Two mathematicians - One puzzle a day - Puzzle Buddies

Puzzle: Two mathematicians(old friends) meet after a long time in a bar. The first one tells the other that he got married and has three daughters. The second friend asked about their ages. To make the matter more interesting first one replies, “The product of their ages is 72.” The second mathematician answers, “OK, but that didn’t help a lot.” — “Then I should tell you that the sum of their ages is equal to the street number of this bar.” The second mathematician leaves the bar, returns, and says, “Great, but I still don’t know their age.” The first mathematician smiles and says, “My youngest daughter just started to play piano.” Now the second mathematician knows their ages.

How old are the three daughters? (The age should be thought of as integers only for this problem).

Thanks to Anirban Chatterjee for pointing us to this puzzle.

Solution: There are 3 conditions in this puzzle

1. The product of the ages of three daughters is 72.

2. The sum of all their ages is equal to a number.

3. The youngest daughter just started to play piano.

Let's start with first. There can be only a limited number of ways in which the result of multiplication can be 72.

          OLD        MID        YOUNG       SUM
    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                 13

Now the mathematician knows the number which we do not know in this puzzle but still 

he could not conclude the answer. 

This means that there are two combinations in which the sum is same.

           OLD        MID        YOUNG       SUM
    8         3           3                 14
    6         6           2                 14

Now we have reduced the problem set to two options only.

The third condition says that the younger one just started to play piano,
and that makes it clearer that younger one can not be twin. 
So the the answer is 6,6,2.
Interesting fact here is that now we know the building number also which is 14 :)

Winners: Once again Subodh Singh is the winner.
 Vinay also answered correctly this time.