Bob and mark talk about their families. bob says he has 3 kids, the product of their ages is 72. he gives another clue: the sum of the ages of his children. mark points out there is still not enough information to accurately guess. finally, bob says" my youngest child called justice". mark can then correctly determine the ages of bob's children. what are the ages? u

I can only give possible combination of the ages. Had the sum of the ages been given, then the 3 specific numbers would have been derived.

We need to do prime factorization of 72.

72 ÷ 2 = 36
36 ÷ 2= 18
18 ÷ 2 =  9
  9 ÷ 3 =  3
  3 ÷ 1 = 1

1 x 2 x 2 x 2 x 3 x 3 = 72

Possible combinations:

1 x 8 x 9 = 72           1 + 8 + 9 = 18
1 x 4 x 18 = 72         1 + 4 + 18 = 23
2 x 4 x 9 = 72            2 + 4 + 9 = 15
3 x 4 x 6 = 72            3 + 4 + 6 = 13