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?
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.
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.
5 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
Zachary says
July 4, 2018 @ 21:05
Thinking of this realistically, even if there were a set of twins the same age, one is still older. Thus, the explanation doesn’t fit.
Charles says
August 5, 2023 @ 00:14
“As triplets’they are all the same age of 24 just the difference in timing at birth is my theory,because 3×24 equals (72)
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