Question

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

Answer 1

Given: 
3 children
Product of their ages is 72.

The sum of the ages of his kids is not stated.So we cannot pinpoint the actual 3 ages. We can only assume the combination of the 3 ages.

We do prime factorization of 72.

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

1 x 2 x 2 x 2 x 3 x 3 = 72
1 x 2³ x 3² = 72

1 x 8 x 9 = 72
1 + 8 + 9 = 18

2 x 4 x 9 = 72
2 + 4 + 9 = 15

3 x 4 x 6 = 72
3 + 4 + 6 = 13

1 x 4 x 18 = 72
1 + 4 + 18 = 23