# Math Help - Number of ways of traversing a square

1. ## 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

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?

3. sorry for the lack of info.
One can move either one step up or one step right at each move.

4. This link might be useful. Are you doing problems in taxicab geometry?

5. 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.

6. Thank you all