Pointing to a picture of a girl, Avin said, “She is the daughter of the only…

Concept

In blood-relation puzzles, a phrase such as “the only child of X” identifies a person uniquely. When a speaker describes himself indirectly through his own parent — for example, “the only child of my father” — the person referred to is the speaker himself, because a person with siblings would not describe himself this way. Once an identity is fixed like this, it can be carried forward through the directly stated relations (parent, spouse, child) to reach the person asked about.

Application

1. Avin says “my father,” so the frame of reference is Avin's own father.

2. “The only child of my father” therefore means the only child of Avin's father, which is Avin himself.

3. So “she is the daughter of the only child of my father” becomes “she is the daughter of Avin.”

4. Avin has two daughters, so the girl in the picture is one of Avin's own daughters.

5. By the standard convention used in these puzzles, a person's spouse is treated as the parent of that person's stated children unless the puzzle indicates a remarriage or step-relation — none is indicated here, so Avin's wife is the mother of that girl.

Cross-check

The family tree confirms this: Avin's father has only one child, Avin himself; Avin and his wife are the parents of two daughters and one son; and the girl in the picture is one of those daughters. This also rules out Niece, Cousin, and Aunt as Avin's wife's relation to the girl: a niece relation would need the girl to belong to a generation above Avin's wife; a cousin relation would need Avin's wife and the girl to be children of siblings; and an aunt relation would need the girl to be the child of a sibling of Avin or of Avin's wife. None of these hold once the only-child clause fixes the girl as Avin's own daughter.

Avin's wife is the Mother of the girl in the picture.