A recent census form included a space for residents to record the ages of all children in the household. One resident wrote: "I have three children. The product of their ages is 72. The sum of their ages is the same as our house number." The census worker who had to process the form phoned this resident to complain that this was not enough information. "I'm sorry," replied the resident. "I forgot to mention that my oldest child likes chocolate pudding." The census worker thanked the resident and hung up the phone. How old were the children? (Hint: list all the ways that 72 can be expressed as a product of thee natural numbers.)
