# Cryptic Woman and a Confused Census-Taker [duplicate]

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I recently found a card on which there were two puzzles, both of which have me stumped; I want to spend a little more time on the other puzzle, but here is one that stumps me:

no 65
A census-taker calls at a house. He asks the woman living there the ages of her three daughters. The woman says, “If you multiply their ages the total is 72; if you add together their ages the total is the same as the number on my front door, which you can see.”
The census-taker says, “That is not enough information for me to calculate their ages.”
The woman says, “Well, my eldest daughter has a cat with a wooden leg.”
The census-taker replies, “Ah! Now I know their ages.”

What are the ages of the three girls?

# Attempt

Let $d_0,d_1,d_2$ be the ages of the three daughters, with $d_i\leq d_{i+1}$. We know that $d_0d_1d_2=72$ and that $d_0+d_1+d_2=n$, $n$ being the house number. The problem does not give the house number; that is where I am stumped. (HINT: The second-to-last line gives that there is an eldest daughter, making true $d_0\leq d_1<d_2$.)