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:

The equations have the following integer solutions:

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

s₁=-5, x₁=-6, y₁=-3, z₁=4
s₂=-2, x₂=-6, y₂=-2, z₂=6
s₃=-1, x₃=-4, y₃=-3, z₃=6
s₄=3, x₄=-4, y₄=-2, z₄=9
s₅=5, x₅=-6, y₅=-1, z₅=12
s₆=7, x₆=-3, y₆=-2, z₆=12
s₇=13, x₇=-4, y₇=-1, z₇=18
s₈=13, x₈=3, y₈=4, z₈=6
s₉=15, x₉=2, y₉=4, z₉=9
s₁₀=17, x₁₀=2, y₁₀=3, z₁₀=12
s₁₁=18, x₁₁=1, y₁₁=8, z₁₁=9
s₁₂=19, x₁₂=1, y₁₂=6, z₁₂=12
s₁₃=20, x₁₃=-3, y₁₃=-1, z₁₃=24
s₁₄=23, x₁₄=1, y₁₄=4, z₁₄=18
s₁₅=28, x₁₅=1, y₁₅=3, z₁₅=24

Number of solutions found: 15

Calculated by our Diofant problems and integer equations.

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