ssd

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    Re: # of ways to go to the opposite corner.

    Nice.
     
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