Question

A saleswoman knocks on an apartment door and a man answers. They have the following conversation:

Saleswoman: Hello sir, how many children do you have and what are their ages?
Man: I have three daughters and I will give you a hint to help you figure out how old they are; if you multiply my three daughters' ages, you will get 36.
Saleswoman: That is not enough information!
Man: Well, if you add up my daughters' ages, the sum is the number of my next-door neighbor's apartment.
Saleswoman (after looking at the number on the front door of the next apartment): That is still not enough information!
Man: The last hint I will give you is that my oldest daughter has green eyes.
What are the ages of the man's three daughters?
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Answer 1

By considering the multiplication and sum of the ages along with the final hint about the eldest daughter's distinct age, we deduce that the ages of the man's daughters are 2, 2, and 9 years old.

Step-by-step explanation:

The ages of the man's three daughters can be determined by using the hints he gave.

First, we know that the product of their ages is 36. The possible combinations of ages for the daughters that multiply to 36 are (1, 1, 36), (1, 2, 18), (1, 3, 12), (1, 4, 9), (1, 6, 6), (2, 2, 9), (2, 3, 6), and (3, 3, 4).

Next, the sum of their ages is the same as the neighbor's apartment number, but since that information didn't help the saleswoman, it means there must be more than one combination with the same sum.

Looking at the combinations, we find that only (1, 6, 6) and (2, 2, 9) add up to the same sum which is 13.

The final hint is about the eldest daughter's green eyes. This information suggests there's a distinct oldest daughter, so the combination (1, 6, 6) is not possible because it has no unique eldest daughter as the ages 6 and 6 are the same. Therefore, the daughters' ages must be (2, 2, 9), with the 9-year-old being the eldest with green eyes.