The Proof Is In the Pudding?

Question

This is my math homework, could someone help me with the answer? It's just so hard.

Coincidentally, that's what she said.
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The host of a party turned to a guest and said "I have three daughters."

"Is that so?" the guest replied. "How old are they?"

"Well, the product of their ages is 72 and the sum of their ages is my house number."

"Hmm," said the guest, "excuse me a moment." The guest rushed to the door, looked at the house number, and returned to the host. "I'm afraid I need a little more information."

"Alright," the host replied. "The oldest likes strawberry pudding."

The guest smiled and announced the ages of the three girls.

Answer 1

As a product of three numbers, 72 can be written in the following ways with the sums following...

numbers sum
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
other ways of having a product of 72 with three numbers repeat the ways already listed.
When the guest rushed out the door and checked the house number, the house number itself did not provide enough information. Since all the sums appear only once except for 14, the house number must be 14. The next clue was that the oldest likes strawberry pudding implying that there is a single oldest child and not a pair of oldest twins.
So the correct ages would be 3, 3, and 8.

Answer 2

3 4 6

Answer 3

3 3 8

Ok explanation.
I worked out the possible factors - clearly there must be more than one answer where the sum of the factors is the same otherwise the house numebr clue would be enough.

I got 3,3,8 and 6,6,2 (both add to 14) This is the dodgy bit as i didn't check ALL options.

If there is a single eldest then the answer must be 3,3,8

Answer 4

3, 3, 8, Nice one! Thank You!

Answer 5

In what way are we concerned with a pudding???

Answer 6

what the f@#k!!!!!!!!!!!!!!!!!!