Daughters

The man conducting the census asks a woman to age of three daughters. Woman says when multiply the age getnumber 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 are her daughter?

Result

x =  3
y =  4
z =  6

Solution:

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

$y=4$

$z=6$

The equations have the following integer solutions:

x*y*z = 72
x<y
y<z
s = x+y+z
x>0
y>0
z>0

Number of solutions found: 8

s₁=13, x₁=3, y₁=4, z₁=6
s₂=15, x₂=2, y₂=4, z₂=9
s₃=17, x₃=2, y₃=3, z₃=12
s₄=18, x₄=1, y₄=8, z₄=9
s₅=19, x₅=1, y₅=6, z₅=12
s₆=23, x₆=1, y₆=4, z₆=18
s₇=28, x₇=1, y₇=3, z₇=24
s₈=39, x₈=1, y₈=2, z₈=36

Calculated by our Diofant problems and integer equations.

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