Challenge of the Week: Crack Dadi's Grandchildren Age Riddle

Pull up a chair, sharpen your pencil, and start the clock. This week's teaser comes wrapped in the warm chaos of an Indian family wedding — the kind where a sharp-eyed grandmother can out-think a roomful of guests before the next round of chai arrives. At first glance it looks like there simply isn't enough information to solve it. There is. The trick is to listen as carefully as the puzzle's hero does. Can you crack it before the timer runs out?

The Challenge

At a wedding in Jaipur, Dadi (grandmother) is gently teasing a new neighbour who has come to pay his respects.

"I have three grandchildren," she says. "Each of their ages, in whole years, is a positive number. Multiply the three ages together and you get exactly 72."

The neighbour thinks for a moment, then asks for more. Dadi points to the big brass numeral nailed above her front gate. "Add the three ages together," she says, "and you get that number — the number of my house, the one you walked past on your way in."

The neighbour knows that gate number perfectly well. He scribbles, frowns, and finally admits: "I'm sorry, Dadiji — even knowing that sum, I still can't be sure of their ages."

Dadi smiles and offers one last morsel. "My eldest grandchild won the school chess trophy last week."

"Of course!" says the neighbour, and states the three ages correctly.

Your task: Find the three ages. The rules: all ages are positive whole numbers, their product is 72, and every statement above is both true and necessary.

Hint

The neighbour could see the gate number with his own eyes, yet that still wasn't enough to decide. Ask yourself: what must be special about that particular sum for an honest, clever person to remain stuck? Then list the possibilities like a detective.