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?

I know this problem is pretty old, but still, things like this really bother me...

As a couple of other people have pointed out, it is very possible for a man to have two offspring which are currently the same age and for there still to be an eldest between the two of them. Setting aside the "twins" issue, which I personally find kinda dumb--I mean, twins are twins, those few minutes between them don't make an "eldest". However, ten or eleven months or so does, and this is a fact that shouldn't simply be ignored. (Of course, there's also the situation where the man has daughters with different women, in which case the eldest daughter could be as little as a day or two older than the next oldest, but that's just silly).

So yeah, knowing that the eldest daughter lives upstairs or has a monkey with a wooden tail or anything like that really doesn't change anything. What the problem could say to address this issue would be something like "My eldest daughter, who just had her birthday today, lives upstairs." This would eliminate the possibility of the eldest and next-eldest having the same age.

Edited on April 3, 2005, 1:19 pm

Posted by yocko on 2005-03-09 23:14:15