A family of six persons A, B, C, D, E and F has six different professions: Lawyer, Doctor, Teacher, Salesman, Engineer and Accountant. There are two married couples. D, the Salesman, is married to the lady who is the Teacher. The Doctor is married to the Lawyer. F, the Accountant, is the son of B and brother of E. C, the Lawyer, is the daughter-in-law of A. E is the unmarried Engineer. A is the grandmother of F. What is the profession of A?

Introduction / Context:
This is a classic logical reasoning and blood relation puzzle combined with assignment of professions. You must track who is married to whom, who is the child of whom and which profession belongs to each family member. The goal is to identify A's profession using all clues without violating the conditions about marriages, genders, generations and unique professions.

Given Data / Assumptions:
- Family members: A, B, C, D, E and F. - Professions (all distinct): Lawyer, Doctor, Teacher, Salesman, Engineer, Accountant. - D is the Salesman and is married to the lady who is the Teacher. - The Doctor is married to the Lawyer. - F is the Accountant, son of B and brother of E. - C is the Lawyer and is the daughter-in-law of A. - E is the unmarried Engineer. - A is the grandmother of F. - There are exactly two married couples in total.

Concept / Approach:
The key is to assign professions and relationships step by step, always respecting uniqueness and the marriage structure. Start by fixing obvious ones (Salesman, Engineer, Accountant, Lawyer) and then deduce who must be the Doctor and Teacher. The information that C is the daughter-in-law of A, and that A is grandmother of F, helps you place generations and determine who is married to whom. Once you know which members already have professions, the remaining unchecked profession must belong to A.

Step-by-Step Solution:
Step 1: From the statements, fix some professions immediately: - D is the Salesman. - F is the Accountant. - C is the Lawyer. - E is the Engineer and is unmarried. Step 2: The Doctor is married to the Lawyer. Since C is the Lawyer and is the daughter-in-law of A, C must be married to A's son. Therefore, C's husband is the Doctor and is a child of A. Step 3: Among A, B, D, E, F only B can still be the Doctor, because D, E and F already have fixed professions, and A is the grandmother of F and hence belongs to an older generation. So B is the Doctor and is married to C, the Lawyer. This is one married couple. Step 4: F, the Accountant, is the son of B and brother of E. Since B and C are a couple, F and E are their children. E is unmarried, which fits the data. Step 5: A is the grandmother of F. Therefore, A is the mother (or mother-in-law) of B or of C. But C is already daughter-in-law of A, so A must be the mother of B, placing A one generation above B. Step 6: D, the Salesman, is married to the lady Teacher. All professions except Doctor, Lawyer, Salesman, Engineer and Accountant are taken, leaving only Teacher unassigned. A and D are the only remaining people without professions assigned. Step 7: The Salesman is D, and he is married to the lady Teacher. The only female left without a profession is A. Therefore, A must be the Teacher, and D is A's husband, forming the second married couple.

Verification / Alternative check:
List assignments: A – Teacher, D – Salesman (married couple); B – Doctor, C – Lawyer (married couple); F – Accountant (son of B and C); E – Engineer (unmarried child of B and C). A is the grandmother of F (through her son B), and C is indeed daughter-in-law of A. There are exactly two married couples, and each profession is used once. All conditions are satisfied, confirming that A must be the Teacher.

Why Other Options Are Wrong:
- Lawyer: C is explicitly stated to be the Lawyer. - Doctor: B must be the Doctor to marry C, the Lawyer, so A cannot also be a Doctor. - Engineer: E is already assigned as the unmarried Engineer. - None of these: Since Teacher fits A perfectly and satisfies all clues, this option is incorrect.

Common Pitfalls:
A frequent mistake is to forget that there are exactly two married couples and to try to marry B with someone other than C. Another pitfall is not noticing that C, as daughter-in-law of A, forces B to be A's son and the Doctor. Students also sometimes leave A's profession as ambiguous because she is older, but careful elimination shows Teacher is the only consistent option.

Final Answer:
A's profession is Teacher.