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 that 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?

Answer 1

I just encountered this question. Here's my answer:

Given:
3 kids
product of their ages is 72.
Youngest child.

The youngest child means that all three kids have different ages.

We need to factor 72. Let us use prime factorization.

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

Based on the factors we can assume the following ages:

2 x 4 x 9   = 72
3 x 4 x 6   = 72
1 x 8 x 9   = 72  I prefer this age combination.
1 x 3 x 24 = 72
1 x 4 x 18 = 72