"Without using an array" generally means "without storing all of the numbers", which means vector is out too. But even if you could store all of the numbers, doing so would be stupid because it's trivial to write a linear algorithm without wasting memory like that.
True enough. I assumed wrongly that it had more to do with setting a specific size of an array, with regards to allocation and things like that. Also, since the program isn't really asking for the set of data but only the largest and smallest out of those entered, it doesn't make sense.
All that's going to happen is they'll hand this in without having much of a clue, so that when next week's homework comes around (say sorting numbers), they're totally screwed (and back asking for more homework).