If the Answers were 20 or 14, you would know what the ages were (1,9,10 or 3,5,6). Since you don't know the answer with those possible combinations, the ages of the girls must be something other than either of those possibilities. But, since knowing the number of birds in the tree doesn't completely define the answer and leaves you 'up the tree' as it were, either (2,5,9) or (3,3,10) are the ages. In either of those cases, their ages total 16 and the multiplication result is 90. So, their ages are either 2, 5 and 9 or 3, 3 and 10, and the number of birds in the tree is 16 as flopsy says.
In other words, knowing the count of birds in the tree to be 16, you still cannot be sure of the breakdown of their ages since there are two possibilities that add up to 16.
If the number of birds was 20, you would know the age distribution.
If the number of birds was 14, you would know the age distribution.
It is the not knowing the distribution that imposes a correct bird count to be 16.
Edited by mehaul (Wed Oct 08 2014 02:56 PM)
If you aren't seeing Heaven while you dream, you're doing something wrong.
Dreams allow escape from the passage of Time.
The ultimate activity is the Dream.