During a recent census, a man told the census taker that he had three children. When asked their ages, he replied, “The product of their ages is 72. The sum of their ages is the same as my house number.”
The census taker ran to the man’s front door and looked at the house number. “I still can’t tell” she complained. The man replied, “Oh that’s right, I forgot to tell you that the oldest one likes chocolate pudding.” The census taker then promptly wrote down the ages of the three children. How old are they?
The key to this brain teaser is that the census taker looks at the house number. In other words, she knows the sum of the children’s ages. However, at that point of the riddle, she still can’t tell how old the man’s children are. Therefore, she has to be stuck between multiple possibilities.
To narrow it down further, only two sets of numbers that multiply to 72 share the same sum: (2,6,6) and (3,3,8). After the man reveals that his oldest child likes chocolate pudding, however, the census taker can differentiate between the two options. That is, only the latter of those two sets has a distinct “oldest” child.