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
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