An insurance salesman knocks at the door of a house. He asks the lady about her family and wishes to know the ages of her children. She informs him that she has 3 children but does not wish to disclose information about them to a complete stranger. So, he asks for a clue.
She tells him as follows: The product of their ages is 36 eg 2x3x6
But there are several possibilities, so he asks for another clue. She then tells him that the number of the house next door is the sum of their ages eg 2+3+6=11 But he still can’t tell what their ages are, so he asks for a final clue.
The lady then tells him that her eldest child plays the piano.
Straightaway, he knows their ages and attempts to sell the woman insurance.
What are the ages of the woman’s children and how did the salesman know?
Answer
Clue 1—all possible solutions:
1,1,36 1,2,18
1,3,12 1,4,9
1,6,6 2,2,9
2,3,6 3,3,4
Clue 2:
1+1+36=38
1+2+18=21
1+3+12=16
1+4+9=14
1+6+6=13
2+2+9=13
2+3+6=11
3+3+4=10
Since he knows what number next door is, he must ask for a third clue only if the number is in 2 of the above, i.e.
1+6+6=13
2+2+9=13
Clue 3:
Her eldest child plays the piano, therefore the eldest cannot be a twin. So, her children are aged 2, 2 and 9 respectively.
