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# Daughter’s Ages Puzzle

**Daughter's Ages Puzzle**

In Daughter’s Ages Puzzle, Raj has three daughters. His friend Shyam wants to know the ages of his daughters. Raj gives him a hint:-

- The product of their age is 72 (However, Shyam cannot guess so he asks for another hint)
- The Sum of their ages is the same as my house number. (Shyam goes out and checks the house number, but he is still unable to find the ages.)
- My oldest daughter loves to paint (With this hint Shyam can guess their ages correctly. What were the ages of the 3 daughters?)

**Daughter’s Age Puzzle**

In Daughter’s Ages Puzzle, Raj has three daughters. His friend Shyam wants to know the ages of his daughters. Raj gives him a hint:-

- The product of their age is 72 (However, Shyam cannot guess so he asks for another hint)
- The Sum of their ages is the same as my house number. (Shyam goes out and checks the house number, but he is still unable to find the ages.)
- My oldest daughter loves to paint (With this hint Shyam can guess their ages correctly. What were the ages of the 3 daughters?)

### Solution

Here we have the solution for the Daughter’s Ages Puzzle –

Let their ages be a, b and c respectively.

**From hint 1:**

We get 12 possible equations, such that a*b*c=72.

1*1*72 = 72

1*2*36 = 72

1*3*24= 72, and so on

**From hint 2 :**

We know that the sum of the ages gives the house number.

Among the 12 possible equations, each combination gives a unique sum except for two combinations, which have the same sum.

` These are:- 2*6*6 and 3*3*8, with sum = 14.`

Since Shyam was unable to guess from the 2nd hint, we can say that the house number was 14, and having 2 combinations resulting in 14 confused him.

**From hint 3 :**

Raj mentions “oldest” daughter, as in one of the three is the oldest. Therefore, we can rule out 2,6,6.

`Thus the ages of the daughters are 3,3.8.`

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