Results 1 to 6 of 6

Math Help - Number of ways of traversing a square

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    95

    Number of ways of traversing a square

    Hi, in how many ways can one travel from corner(0,0) to (a,a) for a square of side a?
    Is there any general formula to it?
    E.g for a = 2, number of ways = 6 ; for a =3 , its 20
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    What are the rules for "traveling"? Do you have to stay on the perimeter of the square? Or can you go straight through it? Or stay on the outside?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2010
    Posts
    95
    sorry for the lack of info.
    One can move either one step up or one step right at each move.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    This link might be useful. Are you doing problems in taxicab geometry?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1
    Quote Originally Posted by pranay View Post
    Hi, in how many ways can one travel from corner(0,0) to (a,a) for a square of side a?
    Is there any general formula to it?
    Yes. It is \dfrac{(2a)!}{(a!)^2}
    Think of a r'a and a u's. We move right a places and up a places.
    The formula I gave is number of ways to arrange a string if a r'a and a u's.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Nov 2010
    Posts
    95
    Thank you all
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Number of ways.
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: May 31st 2010, 08:45 AM
  2. Number of Ways
    Posted in the Algebra Forum
    Replies: 6
    Last Post: May 13th 2010, 11:37 PM
  3. Replies: 4
    Last Post: April 10th 2009, 02:03 PM
  4. Replies: 10
    Last Post: April 8th 2009, 11:56 AM
  5. number of ways
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: May 6th 2008, 06:52 AM

Search Tags


/mathhelpforum @mathhelpforum