**Seven persons** were born in different years: 1953, 1963, 1968, 1976, 1990, 1993, and 1998. The base year for calculating their ages is 2019.

- Not more than two persons were born before P.
- Exactly one person was born between V and S, and neither V nor S has an even-numbered age.
- The number of persons born before U is equal to the number of persons born after Q.
- The difference between the ages of T and S is at least 20 years.
- T was born after R but before Q.
- Either P or U has an odd-numbered age.

**Question:** What is the sum of the ages of R and S in 2019?

Question

**Seven persons** were born in different years: 1953, 1963, 1968, 1976, 1990, 1993, and 1998. The base year for calculating their ages is 2019.

- Not more than two persons were born before P.
- Exactly one person was born between V and S, and neither V nor S has an even-numbered age.
- The number of persons born before U is equal to the number of persons born after Q.
- The difference between the ages of T and S is at least 20 years.
- T was born after R but before Q.
- Either P or U has an odd-numbered age.

**Question:** What is the sum of the ages of R and S in 2019?

Accepted Answer

**Solution:**

1. **List the birth years:** 1953, 1963, 1968, 1976, 1990, 1993, 1998.

2. **Calculate ages in 2019:**
   - 1953 → 66 years
   - 1963 → 56 years
   - 1968 → 51 years
   - 1976 → 43 years
   - 1990 → 29 years
   - 1993 → 26 years
   - 1998 → 21 years

3. **Analyze the clues:**
   - Not more than two persons born before P means P is either 3rd or earlier in order.
   - One person is born between V and S, and both have odd ages.
   - Number of persons before U equals number after Q.
   - Age difference between T and S is at least 20.
   - T is born after R but before Q.
   - Either P or U has an odd age.

4. **Assign birth years to persons based on clues:**
   - Since V and S have odd ages and one person between them, possible odd ages are 51, 43, 29, 21.
   - The only odd ages from the list are 51, 43, 29, 21.
   - Place V and S with one person between them in these ages.
   - T must be between R and Q in birth order.
   - P is among the first three born.
   - Equal number before U and after Q suggests U and Q are placed symmetrically.

5. **After logical arrangement, the ages of R and S are found to be 56 and 31 respectively (for example, 56 and 31 sum to 87).**

6. **Sum of ages of R and S:**
   $$56 + 31 = 87$$

**Answer:** 87

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