Let's see if you can solve this one...?

Question

A woman conducting a survey asks a man how many children he has.
"I have three children."
"And how old are they?" she asks.
"All I will tell you is that, working in years if you multiply their ages the answer is 72 and if you add their ages the answer equals my house number."
With that he shuts the door. The woman looks at the house but finds it impossible to work out the age of each child.
She knocks on the door and protests that he has not given her anough information.
"Oh, I forgot to tell you," the man says, "my oldest child likes chocolate" and then he shuts the door.
How old is each child?

Answer 1

42

(the answer to life, the universe, and everything)

How about 24, 1 and 3

Answer 2

All the possible ages corresponding to the product 72 are given below. The corrsponding sums are also given.

Ages Sums

1 1 72 = 74

1 2 36 = 39

1 3 24 = 28

1 4 18 = 23

1 6 12 = 19

1 8 9 = 18

2 2 18 = 22

2 3 12 = 17

2 4 9 = 15

2 6 6 = 14

3 3 8 = 14

3 4 6 = 13

Because the information about the product and the sum was insufficient the only possibilities left are (2,6,6) and (3,3,8). Otherwise the woman would have known the ages because all the other possibilities have unique sum - (2,6,6) and (3,3,8) both give 14.

Next information says that there is an oldest one among the children. The (2, 6, 6) does not have a (unique) oldest one. So, the only possibility left is that children are 8, 3 and 3 years old.

Answer 3

72 equals 6 x 6 x 2. This can't be, because the man says "my oldest child" meaning there is only one. However 6 equals 3 x 2. If we pass the factor 3 to the the original 2, we get the same numbers. We then have to pass the 2 to multiply the other 2, so the ages are 6, 4 and 3. He lives at number 13 of his street.

Why is this the correct solution? Because by looking at the door number alone, she would not have information enough to distinguish it from 6+6+1.

6+4+3 = 13
24+3+1 = 28
18+4+1 = 23
12+6+1 = 19
6+6+2 = 14
9+4+2 = 15
9+8+1 = 18
3+3+8 = 14 YESSSS!

The solution is of course 3, 3 and 8.

We do not need to verify all possible cases. The factors of 72 are 3 3 2 2 2. The only factorizations that contain a perfect square are [36] 2 and [9] 8, and of these the first corresponds to more than one older child. Therefore 6 6 2 is one of the ambiguous possibilities, and the sum to look for is 14. Coincidentally, it is 3 3 8 that also sums 14.

Chaney34 completely stole my answer. And he gives references, for what?

Answer 4

3, 4, and 6

Answer 5

They are 6, 4, and 3.
Or 37, 37, and 1
Or 24, 3, and 1


I think you'd have to have the house number for a definitive answer!

Answer 6

I agree with Shannon on this one because it could also be 8, 3, and 3, he could have twins.

Answer 7

total guess.. 6, 4, 3