Find ages of daughters || Interview Puzzles || Challenging Job Interview Puzzles

Puzzle Details::

Anand has three daughters. His friend Ravi wants to know the ages of his daughters. Anand gives him the first hint.

1) The product of their age is 72. Ravi says this is not enough information, then Anand gives him a second hint.

2) The sum of their ages is equal to my house number. Ravi goes out and looks at the house number and tells “I still do not have enough information to determine the ages”. Anand admits that Ravi can not guess with these hints, and then he gives him the third hint

3) The oldest of the girls likes strawberry ice cream. now, Ravi is able to guess after the third hint. 

Can you guess what are the ages of the three daughters?

Solution

To start with, list out all possibilities to get 72, from products of three different ages. Because the first clue given is that, the product of 3 daughter ages is 72

• Here are all possibilities to get 72 from products of three different ages:

1 * 1 * 72 = 72

1 * 2 * 36 = 72

1 * 3 * 24 = 72

1 * 4 * 18 = 72

1 * 6 * 12 = 72

1 * 8 * 9 = 72

2 * 2 * 18 = 72

2 * 3 * 12 = 72

2 * 4 * 9 = 72

2 * 6 * 6 = 72

3 * 3 * 8 = 72

3 * 4 * 6 = 72

since there are multiple possibilities it is difficult to guess the ages of the 3 daughters.

• let's check the 2nd clue now, 

second clue is The sum of their ages is equal to my house number. we have already possibilities of the product of 3 daughters age.

here is the sum of their ages 

1 + 1 + 72 = 74

1 + 2 + 36 = 39

1 + 3 + 24 = 28

1 + 4 + 18 = 23

1 + 6 + 12 = 19

1 + 8 + 9 = 18

2 + 2 + 18 = 22

2 + 3 + 12 = 17

2 + 4 + 9 = 15

2 + 6 + 6 = 14

3 + 3 + 8 = 14

3 + 4 + 6 = 13

All sums are unique except 14. So the age sum must have been 14, otherwise, Ravi would have guessed the ages from hint 2 only. So we have two possible combinations to get a sum of 14

2 + 6 + 6 = 14

3 + 3 + 8 = 14

since there are 2 possibilities it is difficult to guess the ages of the 3 daughters.

• let us check the 3rd clue

The oldest of the girls likes strawberry ice cream. which clearly says that Anand has the oldest girl (and not two!!). hence we can rule out 2 + 6 + 6 = 14 this option because oldest daughters  are 2.

So the ages must be 3, 3 and 8.