Question

Bill and Matt are discussing their children. Bill tells Matt that he has 3 kids, and the product of their ages is 72. He also tells him the sum of the ages of his kids. Matt says there is still not enough information to correctly guess the ages of Bill's kids. Finally, Bill says, "My youngest child's name is Joy." Matt can then correctly guess. What are the ages?

Answer 1

In the first part, where Bill tells Matt that he has three kids and the product of their ages as well as the sum, there are two possible combinations of ages that have the same sum; 3, 3, and 8, as well as 2, 6, and 6. However, once Bill says that he only has a youngest child, no two youngest children, we can eliminate 3, 3, and 8, and the ages are 2, 6, and 6.