Salutations of the night. Would you believe that just yesterday I was doing this problem. It's called the Census-Taker problem. I ended up looking for the solution on the internet and got extremely irritated when I found out how close I was to the solution. Now I'm hooked on these problems.
From hint 1 we can see that the age of each child is a factor of 36.
The crux of the problem is that he could not figure it out from observing the neighboring house number. From this we deduce that there are triplets of the factors of 36 whose sums are equal.
From observation we see that the only triplets for which this is true are (9,2,2) and (6,6,1).
Hint 2 states that there is an oldest child, therefore (6,6,1) is not the solution.
Ages of the children are (9,2,2)