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How Old are Three Daughters?

A census taker walks up to a house and asks the man answering the door to state the number of people in his household. "Five," he says. "There's me, my wife, and my three daughters."

"How old are your daughters?" the census taker asks.

"The product of their ages is 72, and the sum of their ages is the number on my house."

The census taker leaves, but soon he comes back and replies, "That's not enough information."

"Oh, I forgot, the youngest one likes chocolate pudding."

How old are the three daughters? Explain how you found the result.

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