A man in my neighbourhood has three daughters. One day when I asked their ages he said:

"*The product of their ages is 36*".

When I still couldn't find their ages he said:

"*Ok. I'll give you another clue: the sum of their ages is same as the number of my house*".

I knew the number but still couldn't calculate their ages. So the man gave me a last hint, he said:

"*My eldest daughter lives upstairs*".

Finally I was able to find their ages. Can you?

Before viewing the solution, I also constituted a table of positive

integer triptets having a product of 36. It has been observed from the table, that with the exception of two of these triplets, all the other triplets yield distinct sums. Since, the answerer was not able to deduce the ages despite the neighbor's second tatement, it follows that the triplet sum cannot be distinct.

The two triplets having equivalent sums are (a, b, c) = (1, 6, 6),

(2, 2, 9), after imposing the restriction a>= b>= c. But having b=c=6, would imply that there are two eldest daughters instead of one. This would be a direct contravention of the statement of the neighbor.

Thus, the only possible triplet (a, b, c) in increasing order of magnitude is (a, b, c) = (2, 2, 9); implying inter alia that the age of the three daughters are 2 years, 2 years and 9 years.

*Edited on ***October 15, 2007, 5:18 am**