A girl introduced a boy as the son of the daughter of the father of her uncle.…

Concept

Relation-chain puzzles often leave the SIDE of a relative (paternal or maternal) unspecified — e.g. 'uncle' could be either parent's brother. Resolve that kind of ambiguity with two rules together: (1) since this is a single-answer puzzle, the reading that matches an actually offered choice is the intended one — a reading that can only ever land on a relation not in the option list is discarded; (2) among the readings that survive rule 1, the standard convention is to assume no additional unstated relatives — each remaining phrase names the person already required to connect the chain back to the querent, not a hypothetical extra sibling. Apply the general definitions — 'father of X' is X's parent, 'daughter of Y' is Y's female child, 'son of Z' is Z's male child — and sketch a small family tree as you trace the chain.

Step-by-step application

1. Let U = the girl's uncle; in principle U could be her father's brother or her mother's brother.

2. If U is the girl's PATERNAL uncle, “the father of U” is her paternal grandfather, and “his daughter” can only be U's sister — the girl's father's sister, i.e. an aunt (never the girl's mother, since the mother married into that family and isn't the paternal grandfather's own daughter). That aunt's son would be a cousin, a relation that isn't among the offered options — so by rule 1 this reading is discarded.

3. So U must be the girl's MATERNAL uncle. “The father of U” = the girl's maternal grandfather, F.

4. “The daughter of F” is a sister of U — either the girl's own mother, or a different sister of U (a maternal aunt). By rule 2 (no extra unstated relative), this daughter is the one already required to connect the chain back to the girl: her own mother, M.

5. “The son of the daughter of F” = M's son, i.e. the girl's mother's son.

6. A mother's son, being a person distinct from the girl, is the girl's brother.

Cross-check

Checking in reverse: the boy is F's grandson through his mother M; M is F's daughter and a sibling of the maternal uncle U — exactly the family tree the given diagram shows. Both decision points are load-bearing: taking U as the paternal uncle, or taking F's daughter as a different maternal aunt, would each land on a 'cousin' relation that has no matching option — only the fully maternal, direct-lineage reading lands on an offered choice, which is why the standard, published resolution of this well-known puzzle gives 'brother'.

Visual family tree