I am having trouble with this problem.

A network of city streets forms square bloacks as shown in the diagram below.

ImageShack - Hosting :: librarypoolqs6.jpg

Jeanine leaves the library and walks toward the pool at the same time as Miguel leaves the pools and walks toward the lbrary. Neither person follows a particular route, except that both are always moving toward their destination. What is the probability that they will meet if they both walk at the same rate?

In addition, how would I solve this for a 1 by 1 grid, 2 by 2 grid, 3 by 3 grid,etc.?

I know that you have to use Pascal's Triangle and the answer in the book is 35/128 but I don't know how to get this.