Hey guys, another one of these crazy probability questions...

Let X and Y be independent, each uniformly distributed on {1, 2, ... , n}.

Find P(X + Y = k) for 2 <= k <= 2n.

This is the last of a series of problems, all of the previous ones which were easily solved by drawing up a grid of possible choices. Is there a way to figure this out WITH OUT a grid?

A gentle shove in the right direction would be helpful! Thanks!