How Old Are the Children?

The children are 9, 2 and 2 years old, which adds up to 13 as the observed house number. But, for that house number, the children could also have been 6, 6, and 1. For any other house number, there is only one possible solution for the children's ages, and Bill would not have felt it necessary to require more information. Since he did ask for more help, 13 must have been the number he observed. Being told that the oldest child had red hair informed him that there was, in fact, an oldest child, elimimating the solution with six year old twins.