In a certain code language, ‘A ÷ B’ means ‘A is the sister of B’, ‘A # B’…

Concept:

In coded blood-relation puzzles, each symbol stands for one direct family relation (parent-of, sibling-of, spouse-of). To find how one person relates to another placed several links away, decode every symbol in the chain one link at a time, then combine the direct relations using standard family rules: siblings share the same parents, and a person's spouse holds the same parental relation to that person's children.

Application:

1. Decode each symbol used in ‘A + B % G ÷ H # K’: ‘+’ = wife of, ‘%’ = father of, ‘÷’ = sister of, ‘#’ = brother of.

2. A + B → A is the wife of B.

3. B % G → B is the father of G.

4. G ÷ H → G is the sister of H, so G and H share the same parents.

5. Since B is the father of G, and H shares G's parents, B is also the father of H.

6. H # K → H is the brother of K, so H and K share the same parents.

7. Since B is the father of H, and K shares H's parents, B is also the father of K.

8. A is the wife of B, and B is the father of K, so A is the mother of K.

Cross-check:

Retracing the chain independently: A's own generation is fixed only by the '+' (wife-of) link to B, so A and B belong to one generation. Every later step (the '%' link to G, then the shared-sibling steps to H and K) stays inside B's child generation. So G, H, and K are all one generation below A and B, and A's relation to any of them, including K, is that of mother.