Joel introduces Mary as "the daughter of the only son of my father's wife." How is Joel related to Mary?

Introduction / Context:

This is a compact blood-relation puzzle focusing on phrases like "my father's wife" and "only son". Such phrases are commonly used in reasoning questions to indirectly refer to the speaker himself. Once we recognize that the "only son" being described is Joel, the relationship between Joel and Mary is straightforward.

Given Data / Assumptions:

• Joel is speaking.
• He says: "Mary is the daughter of the only son of my father's wife."
• "My father's wife" is Joel's mother (assuming one marriage).
• "The only son of my father's wife" refers to a single male child of Joel's mother.
• We assume standard monogamous family and no step-children unless stated.

Concept / Approach:

We first replace "my father's wife" with "my mother". Then "the only son of my mother" must be Joel himself, since he is speaking and no other sons are mentioned. Mary is then the daughter of that only son. Once this substitution is done, we can express Joel's relation to Mary in a single word: he is her father.

Step-by-Step Solution:

Verification / Alternative check:

Let M be Joel's mother. If M has one son, J (Joel), and J has a daughter Mary, then Mary is naturally "the daughter of the only son of my father's wife" when Joel speaks. This is consistent and does not require any additional assumptions. Thus, the relationship of Joel to Mary is clearly that of father and daughter.

Why Other Options Are Wrong:

Joel cannot be Mary's brother, because Mary is explicitly a child of the only son, not a sibling of the only son.

He cannot be her son or daughter, as that would invert the generational direction indicated by the phrase "her father's wife's only son".

Common Pitfalls:

Many learners initially treat "my father's wife" as a new person instead of recognizing that, in a typical family, it is simply the speaker's mother. Additionally, they might overlook the word "only", which uniquely identifies Joel as the son being discussed. Always simplify nested phrases by replacing them with simpler equivalents and then re-reading the sentence.

Final Answer:

Joel is Mary's father.