Something not identical but similar happened to me (and my mom, and my brother): the last of my milk teeth was happy to stay where it was, and finally it had to be extracted, complete with roots. It took some two years for the adult tooth to emerge.
As a kid I always agreed with Calvin: " I have to say, I’m not entirely comfortable holding a piece of my own head."
TheKid was bummed that other kids received little plastic treasure chests for their extracted teeth, but hers were too long to fit. They came home in a plastic baggie.
Likewise; of my first molars, three of the four never came in as adult teeth. Since the primary teeth are actually larger than the adult teeth, it was causing crowding in my mouth. My dentist pulled all four (including the one unoffending adult molar) when I was 13, and I then wore braces for two years – to both straighten the crooked teeth, and to pull the remaining molars (all of which were adult teeth) “up” one space.
Im 16, and I was extremely worried a year ago when I realised many of my younger molars hadn’t fallen out. I had an x-ray, and it showed that all my teeth were infact adult teeth. Therefore, 8 of my teeth have never fallen out. It is possible that I never had milk teeth in these areas, so you may have the same problem as me 
This site suggests its possible, though it does not explicitly say all permanent teeth.
There’s even a term for it: hypodontia
What’s cool are third sets of teeth.
Yeah, you can take them out and put them in a glass at night.
How did you know your molars hadn’t fallen out? I mean, were you keeping track of which ones fell out? I don’t think I had any idea, even back at 16, what teeth I had and hadn’t lost.
Makes visits to the dentist so easy, too - just hand him your teeth and leave. 