# 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=-8, x1=-8, y1=-3, z1=3s2=-7, x2=-6, y2=-4, z2=3s3=-7, x3=-9, y3=-2, z3=4s4=-5, x4=-6, y4=-3, z4=4s5=-2, x5=-6, y5=-2, z5=6s6=-2, x6=-9, y6=-1, z6=8s7=-1, x7=-4, y7=-3, z7=6s8=0, x8=-8, y8=-1, z8=9s9=3, x9=-4, y9=-2, z9=9s10=5, x10=-6, y10=-1, z10=12s11=7, x11=-3, y11=-2, z11=12s12=13, x12=3, y12=4, z12=6s13=13, x13=-4, y13=-1, z13=18s14=15, x14=2, y14=4, z14=9s15=17, x15=2, y15=3, z15=12s16=18, x16=1, y16=8, z16=9s17=19, x17=1, y17=6, z17=12s18=20, x18=-3, y18=-1, z18=24s19=23, x19=1, y19=4, z19=18s20=28, x20=1, y20=3, z20=24s21=33, x21=-2, y21=-1, z21=36s22=39, x22=1, y22=2, z22=36

Number of solutions found: 22

Calculated by our Diofant problems and integer equations.

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