@Olim-Nagev It's funny you mention that challenge because I have done that, although it was only with computers in a single player game. Doing it in an online automatch would certainly raise the bar. Therefore I will add it to the list!
@Administrator Thank you for your reply. Yes I remember this also with the robber. In the Catan Universe app however if you put a robber on the hex of multiple opponents and select an opponent with no cards you do not get anything from the opponent so this is also a loophole of not robbing the opponent who had cards as it should not give you the option to rob an opponent with no cards and only the ones who have cards if they are on the same hex being robbed. I know that there is the encyclopedia catanica online but it is only in German and I do not trust the translation of my web browser for all these tricky rules.
Secondly the reason I bring up the aqueduct rule is that when playing the baordgame players with aqueduct often forget to pick up their cards if their numbers do not roll whereas the app does not allow the human error to be a factor in the game.
So, from that PDF: Page 7. City Improvements. (right hand column)
"The first improvement in each area always costs 1 commodity of the matching type. The second improvement in each area costs 2 of that commodity. The cost of each subsequent improvement is again increased by 1. "
So, to elaborate, the first city improvement costs 1 commodity. The second 2; third 3; etc. If you have more of the correct and matching commodity (and a city, as stated further in the rules) then you can do as many improvements as you can afford per turn. Example: if I have 6 paper, I can make the first, second and third city improvements for "instants" aquaduct.
I would love to jump over the lower improvements and get a metropolis right away, but alas, we have to pay for it. I hope that helps.