Three Daughters

I was visiting a friend one evening and remembered that he had three daughters. I asked him how old they were. "The product of their ages is 72," he answered. Quizzically, I asked, "Is there anything else you can tell me?" "Yes," he replied, "the sum of their ages is equal to the number of my house." I stepped outside to see what the house number was. Upon returning inside, I said to my host, "I'm sorry, but I still can't figure out their ages." He responded apologetically, "I'm sorry, I forgot to mention that my oldest daughter likes strawberry shortcake." With this information, I was able to determine all of their ages. How old is each daughter? You have enough information to solve the puzzle.

Solution »

3, 3, and 8. The only groups of 3 factors of 72 to have non-unique sums are 2, 6, 6 and 3, 3, 8 (both add up to 14). The presence of a single oldest child eliminates 2,6,6.