If someone had three kids and the product of their ages is 72 and the sum is the person's house number and said that his oldest child likes strawberry ice cream how old is the oldest son?

Answer 1

Find all the sets of 3 factors of 72. Here they are: (1, 2, 36), (1, 3, 24), (1, 4, 18), (1, 6, 12), (1, 8, 9), (2, 2, 18), (2, 3, 12), (2, 4, 9), (2, 6, 6), (3, 3, 8), (3, 4, 6), and the highly improbable but theoretically possible (1,1, 72).

Since the guest does this and still needs one more piece of information, you know that there is more than one set of numbers that totals the guest's house number. So you can eliminate all sets that have unique totals. This leaves you with (2,6,6) and (3,3,8) which both total 14.

The hosts ice cream flavor clue tells you that there is one oldest child. That eliminates the set (2,6,6) and leaves only (3,3,8). The oldest child, then, is 8.

Good luck with that!