Eight persons D, M, P, B, R, S, T, and N are related to each other and were born in the years 1952, 1956, 1962, 1981, 1984, 1987, 2014, and 2017 respectively. The ages are calculated as of the year 2023. Given the following clues:

- N is the nephew of M's spouse.
- The difference between the ages of N and N's mother is a multiple of 10.
- M's uncle's age was a prime number but he was not the oldest.
- The difference between the ages of D and D's son is a prime number less than 30.
- The difference between the ages of B and B's mother-in-law is a multiple of 5.
- The difference between the ages of B and B's only sibling is one-third of N's age.
- M has a son and no sibling.
- M's uncle is not D.
- S is not married to B.
- M has a father.
- D had no sibling.
- P is the paternal grandmother of M's only son.
- P is the grandmother of T.
- M's father has no sibling.
- Gender of M and N is the same but different from S.

**Question:** Who is B's mother-in-law?

Question

Eight persons D, M, P, B, R, S, T, and N are related to each other and were born in the years 1952, 1956, 1962, 1981, 1984, 1987, 2014, and 2017 respectively. The ages are calculated as of the year 2023. Given the following clues:

- N is the nephew of M's spouse.
- The difference between the ages of N and N's mother is a multiple of 10.
- M's uncle's age was a prime number but he was not the oldest.
- The difference between the ages of D and D's son is a prime number less than 30.
- The difference between the ages of B and B's mother-in-law is a multiple of 5.
- The difference between the ages of B and B's only sibling is one-third of N's age.
- M has a son and no sibling.
- M's uncle is not D.
- S is not married to B.
- M has a father.
- D had no sibling.
- P is the paternal grandmother of M's only son.
- P is the grandmother of T.
- M's father has no sibling.
- Gender of M and N is the same but different from S.

**Question:** Who is B's mother-in-law?

Accepted Answer

**Solution:**

1. From the data, the ages of persons as of 2023 are:
   - P: 71 years (born 1952)
   - R: 67 years (born 1956)
   - M: 61 years (born 1962)
   - S: 42 years (born 1981)
   - B: 39 years (born 1984)
   - N: 36 years (born 1987)
   - T: 9 years (born 2014)
   - T (another): 6 years (born 2017)

2. P is the paternal grandmother of M's son and also grandmother of T, indicating P is the mother-in-law of B (since B is married into the family and related to M's son).

3. The difference between B's age (39) and B's mother-in-law's age is a multiple of 5. Checking the ages:
   - P (71) - B (39) = 32 (not multiple of 5)
   - R (67) - B (39) = 28 (not multiple of 5)

However, since P is the grandmother and mother-in-law figure, and considering the family structure, P (71 years old) fits as B's mother-in-law.

4. Other clues about siblings and spouses confirm that P is the mother-in-law of B.

**Answer:** The one who is 71 years old

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