Find Ages of Daughters | Puzzles for Interview - Interview Preparation PDF Download

Introduction

Alok has three daughters and his friend Shyam wants to know their ages. Alok gives Shyam three hints to guess their ages. Let's find out how Shyam guesses their ages.

Hint 1: Product of Ages

Alok tells Shyam that the product of his daughters' ages is 72. Shyam finds out that there are 12 possible combinations to get 72 by multiplying three different numbers. These combinations are:
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

Hint 2: Sum of Ages

Alok gives Shyam a second hint that the sum of his daughters' ages is equal to his house number. Shyam goes out to look at the house number but still can't determine their ages. Shyam then realizes that the sum of their ages must be 14 because all other sums are unique. If the sum was any other number, Shyam would have been able to guess their ages from the second hint only. So, the possible combinations that give a sum of 14 are:
2 + 6 + 6 = 14
3 + 3 + 8 = 14

Hint 3: Oldest Daughter

Alok gives Shyam the third hint that his oldest daughter likes strawberry ice cream. Shyam now knows that the ages must be 3, 3, and 8 because there is only one oldest daughter.

Conclusion

Alok's daughters' ages are 3, 3, and 8. Shyam was able to guess their ages after the third hint.