Sum of My Daughters ages is My house Number :Nice puzzle

Recently i have attended a test for a job,where i have 38 questions with time of 100 minutes….i have solve all the questions except three…One of them is this puzzle…The question goes like this

A census taker came to a house where a man lived with three daughters.”What are your daughters’ ages?” he asks. The man replied, “The product of their ages is 72, and the sum of their ages is my house number”. “But that’s not enough information,” the census taker insisted.All right,” answered the farmer, “the oldest loves chocolate”.What are the daughters’ ages?

i have spent lot of time in this question searching for a clue but invain.After coming to home i have asked my father to solve this and he solved it easily…i was thinking that there is some clue in “the oldest loves chocolate”.what i have done is i have taken all the possible multiples of 72, i assumed something and wrote answer as 6,4,3.

but i was wrong….My father solved it as follows…

write down all the possible combination of multiples of 72

we get the following possibilities….

S.NO

Youngest

Middle

Oldest

Sum (Houseno)

1

1

1

72

74

2

1

2

36

39

3

1

3

24

28

4

1

4

18

23

5

1

6

12

19

6

1

8

9

18

7

2

2

18

22

8

2

3

12

17

9

2

4

9

15

10

2

6

6

14

11

3

3

8

14

12

3

4

6

13

 

after that we can get a hint that the census taker said “But that’s not enough information”.With this we knew that there is more than one possibilty of sum with that house no.So we have that only if the sum is 14

so the final possibilities cut down to case 10 and case 11

10

2

6

6

14

11

3

3

8

14

here if we consider case no 10 we have two daugther of age 6 , but the man said that the oldest lieks chocolate,the eldest implies there is only 1 daughter older than others..

so the final possibity which satisfies all the conditions is Case 11

11

3

3

8

14

hence the answer….

that was the moment i thought my father is a genius.

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