# Puzzle-15

Two friends, Kaval and Prashant, meet after a long time.
Kaval: Did you marry at last or still single?
Prashant: As a matter of fact, I got married and I have three kids now.
Kaval: That’s awesome. How old are they?
Prashant: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Kaval: Arghhh. I need more than that to solve this riddle. I am no mathematician.
Prashant: My eldest kid, Niharika, just started with her tennis classes.
Kaval: Ah, that does it.
How old are Prashant’s kids?

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Ages of the kids: 3,3,8 Let’s break it down. The product of their ages is 72. So what are the possible choices?

Product: 2, 2, 18 Sum of (2, 2, 18) = 22 Product: 2, 4, 9 Sum of (2, 4, 9) = 15 Product: 2, 6, 6 Sum of (2, 6, 6) = 14 Product: 2, 3, 12 Sum of (2, 3, 12) = 17 Product: 3, 4, 6 Sum of (3, 4, 6) = 13 Product: 3, 3, 8 Sum of (3, 3, 8 ) = 14 Product: 1, 8, 9 Sum (1,8,9) = 18 Product: 1, 3, 24 Sum (1, 3, 24) = 28 Product: 1, 4, 18 Sum (1, 4, 18) = 23 Product: 1, 2, 36 Sum (1, 2, 36) = 39 Product: 1, 6, 12 Sum (1, 6, 12) = 19

The sum of their ages is the same as your birth date. That could be anything from 1 to 39 but the fact that Kaval was unable to find out the 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 Since the eldest kid is taking piano lessons, we can eliminate combination 1 since there are two eldest ones. The answer is 3, 3 and 8