Since there are only a few ways to multiply three numbers and get 72, we have the following possibilities:

Code:

Child1 Child2 Child3 Sum of ages
2 2 18 22
2 3 12 17
2 6 6 14
2 4 9 15
3 3 8 14
3 4 6 13

I don't think I missed out some possible combinations.

Since knowing the sum of the ages did not provide an answer to the census taker, the sum of ages must have been 14 (it's the non-unique occurrance of the sums).

Since the father mentiones "the oldest" in singular form, the possibility of 2+6+6 is out, since it would have left the sensus taker with two oldest. There must therefore be twins at age of three, and one eight-year old.