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The Census Taker Problem

A census taker knocks on a door. A woman answers. The census taker says, "I need to know the number of children you have, and their ages". The woman responds, "I have three daughters, the product of their ages is 36 and the sum of their ages is equal to the house number next door". The census taker says "Thank you", and leaves.

A minute later the census taker returns and says, "I need more information". The woman responds, "My oldest daughter is upstairs taking a nap". The census taker writes down the correct ages and leaves.

How old are the children?

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