Puzzle -58 | Friends after ages

Two old friends, Jacky and Bob, meet after a long time.
Jacky: Hey, how are you man?
Bob: Not bad, got married and I have three kids now.
Jacky: That’s awesome. How old are they?
Bob: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jacky: Cool… But I still don’t know.
Bob: My eldest kid just started taking piano lessons.
Jacky: Oh now I get it.

How old are Bob’s kids?

Answer:
3,3,8
Solution:
All we have gained from the conversation is that the product of their ages is 72 and the sum lies between (1,31) ;           ie; (possible dates a month can have ).
So what are the possible choices?
2, 2, 18 sum(2, 2, 18) = 22
2, 4, 9 sum(2, 4, 9) = 15
2, 6, 6 sum(2, 6, 6) = 14
2, 3, 12 sum(2, 3, 12) = 17
3, 4, 6 sum(3, 4, 6) = 13
3, 3, 8 sum(3, 3, 8 ) = 14
1, 8, 9 sum(1,8,9) = 18
1, 3, 24 sum(1, 3, 24) = 28
1, 4, 18 sum(1, 4, 18) = 23
1, 2, 36 sum(1, 2, 36) = 39
1, 6, 12 sum(1, 6, 12) = 19

But we remember that Jacky still had a problem figuring out their ages. It means there are two or more combinations with the same sum. From the choices above, only two of them are possible now.

2, 6, 6 sum(2, 6, 6) = 14
3, 3, 8 sum(3, 3, 8 ) = 14

Now since the eldest kid is taking piano classes, we can eliminate combination 1 since there are two eldest ones. The answer is 3, 3 and 8.

Reference: http://dailybrainteaser.blogspot.in/2011/07/popular-age-problem.html

This puzzle is contributed by Pragya Gupta.