Thanks so much for all your helpful advice
But I think some of you might have misunderstood. I'm not asking for 18 different letters, but one generic letter for 18 different programs. All programs use online application systems. I know 18 sounds insane, even to myself...But it's common here. Even so every year one or two students in my department don't get any offer at all.
Two weeks ago I have sent the professor a list of programs I planned to apply for. I also asked her if she mind my applying for so many. But she didn't reply...
Anyway, I think I might just as well let her upload the 13 letters due on December 15th, and find another professor for the rest.