Explanation
To solve this, we need to break down the information step-by-step.
Step 1: Find all combinations of three numbers whose product is 36.
Let the ages be x,y,z. We are looking for triples where x⋅y⋅z=36.
| Ages (x, y, z) |
Sum (x+y+z) |
| 1, 1, 36 |
38 |
| 1, 2, 18 |
21 |
| 1, 3, 12 |
16 |
| 1, 4, 9 |
14 |
| 1, 6, 6 |
13 |
| 2, 2, 9 |
13 |
| 2, 3, 6 |
11 |
| 3, 3, 4 |
10 |
Step 2: Use the "Sum" information.
The second man knows the house address (the sum). If knowing the sum wasn't enough to give him the answer, it means there must be more than one combination with the same sum.
Looking at our table, there are two sets of ages that sum to 13:
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1, 6, 6 (Sum = 13)
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2, 2, 9 (Sum = 13)
Step 3: Use the "Oldest Daughter" clue.
The first man says, "My oldest daughter wears a red dress." This implies there is a single oldest daughter.
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In the combination (1, 6, 6), the oldest daughters are twins (age 6). There is no single "oldest" daughter.
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In the combination (2, 2, 9), there is a clear oldest daughter who is 9 years old.
Therefore, the ages of the daughters are 2, 2, and 9.
Final Answer:
The age of the oldest daughter is 9.
Correct Option: (a) 9
