Guessing age of 3 daughters puzzle

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A mathematician and a lady strike conversation during a flight.

The lady asks the mathematician to guess the age of her three daughters. Mathematician, being unable to answer the questions, asks for some hint(s).

The lady replies: The product of their ages is 36.

Hint 2: The sum of their ages is equal to your (i.e. mathematician’s) seat number.
Mathematician still cann’t answer the question.

Final hint: My (i.e. the lady’s) youngest daughter has blue eyes.

Listening to the final hint, mathematician is able to answer the question.
Can you too? How?

SherlockHolmes Expert Asked on 11th March 2016 in

1, 6, 6.
There are 8 combinations { (1, 1, 36), (1, 2, 18), (1, 3, 12), (1, 4, 9), (1, 6, 6), (2, 2, 9), (2, 3, 6), (3, 3, 4) } of ages whose product is 36. After II hint of sum of ages, mathematician is unable to answer so there must be at least two combination of ages whose sum is same (Sum doesn’t matter) . Out of 8 combinations of ages only (1, 6, 6) and (2, 2, 9) have same sum.  Finally, III hint implies one is youngest so (2, 2, 9) is n’t possible as it has two youngest. So answer is (1, 6, 6)  which has elder twins.

anoopk Scholar Answered on 12th March 2016.

1,4,9

lakshminarayanan Scholar Answered on 10th May 2017.

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