The reason the Census taker could not figure out the children's ages for the first time was even having known the number on the house next door-- there were still 2 possibilities. The only way that the product could be 36 and still leave two possibilities is if the sum equals 13. These possibilities are 2+2+9 and 1+6+6. When the lady said that her "oldest" child is sleeping whe was giving a hint to the Census taker that there is an "oldest" child. Therefore, the ages of the children are 2,2, and 9.