This is much like Student Ages question although a bit easier. You first must factor 72 which breaks down into 1x2x2x2x3x3. Combining these numbers to make 3 ages reveals 11 combinations: (1 2 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), and (3 4 6).

The host says that their sum is equal to the house number of the guest. If the guest (who should know his/her own house number) has to ask for more information then some of the combinations must add up to the same number. By adding up all of the combinations, we find that (2 6 6) and (3 3 8) both add up to 14 so the house number must be 14 and one of the combinations must be correct.

Then the host says that the oldest likes strawberry ice-cream which tells you that there is an oldest. Since (2 6 6) implies that two of his children have the same age, the answer must be (3 3 8).

So her oldest child is 8.