# 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 = 721*2*36 = 721*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.`

## Get over 200+ course One Subscription

Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others

## Checkout list of all the video courses in PrepInsta Prime Subscription

• Rectangular Cake Puzzle
• Truth and Lie Puzzle
• Aircraft PuzzleHorse
• Ratio of Boys and Girls
• Blind Games
• Chaos in the Bus Answer
• Birthday Puzzle
• Measuring 7 litres
• Bulb in the Next Room
• Arranging 10 coconuts
• Married or Unmarried
• Gold Bar Puzzle