List every set of three ages that multiplies to 36 and only two share a total: 1, 6 and 6, and 2, 2 and 9, which both come to 13. That is why the door wasn’t enough. Having one eldest rules out a pair of six-year-olds at the top.
A census taker asks a woman the ages of her three children. She tells him their ages, in whole years, multiply to 36 and add up to the number on her front door. He looks at the door and says he still can’t work it out. “My eldest is upstairs in bed with measles,” she says, and now he can. How old are they?
Give me a hintThe hint
Why wasn’t the door number enough on its own?