I lived in a building (6 floors) where the elevator appeared to be always in one of four states: Door opened, going to floor n, waiting for input inside elevato

I lived in a building (6 floors) where the elevator appeared to be always in one of four states: Door opened, going to floor n, waiting for input inside elevator, waiting for input from anybody. It only remembers a single floor - where it's going now. Once it goes into the input state, it's a race among everybody who wants to take the elevator to push the buttons. I was never quite sure whether the 'waiting for input inside elevator' actually existed, because every once in a while the elevator would get summoned by someone else before I could give it a destination when inside. I guess this is a bit off-topic, it's just to say that even very simple logic can solve the problem, in a possibly infuriating way. ;)