F is the father of I. I is the brother of G. W is the father of Z. Z is the…

Concept

In a blood-relation chain every statement fixes two things: the generation gap between the two people, and often the gender of one of them. A statement of the form “X is the father of Y” makes X male and places X one generation above Y; “P is the son of Q” makes P male and Q a parent of P. When two different people are named as parents of the same person and one of them is explicitly the father, the other must be the mother — that is how an unstated gender gets fixed. The required relation is then read off by composing the links along a single path.

Applying it here

1. F is the father of I: F is male and stands one generation above I.

2. I is the brother of G: G is a sibling of I, so G is also a child of F and stands in the same generation as I.

3. W is the father of Z: W is the male parent of Z.

4. Z is the son of G: Z is male and G is a parent of Z.

5. Z therefore has two named parents, W and G. The father's place is already occupied by W, so G must be Z's mother. G is female, that is, a daughter of F.

6. Composing the path gives F to his daughter G to her son Z, so Z is the son of F's daughter.

Cross-check

• F and Z are separated by two generations, so a same-generation relation such as brother, or an upward relation such as father, cannot describe Z.

• Z's link to F runs entirely through birth (F to G to Z) and not through marriage; the person joined to F's family by marriage here is W, who married F's daughter.

• Reading the chain in reverse confirms it: G, Z's mother, is F's child, so F is Z's maternal grandfather, and the reciprocal of maternal grandfather is daughter's son.

Hence Z is F's daughter's son.