Here is a puzzle about combinatorics.

Suppose you have a square grid with $n^2$ points. You want to go from the origin $(0, 0)$ to $(n-1, n-1)$. Assuming you can only go right or up, in how many ways can you reach destination?

-
Now that you know how to deal with squares, generalize. In how many ways can you get from $(0,0)$ to $(6,10)$ only going right or up, if you must follow grid lines? – André Nicolas Jun 15 '11 at 22:18
Are you restricted to moving one unit at a time or can you go directly to any point that is right and/or up from the current one? – Mitch Jun 16 '11 at 15:29

Hint: Since you can move either right or up at each step, you can encode a path from $(0,0)$ to $(n-1,n-1)$ using a sequence of letters R and U. For example, if you have a $4 \times 4$ grid, a sequence R,U,R,U,R,U will take you from $(0,0)$ to $(3,3)$. Now try and generalize to the $n \times n$ grid and count the number of possible strings.