what happens after all 16 puzzles are solved?
how come when i put them in the cave it just says that someone may be in there....cant they go through it?

They cannot go through the cave (yet, maybe in a sequel!). Once you finish the 16 puzzles, that particular game is done. You can start another one, try a harder game if you played on easy or normal, or just watch your villagers for a while. They do so many amazing things.

I never deleted my first game ever. Just keep checking in on them and watching them while trying to complete harder newer games.

yeah, I was wondering the same thing ! is that the end of the game?

There has been a lot of good discussion about that topic in the forums. Here are links to some of the threads:

look here
and here
and here
and here