A Math Riddle...
 

My son came home with this math riddle (he's 13 and was able to solve it):

Mrs. Counts, a census taker, went to Mr. Smith’s house. Mr. Smith tells Mrs. Counts that he has
three daughters. Mrs. Counts asked for his daughters’ ages. Mr. Smith tells her that the product
of their ages is 72, and the sum of their ages is my house number. Mrs. Counts did some
calculations, and then she went out and checked his house number. She came back frowning and said,
“I’m afraid I can’t figure out your daughters’ ages”. Mr. Smith said, “Oh! I almost forgot to tell
you, my oldest daughter likes chocolate pudding.” Mrs. Counts immediately figured out their ages,
wrote it down, and went on to the next house.

What are the three girls ages?

Answer: Spoiler: Three, Three, and Eight

Hmm, with time it could be solved- and a lot of estimations. But what does the chocolate pudding have to do with anything?

No estimation required.

8. Because 8 is great. The other 2? Hell, I dunno. Riddles make my head explode.

Sorry, my brains ain't work good like yurs.

Spoiler: three, four and six also works. Without the house number, there is no way to solve. Pudding adds no information as far as I can tell.

Nope that doesn't work.

And the pudding line is important.

And it can be solved without knowing the house number.

The reason your answer doesn't work is:
Spoiler: If the answer had been three four and six, the census taker would have been able to answer straight away: he knows what the house number is. If it had been 13 he would have been able to answer. But he wasn't able to answer, so we can conclude the the house number wasn't 13. He needed one more clue to be able to answer: i.e. that the eldest like chocolate pudding.

Ok, for those that want to work it out, here is a hint:

Spoiler: The key to the puzzle is to realize that after recieving two clues, he was still unable to work it out. That is important



And the full solution is here:
Spoiler: First, we know that their ages when multiplied together give 72. So we write out all of the "triplet-factors" of 72.
1 3 36
1 3 24
1 4 18
1 6 12
1 8 9
2 2 18
2 3 12
2 4 9
2 6 6
3 3 8
3 4 6
Next we know that they all add up to give the number next door. So we add them up:
1 + 3 + 36 = 39
1 + 3 + 24 = 28
1 + 4 + 18 = 23
1 + 6 + 12 = 19
1 + 8 + 9 = 18
2 + 2 + 18 = 32
2 + 3 + 12 = 17
2 + 4 + 9 = 15
2 + 6 + 6 = 14
3 + 3 + 8 = 14
3 + 4 + 6 = 13
We now have another piece of information: The fact that the census taker was unable to solve the problem with this information. He what the sum of their ages was (the house number) but was still unable to solve it. So we know that the sum must not be unique. We look through the list to find non-unique sums:
2 + 6 + 6 = 14
3 + 3 + 8 = 14
We know that it must have been one of these two. The lady tells the census taker that the eldest likes chocloate pudding. The choclate pudding is irrelevant. The point is that we know there is an eldest
It has to be 3,3 and 8.

AH!

That's pretty neat! Thanks.

Oh, and I'm impressed by your 13 year old!

Don't we need to know the house number to solve it?

Nope.

CSFilm gave the full solution. Good job! To clarify, the pudding statement is very important because it tells us that the family has an eldest child, not two eldest children (twins). If the twins had been the oldest (2, 6, 6), then the man would have stated "my oldest daughters like chocolate pudding".