Daughter’s Ages Puzzle

March 21, 2023

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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