Tom should have been able to immediately get the answer, since he knows his own house number, but he can’t.  This is because two solutions have the same sum of 13: (2,2,9) and (1,6,6).  Only when he knows the “eldest” is doing the laundry can he distinguish which set of ages is possible.  A 9 year old can do the laundry and is the oldest child.  A 6 year old is too young and would be one of two children with the same age.