Answer
Susan needs at least 7 plates.
Why?
- The grandfather is also a father and a father-in-law.
- The grandmother is also a mother and a mother-in-law.
- The father is also his parents’ son (and child).
- The daughter-in-law is also a mother.
- The grandson is also a brother and his parents’ son (and child).
- The two granddaughters are also sisters and their parents’ daughters (and children).
So we have
- one grandfather
- one grandmother
- two fathers (grandfather, father)
- two mothers (grandmother, daughter-in-law)
- four children (father, grandson, 2 granddaughters)
- three grandchildren (grandson, 2 granddaughters)
- one brother (grandson)
- two sisters (2 granddaughters)
- two sons (father, grandson)
- one father-in-law (grandfather)
- one mother-in-law (grandmother)
- one daughter-in-law