When do colonizers start marrying cousins? Suppose a group of humans, with $n$ males and $n$ females, colonizes another planet.  Suppose they all pair up in the usual way, and each couple has two children--one boy and one girl.  Then the process repeats. 
Question: How many generations can pass before somebody has to marry their cousin?

EDIT: 
To clarify:


*

*Each member of a generation marries someone of the same generation.  

*We assume that the original colonists are all unrelated. 

*Nobody marries their sibling, though if you broaden the definition of "cousin" to include "anybody who shares a common ancestor" then you don't need to make this assumption.  (So in light of the above point, the question can be restated "How many generations can pass before someone marries a relative.")

 A: If no-one marries a relative for the first $k$ generations, then everyone in the next generation will have $2^k$ ancestors from the first generation, which must all be distinct. So we must have $2^k\leq 2n$.
If $2n$ is a power of $2$, say $2n=2^k$ then you can have $k$ iterations without anyone marrying a relative. You start of with $2^k$ family groups of $2^0$ people each; pair off groups and have everyone marry someone from the paired group, resulting in $2^{k-1}$ groups of $2^1$ people each in the next generation. Carry on in this manner, so that after $j$ generations you have $2^{k-j}$ family groups of $2^j$ people each, with different groups being unrelated. (After the first generation, every group has the same number of each sex, so the pairing off can be done ok.)
If $2n$ is not a power of $2$ you will have to work a bit harder to get a construction for $\lfloor\log_2(2n)\rfloor$ generations, but I imagine it's possible.
A: In the first generation, each person has one ancestor of a given sex.  In the second, two, in the third, four.  In the $k^{th}$ generation, $2^k$.  The two who will get married then have to have $2\cdot 2^k=2^{k+1}$ choices for ancestors.  As soon as $2^{k+1} \gt n$ you will have to have someone marry a cousin, which happens when $k \gt \log_2 n -1$
