# Number of ways of traversing a square

• Mar 7th 2011, 06:04 AM
pranay
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
• Mar 7th 2011, 06:06 AM
Ackbeet
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?
• Mar 7th 2011, 06:13 AM
pranay
sorry for the lack of info.
One can move either one step up or one step right at each move.
• Mar 7th 2011, 06:22 AM
Ackbeet
This link might be useful. Are you doing problems in taxicab geometry?
• Mar 7th 2011, 06:31 AM
Plato
Quote:

Originally Posted by pranay
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.
• Mar 7th 2011, 06:47 AM
pranay
Thank you all :)