Answer: The three kids are 3, 3, and 8 years old. The Census taker looks at the house number and sees 14. So she knows that she needs 3 numbers that multiply to 72, but add up to 14. She ended up with 2 possibilities (2,6,6) and (3,3,8).
When the man tells her that the oldest loves chocolate pudding, he realizes it’s the second option.