The Ages 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?

How old they are? Click here! 

Source 

Calculation of The Ages of Three Daughters

How it was asked to find with some clues? 

The product of their age is 72; so possible combinations are,

3 x 3 x 8 = 72                       3 + 3 + 8 = 14

2 x 6 x 6 = 72                       2 + 6 + 6 = 14

2 x 2 x 18 = 72                     2 + 2 + 18 = 22

2 x 3 x 12 = 72                     2 + 3 + 12 = 17

2 x 4 x 9 = 72                       2 + 4 + 9 = 15

3 x 4 x 6 = 72                       3 + 4 + 6 = 13
 
If any of last 4 combinations was correct then I would have come to know ages of daughter straightaway as their sum is unique. So friend's house number as he must have told must be 14. That's why I was uncertain with the correct combination as they are appearing twice.

In next clue, he indirectly suggest he has only 1 oldest daughter. So 2,6,6 is eliminated as in that case he would have 2 oldest daughters.

So the correct combination is 3,3,8. That means he had oldest daughter of age 8 & younger twins.