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?
We first find all the possible factors into which the number 36 can be split into and then note down the sum of those factors. They are as follows:
36 = (1)(2)(18) and their sum is 21.
36 = (1)(3)(12) and their sum is 16.
36 = (1)(4)(9) and their sum is 14.
36 = (1)(6)(6) and their sum is 13.
36 = (2)(2)(9) and their sum is 13.
36 = (2)(3)(6) and their sum is 11.
36 = (3)(3)(4) and their sum is 10.
Now, we see that when the man gave me the house number (which is eual to the sum of the ages of his three daughters), I was still not able to determine their ages, which implies that of all the sums that I had obtained, there was at least one pair which had the same sum and it is clear from above that there is exactly one pair which has the same sum (13), the pairs being (6,6,1) and (2,2,9). Now, the moment he says that his eldest daughter lives upstairs, it is obvious that the combination (6,6,1) is rejected and hence we get the daughters' ages as 9, 2 and 2 years.