A boy and a girl are playing in a park. The only daughter of the maternal grandfather of the girl is the sister of the boy's father. How is the boy related to the girl?

Introduction / Context:
This final blood relation question links a boy and a girl through the girl's maternal grandfather and the boy's father. You are told that the only daughter of the girl's maternal grandfather is also the sister of the boy's father. You must use this information to determine how the boy and the girl are related, choosing among options like father, son, cousin and so on.

Given Data / Assumptions:

• The girl has a maternal grandfather; this is her mother's father.
• The only daughter of this maternal grandfather is the girl's mother, since maternal refers to the mother's side.
• This same daughter (the girl's mother) is also the sister of the boy's father.
• The sister of the boy's father is the boy's paternal aunt.
• We assume standard family structures without additional hidden relations.

Concept / Approach:
The only daughter of the girl's maternal grandfather must be the girl's mother. When the question says that this daughter is the sister of the boy's father, it places the girl's mother and the boy's father as siblings. Therefore, the boy's father is the girl's maternal uncle, and the boy is the child of her maternal uncle. The child of one's maternal uncle is one's cousin, so the boy is related to the girl as her cousin.

Step-by-Step Solution:
Step 1: Let the girl's maternal grandfather be GF. He is the father of the girl's mother.Step 2: Because the only daughter of GF is the girl's mother, she is his sole daughter.Step 3: The problem states that this same daughter is the sister of the boy's father. So the boy's father and the girl's mother are siblings.Step 4: If the boy's father is the brother of the girl's mother, he is the girl's maternal uncle.Step 5: The boy is the son of that maternal uncle.Step 6: The child of one's maternal uncle is one's cousin, so the boy is the girl's cousin.

Verification / Alternative check:
Visualise the family: GF has a daughter M (the girl's mother) and a son S (the boy's father). M has a daughter G (the girl). S has a son B (the boy). The relationship between G and B is that they share the same grandparents (GF and his wife), and their parents M and S are siblings. This is exactly the definition of cousins. There is no way to interpret the description so that the boy becomes the girl's father, son or grandfather while still keeping the statement about maternal grandfather and only daughter intact.

Why Other Options Are Wrong:
Father would require the boy to be in a generation above the girl, which is not suggested anywhere.Grandfather is even further off in terms of generational distance.Son would require the girl to be the boy's mother, which contradicts the cross-cousin structure.Brother would need them to share the same parents, but here their parents are siblings, not the same person.

Common Pitfalls:
A frequent mistake is to misinterpret only daughter and think the described daughter belongs to some other part of the tree, or to misread maternal grandfather as paternal, which would place the relationships on the wrong side of the family. Carefully anchoring maternal to the girl's mother's father and then following the brother sister relation step helps avoid these errors.

Final Answer:
The boy is related to the girl as her Cousin.