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=22233=2332 D(72)={1,2,3,4,6,8,9,12,18,24,36,72}  72=346 x<y<z<10 x=3 y=4 z=6 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=4y=4
z=6z=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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