There is a group of $20$ children and a group of $n$ grandparents to these children. Each of these grandparents is either father's father or mother's father to at least one of these children. Now, following constraints are given:
- Each pair of children has at least one grandparent in common who is also present in this group of grandparents.
- Every grandparent has at least two grandchildren in this group of children.
Find upper bound on $n$, the number of grandparents present in the group such that above constraints can be satisfied.
"is either father's father or mother's father to at least one of these children" -> this means we are talking only about grandfathers.
See this answer.
In short each child can have max 2 grandfathers and the upper bound for n is 3 in order for the first constraint to be satisfied.