Question 99257
The product of the ages is 36. Possibilities are:

2*2*3*3

1, 2, 18 -> sum: 21
1, 3, 12 -> sum: 16
1, 4, 9 -> sum: 14
1, 6, 6 -> sum: 13
2, 2, 9 -> sum: 13
2, 3, 6 -> sum: 11
3, 3, 4 -> sum: 10

If the censur taker walked to the next house and couldn't figure out what the ages were, this means it had to be one of the sums with more than one occurrance (only 13 in our case).

So we're left with 1, 6, 6 and 2, 2, 9. But the woman mentioned an oldest child. If the children's ages were 1, 6, 6 there would be no "oldest" child, so it must be 2, 9, 9.