Question

At a family reunion were the following people: one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law. But not as many people attended as it sounds. How many people were there?

• A. 5
• B. 10
• C. 15
• D. 7

Hint:

Most of the roles overlap: one person can be a father, a son, and a son-in-law all at once. Try to build the smallest possible three-generation family that covers every role listed.

Answer 1

The Correct Option is D

Another way to solve this is to sort the family into three generations and check that the role list needs nothing more than a small family spanning those three generations.

1. Generation 1 (grandparents): one grandfather and one grandmother. Since their son is married, the grandfather automatically becomes a father-in-law and the grandmother automatically becomes a mother-in-law to the son's wife, with no extra people needed.
2. Generation 2 (parents): the grandparents' son and his wife. The son is a father to his own children and a son to his parents, filling one "father" role and one "son" role at once. His wife is a mother to her children and a daughter-in-law to his parents, filling one "mother" role and the "daughter-in-law" role at once.
3. Generation 3 (children): one son and two daughters born to the couple in generation 2. The son is a brother to his sisters and the second "son" in the list. The two daughters are sisters to their brother and the two "daughters" in the list. Together, these three are also the three grandchildren of generation 1.

Every phrase in the question now has an owner: two fathers (generation 1's father and generation 2's father), two mothers (generation 1's mother and generation 2's mother), four children (the generation 2 son counts as a child of generation 1, plus the three generation 3 kids), three grandchildren (generation 3), one brother and two sisters (generation 3), two sons and two daughters (spread across generations 2 and 3), and one father-in-law, one mother-in-law, one daughter-in-law (generation 1 paired with generation 2's wife).

Let's summarize:

• Three generations are enough: 2 grandparents, 2 parents, and 3 children.
• Every role in the long list is one of these 7 people viewed from a different relationship.

So exactly 7 people attended the reunion.