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? Answer:
The first clue is that the product of their ages is 72. Therefore, the list of all possible sets of numbers whose product is 72 is:
72 1 1 36 2 1 24 3 1 18 4 1 18 2 2 12 3 2 12 6 1 9 8 1 9 4 2 8 3 3 6 6 2 6 4 3The second clue involves the sums of their ages which are:
72 + 1 + 1 = 74 36 + 2 + 1 = 39 24 + 3 + 1 = 28 18 + 4 + 1 = 23 18 + 2 + 2 = 22 12 + 3 + 2 = 17 12 + 6 + 1 = 19 9 + 8 + 1 = 18 9 + 4 + 2 = 15 8 + 3 + 3 = 14 6 + 6 + 2 = 14 6 + 4 + 3 = 13Out of all these sums, two of them are equal:
8 + 3 + 3 = 14 6 + 6 + 2 = 14The final clue is that his "oldest" daughter likes cake, which means that we can eliminate the second one of the above. Therefore, his daughter's ages are:
8 + 3 + 3 = 14More Interview Posts