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.** Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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