Blue eyed boy- puzzle

This is conversation between two friends Ram and Shyam

Ram: Hey Bro, long time! How are you?
Shyam: I am good, How are you?
Ram: How are three boys, they must have grown up now. How old are they?
Shyam: Hmm, let me put it like this, if you multiply their ages, you will get the product as 36. And if you add their ages, you will get my house number.
Ram: Interesting, give me some more hint?
Shyam: Ok, my oldest son has blue eyes.
Ram: Awesome, so their ages are …

Puzzle: So what is the age of three boys?


There are three hints

1. Product of the ages is 36.
2. Sum of the ages is same as house number. Interesting, we do not know house number, we will see how to use it.
3. Oldest is blue eyed boy. How is that useful?

Ok, lets start

1. Product of 3 ages is 36, so possible solutions are

1, 1, 36= 38(sum)
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

2. Sum of the ages is house number
Looking at the above numbers, its clear that all the sums except 13 are unique, so if the house number was anything other than 13, Ram would have answered easily. But as he asked for one more hint, we now know that the house number is 13 and we are left with 2 possible solutions.
1, 6, 6=13 *
2, 2, 9=13 *

3. Oldest boy has blue eyes.
Out of the two options mentioned above, option 2 has a clear cut oldest age, i.e. 2, 2, 9. In case of 1, 6, 6, statement should have been one of the older boys or both old boys.

So ages are – 2, 2, 9