What is the linguistic purpose of 'one' as an adjective preceding a noun?

For example, I have heard people say 'remember when we saw that one guy?', or 'my one exam just got postponed'. Is it a form of hedging?


Solution 1:

'remember when we saw that one guy?'

I interpret this as meaning "unique". For example, suppose we attended an entertainment event and there were ten players and one of them was wearing a bear's head. Later we might say, "Remember when we saw that one guy - the one with the bear's head?"

'my one exam just got postponed'

I interpret this as meaning "one-and-only". I had only one exam and it was postponed.