[luikore]

The ages can be:

    3 + 3 + 4 = 10
    1 + 4 + 9 = 14
    2 + 2 + 9 = 13
    1 + 6 + 6 = 13

If the sum is 10 or 14, B would have had enough information for the answer at once. So the sum should be 13.

And "oldest kid" is not "oldest kids", so 2, 2, 9 is the answer.