Detect Numbers In A Cell Range And Then Change Cells Based On What Numbers Are Found?

I'm going to be using a spreadsheet to keep track of where different people are at. So if Person 1 is in Room 3, I will stick a 3 in the box next to their name and then can look at the spreadsheet whenever I need and see what room they are in. When I'm deciding what room to put a person in, though, I need to be able to quickly glance at a list of Room #'s and see what one's are still available. So I have a bank of Room #'s in the spreadsheet....1,2,3, etc.

What I'd like, is some way to set this up so that when I put, for example, "3" in the cell next to "Person 1" the spreadsheet automatically removes "3" from the bank of available Room #'s and when I delete the "3" because the person has left, it adds "3" back to the bank of available Rooms.