Daughters

The man conducting the census asks a woman the age of her three daughters. The woman says when multiplying the age, get the number 72; if their ages add up, get a number of our house, as you see. The man says: That is not enough to calculate their ages. She says, "My oldest daughter has a cat with a wooden leg." The man replies: So now I know their age.

How old is her daughter?

Correct answer:

x =  3
y =  4
z =  6

Step-by-step explanation:

$$\begin{gathered} 72=2\cdot 2\cdot 2\cdot 3\cdot 3=2^3\cdot 3^2 \\ D(72)=set(1,2,3,4,6,8,9,12,18,24,36,72) \\ 72=3\cdot 4\cdot 6 \\ x<y<z<10 \\ x=3 \end{gathered}$$

$y=4$

$z=6$

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