Pointing to a man, a woman said, "His mother is the daughter of my mother's only daughter." How is the man related to that woman?

Introduction / Context:

This blood-relation puzzle features a woman describing a man using a chain of relationships that runs through "my mother's only daughter". The key is to interpret who that "only daughter" is and then work downwards through "her daughter" to reach the man. Once we know the generational positions, we can name the relationship correctly.

Given Data / Assumptions:

• A woman is speaking about a man.
• She says: "His mother is the daughter of my mother's only daughter."
• "My mother's only daughter" refers to a single female child of the woman's mother.
• We assume standard family structure and that the speaker herself is that only daughter.
• We need the relation of the man to the woman.

Concept / Approach:

The structure of the phrase suggests that the speaker is the unique daughter of her mother. Then, the daughter of that "only daughter" is the speaker's own daughter. Finally, the man being described is the child of this daughter. That places the man two generations below the speaker. We then choose the correct kinship term for a male two generations down: grandson.

Step-by-Step Solution:

Verification / Alternative check:

We can give the people simple labels: Let the speaker be W, her mother be M, W's daughter be D, and the man in question be X. Then the mother M has exactly one daughter, W. The daughter of W is D. The statement says X's mother is D, which makes X the son of D. From W's point of view, D is her daughter and X is her daughter's son, making X her grandson. This matches the reasoning.

Why Other Options Are Wrong:

He cannot be the woman's direct son, because he is explicitly stated to be the child of the woman's daughter, implying one extra generation.

He is not her brother, as brothers share parents; here the man is a descendant, not a sibling.

He is not her father; that would reverse the generational direction.

Common Pitfalls:

A frequent confusion arises when students misinterpret "my mother's only daughter" as someone other than the speaker, or mistakenly think it might refer to the speaker's sister. The word "only" means there is exactly one daughter, and that must be the speaker herself. Always pay attention to such uniqueness words ("only", "single", "just one"), as they greatly simplify the chain of reasoning.

Final Answer:

The man is the woman's grandson.