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?
The factors of 36 are 1 * 2² * 3²
We get the follwing possible age distributions:
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 knowing the sum (in parentheses above) didn't help, then tat sum must belong to two different possibilities. So it must be 13, which means that the gils are either 1, 6, and 6; or 2, 2, and 9. Since one girl is "the oldest," we are supposed to be able to eliminate the 1, 6, 6 and arrive at the answer 2, 2, 9.
NOTE:
However, parents usually know which twin is older, and there is the possibility that the oldest two are ten or eleven months apart and it is the month or two between their birthdays.
On the other hand, the neighbor would not have offered the existance of an "eldest" as a clue unless it could be used as a clue, so his twins are younger than their sister, and he just didn't think through the "older twin" possibility.

Posted by TomM
on 20021031 21:24:24 