## The Age of 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 three of their ages. How old is each daughter?

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” (with a sum of 14). The rest have unique sums:

2 + 2 + 18 = 22

2 + 3 + 12 = 18

2 + 4 + 9 = 15

3 + 4 + 6 = 13

The house number alone would have identified any of these groups. Since more information was required, we know the sum left the answer unknown. The presence of a single oldest child eliminates “2 6 6”, leaving “3 3 8” as the only possible answer.

3 Comments on "The Age of Three Daughters"Kundabarandadi says

April 17, 2016 @ 04:35

Thank you

Steve says

April 22, 2016 @ 12:23

The Age of Three Daughters:

You missed 1 x 8 x 9 = 72 and 1 + 8 + 9 = 18 so there is another group of non-unique sums: 2, 3, 12 and 1, 8, 9 and both of these groups have a single largest number.

Lana says

April 30, 2016 @ 20:11

2+3+12=17 not 18 so there is only 1 group of non-unique numbers.

Ages: Sum of ages:

1 1 72 74

1 2 36 39

1 3 24 28

1 4 18 23

1 6 12 19

1 8 9 18

2 2 18 22

2 3 12 17

2 4 9 15

2 6 6 14 **

3 3 8 14 **

3 4 6 13

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