The Census Taker Problem


During the 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 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 promptly wrote down the ages of the three children.

How old are they?

Hint?   Click here for a spreadsheet showing one way to enumerate possibilities.