Beth and Lisa, who had been math majors and roommates in college, meet on the st

Question

Beth and Lisa, who had been math majors and roommates in college, meet on the street. Here is part of their conversation:

Beth: You have three daughters? How old are they?
Lisa: The product of their ages is 36.
Beth: That's not enough information.
Lisa: Do you remember our room number at college? The sum of their ages is the same as that room number.
Beth: Of course I remember our room number, but that's still not enough information.
Lisa: My oldest daughter wishes she had a twin sister.
Beth: OK. Now I know their ages.

Is there enough information for Beth to deduce the ages of Lisa's three daughters? If yes, explain how Beth determined the ages, and state what the ages were. If no, explain why not.

So far what I have been thinking is that the only combinations of the three daughters are

4,3,3

6,2,3

2,2,9

these are the only combinations that I could find that there are three of them and they all multiply to get 36.

Based on Beth's third statement, I assume that one of these combinations when added together have to equal each other as then they wouldnt be distinguishable. But they dont.

4 + 3 + 3 = 10

6 + 2 + 3 = 11

2 + 2 + 9 = 13

Am I doing something wrong or is it not solveable? Thanks

Explanation / Answer

Solution: There are only so many ways that three numbers can have a product of 36:

1

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