SOLUTION: Hello! This problem has got me here for a good hour and I still cannot figure it out. A traveling salesperson shows up at the apartment of a math teacher to peddle her wares.

Question 95189: Hello! This problem has got me here for a good hour and I still cannot figure it out.
A traveling salesperson shows up at the apartment of a math teacher to peddle her wares. During the course of her spiel, the salesperson discovers that the teacher has 3 children and inquires as to their ages.
The teacher answers, "The sum of my children's ages is 13."
The salesperson immediately declares, "That's not enough information to deduce your kid's ages!"
The teacher continues, "Well, the product of their ages is the same as my apartment number."
After taking a quick check of the apartment number, the salesperson thinks for a minute but then sighs, "That's STILL not enough information for me to figure out."
So the teacher says, "Oh, I forgott to mention, my eldest child is allergic to chocolate."
At which point the salesperson exclaims, "Aha, now I know all their ages!"
What are the ages of the children?

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the possible ages and their products (p) are:

1, 1, 11 p11
1, 2, 10 p20
1, 3, 9 p27
1, 4, 8 p32
1, 5, 7 p35
1, 6, 6 p36
2, 2, 9 p36
2, 3, 8 p48
2, 4, 7 p56
2, 5, 6 p60
3, 3, 7 p63
3, 4, 6 p72
3, 5, 5 p75
4, 4, 5 p80

there are only 2 cases where the products are not unique ... so the apartment number is 36

the comment about the chocolate implies that the eldest "child" is not a twin, so 2, 2, and 9 are the ages
RELATED QUESTIONS
Good Morning, I have a mark-up problem that is haunting me. Could you please show me... (answered by KMST,josmiceli)

I attempted to try this problem for myself, yet I still got the wrong answer. So can you... (answered by rothauserc,MathTherapy)

Hello, Can someone please help me solve this problem, I tried and I still can not... (answered by richwmiller)

Dear tutor, for whatever reason i cannot figure out this probability question. Can you... (answered by askmemath)

Here is the problem. I have been at it for an hour and still can't seem to figure it out. (answered by jim_thompson5910)

Karen�s boat has a top speed of 10 miles per hour in still water. While traveling on a... (answered by josmiceli)

Will you please help me solve this problem? i have tried, but i just cannot figure out... (answered by scott8148)

A river flows at 3mph. A boat takes 1 hour longer to sail 36 miles upstream than to... (answered by ptaylor)

This is a strange problem our instructor gave us to solve. I cannot figure out how to do (answered by ankor@dixie-net.com)