The problem is as follows:
At Emily's birthday, Charlie counted the number of all the women who participated on the celebration. He found there were only three mothers, three daughters, two grandmothers, two grand daughters, one great grandmother and one great grand daughter. What is the least number of women in Emily's birthday?
I'm not sure if this is any trick in problem other than just gender, but what I did was what I felt obvious, to pick one from each group.
Hence:
$\textrm{Mother = 1}$
$\textrm{Daughter = 1}$
$\textrm{Grandmother = 1}$
$\textrm{Granddaughter = 1}$
$\textrm{Great grandmother = 1}$
$\textrm{Great granddaughter = 1}$
Thus the sum is $6$ for the least number, but Is this the right interpretation or I ignored some details?.
The answer is at least $4$ women. Imagine than $A$,$B$,$C$,$D$ are $4$ distinct women. $A\rightarrow B$ means A is the mother of B.
Consider, $A\rightarrow B\rightarrow C\rightarrow D$
A is a great grand mother; A,B are grand mothers; A,B,C are mothers.
The daughter relation is the
reflectionof the mother relation so you do not even need to check for the daughters.Indeed if you order the information you have from great grand mother to great grand daughter you can see the symmetry of the problem.
Generalization:
Consider you have $1$ predecessor of degree $k$ and $2$ predecessors of degree $k-1$, $\dots$, $k$ predecessors of degree $1$
Well, it is exactly the same as considering that you have $1$ successor of degree $k$ and $2$ successors of degree $k-1$, $\dots$, $k$ successors of degree $1$.
The least number of person you need is k persons all recursively related to each other.