Largest age difference between great-great-...-grandparents? If I go up $n$ generations, with some assumptions, I will have exactly $2^n$ ancestors of different ages. For simplicity, I'll call these ancestors my $n$-parents. Let $A_n$ be the difference between the maximum and minimum ages of my $n$-parents.
For instance, suppose I have parents aged 56 and 53. Then $A_1 = 3$. If I have grandparents aged $82,84,79$ and $80$, $A_2 = 84-79 = 5$.
Now suppose the age of your parent at your birth is a random variable $X$ with mean $\mu$ and standard deviation $\sigma$. Then $E[A_1] = |X_M-X_F| = \max(X_M,X_F)-\min(X_M,X_F)$, where $X_M$ is the age of the mother and $X_F$ is the age of the father. For $n=2$, we have 
$$E[A_2] = \max(X_{MM}, X_{MF},X_{FM}, X_{FF})-\min(X_{MM}, X_{MF},X_{FM}, X_{FF})$$
where $X_{MM} = X_M^{(2)} + X_M$ and so on. I think $X_{Z}$ where $Z$ is a string of length $n$ is a normal distribution with mean $n\mu$ and variance $m \sigma^2$ so the problem simplifies to computing the expected value of 
$$\max(Y_1, \dots, Y_{2^n})-\min(Y_1, \dots, Y_{2^n}) $$
with $Y_i$ I.I.D., mean $n \mu$, variance $n \sigma^2$. I'm not positive about this, though.
How should $E[A_n]$ be computed? I'm not sure how to approach this in a way that isn't tedious. This is my own question where I'm basically wondering how many "generations" back it would take for great-grandparents (etc) to not really be in the same generation say with $\mu=30$ and $\sigma = 8$.
 A: My simulation suggests that $A_3$ has mean about $4.25\sigma$ and standard deviation about $1.75\sigma$. (I didn’t look to see if it’s normally distributed.) $A_{10}$ has mean about $18.1\sigma$ and standard deviation about $2.25\sigma$.
So for $\mu=30$ and $\sigma=8$, the maximum age difference between great-grandparents, $A_3$ is typically 34 years.
Here’s my Mathematica code to generate 5000 sets of ancestors 10 generations back and give the mean and standard deviation of the maximum age difference within each set.
I use $1$ for the standard deviation; $A_i$ appears to scale linearly with $\sigma$, and it was easiest to see the multiple for a given $i$.
    Clear[Ancestors];
    generations := 10;
    greatgreats :=
    Module[
      {Ancestors},
      Ancestors[0]={0};
      Ancestors[n_]:=
      Ancestors[n]=
      Flatten[Function[x,RandomVariate[NormalDistribution[30+x,1],2]]
        /@Ancestors[n-1]];
      Ancestors[generations]]
    results=Table[Max[greatgreats]-Min[greatgreats],{i,1,5000}];
    Mean[results]
    StandardDeviation[results]

