Earlier quoted context omitted.
I feel for you - those buttons will stop working very well quite soon and trying to enter "12" will get you 1, 2, and finally 12. Check every elevator carefully, ADA regulations sometimes require at least ONE elevator in the building to have real buttons (for the blind, for example).
Sounds like the buttons are all real, there are just only 10 of them.
A hotel I stayed at had touchscreen "requests" for elevators (you put in your floor and it would call a elevator for you) and it was super annoying (trying to get floor 12 would doublebounce on 1 and 2 so you'd often get 11 and 22 before getting 12) until I found a pedestal out of the way that had real buttons for all floors.
The "hold your keycard up against the thing" is also really annoying when it is 5 feet off the ground; imaging having to wait for an elevator until someone comes along who can hold your card up there for you.