Best Answer bonanova, 04 April 2013 - 09:03 AM

. . . Bulls Cows Total

white . a . . b . a+b

black . c . . d . c+d

spotted e . . f . e+f

brown . g . . h . g+h

Equations:

(1) a = g + (5/6)c

(2) c = g + (9/20)e

(3) e = g + (13/42)a

(4) b = 7/12 (c+d)

(5) d = 9/20 (e+f)

(6) f = 11/30 (g+h)

(7) h = 13/42 (a+b)

These equations are invariant under multiplication,

so we can only determine relative numbers.

The first three equations lead to

2376a = 5936g

If we set

a = 5936

g = 2376

we get

c = (a-g)(6/5) = 4272

e = (c-g)(20/9) = 4213.3333

So we multiply all values by 3:

a = 17808

c = 12816

e = 12640

g = 7128

Substituting into (4)-(7) we get

b = bo + (7/21)d where bo = (7/12)c = 7476

d = do + (9/20)f where do = (9/20)e = 5688

f = fo + (11/30)h where fo = (11/30)g = 2613.6

h = ho + (13/42)b where ho = (13/42)a = 5512

Because (11/30)g is not integral, we multiply a c e and g by 10

and also bo do fo and ho

a = 178080

c = 128160

e = 126400

g = 71280

Substituting to eliminate d, f, h gives

b{1-(7/12)(9/20)(11/30)(13/42)} = bo + (7/12)do + (7/12)(9/20)fo + (7/12)(9/20)(11/30)ho

0.9702083333b = 120106

b = 123794.0305

Now to get integer values we multiply by 10000

b = 1237940305

substituting, we get

h = 934371999.2

f = 603963066.3

d = 840583379.7

b = 1237940305

On final multiplication by 10 gives

a = 17808000000

c = 12816000000

e = 12640000000

g = 7128000000

h = 9343719992

f = 6039630663

d = 8405833797

b = 12379403050

A large herd, even by Texas standards.