I was working with the theory that a combination of the idol and a master parent would generate this golden child I've been reading about. (I'm trying not to cheat too much).

I'm down to puzzles 10, and 13-16 left. Since 13 requires the idol, and is the prereq for most of the others, that is how I came to my conclusion.

Am I way off-base?

And just for my $.02 -- where is the logic that states that 15 villagers require 4 huts, and 90 villagers fit in 5?

yah you're offbase I'm afraid

yeah you are pretty far offbase but one of two things you mentioned is needed for the gc though