There is a myth that I heard from some residents as I was going through the application process. They said that as long as you go to 8 interviews, statistically, you will get into one of the program. I know this is probably garbage, but take it for what it's worth.
I applied to 24 programs, recieved 10 invites (technically 11..........long story), went to 7, and ranked 6. Most of the people from my school also did 20+ programs and 75% of them got into a program. A lot of people I met on the interview circuit mentioned that they applied to around 15 or so programs. I applied to more programs cuz wanted to stay on the safe side.....it's a good thing I did since 4 programs that I was sure to recieve interviews from dropped me faster than bad ****.