How many numbers must be selected from the set {1,2,3,4,5,6}to guarantee that at least one pair of these

numbers add up to 7?

The answer ends up involving the fact that, since there are only three subsets--namely, {1,6}, {2,5}, and {3,4}--a person is only required to select four numbers from the set. This is due to the fact that at least two of them must fall within the same subset.

I am very frustrated right now (which is probably why I can't think properly, at the moment); and I am becoming more frustrated because the book gives the impression that it is so simple. I don't understand this--not one bit. Can someone please help me?

EDIT: I am having a lot of difficulty, right now. I seem to be questioning every single thing that I do, and sometimes I can just accept an idea, even the ones that appear to be most intuitive. What's wrong with me? How did I get myself into this sort of mindset?