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

Number of solutions found: 15

Calculated by our Diofant problems and integer equations.

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