How Old Is Fortinbras?

So I was thinking about Hamlet this morning on the drive in to work (what, doesn’t everybody?)  I realized that there’s a gap in my understanding of the timeline. Maybe I’m missing something obvious, but this is why I have this site, so I can brain dump random Shakespeare thoughts and have people either learn the same things I’m learning, or else correct me where I’m mistaken.

We all should know the basic plot from high school – Hamlet’s father (“Old Hamlet”) defeated Fortinbras’ father (“Old Norway”) years ago in fair combat, and won some lands from him. Young Fortinbras has a problem with this, and eventually invades Denmark by the end of the play.  We also learn from the gravedigger that Hamlet was born on the day that “our last king Hamlet overcame Fortinbras.”

So “the grudge,” for lack of a better term, is as old as Hamlet.  Am I right so far?  That must mean that either:

Fortinbras is younger than Hamlet, and thus was born after the combat, and is avenging a dishonor that is just entirely abstract to him, or,

Fortinbras is older than Hamlet, so then I ask, how much older?  If he’s old enough to remember the combat and to have taken it as a slight to his family honor, he had to be what, ten years old at least?

I might be missing a textual clue that tells me the actual answer.  I was just pondering it in relation to how Hamlet (who is supposed to be thirty, by most interpretations) is still relatively whiny and immature.  So if Fortinbras is ten years older than that, and still being referred to as “young” and of “unimproved mettle hot and full,” that seems a little strange.  How old you gotta be in this world for people to stop calling you young?