Thoughts on Little Lamplight
If there were only 82 original kids, all the adults were dead within months of the apocalypse, and they were kicking out the 16 year olds by the end of that first year...
How in the hell are there any kids in 2277 when I stumble in?
Bare minimum, you need 40/40 male/female to sustain the population for 200 years, and all 40 females must successfully give birth at least once a year for the first five years. Then the female offspring need to wait until they're about 35 years old before they have the next batch of kids; and let's just conveniently ignore the lack of appropriate medical supplies and skills, and the fact that everyone is living in a cave, post-nuclear winter...
