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?

Bob must have said that the sum of the ages of the children is 14. There are two sums that are 14. The children could be 2, 6, and 6 or the children could be 3, 3, and 8. The third clue says that the youngest child is called Justice. This implies that the two youngest must not be the same age. The youngest must have a distinct age different from the others. This means that the children can't be 3, 3, and 8 because the two youngest would be the same age. The ages must therefore be 2, 6, and 6, making only the youngest having a distinct age of 2. If the sum of the ages was any other sum, 39, 23, 18, 28, 17, 15, 13, or 22, then Mark could have determined the ages without any more clues. I learned this in math last year.