# Inheritance vaccine

A farmer had 30 cows and 60 calves. 10 of the cows were white, 10 were black and 10 were brown. Each of the white cows had 3 calves, each of the black cows had 2 calves and each of the brown cows had 1 calf.

When he died, he wrote in his will that each of his three children should receive the same number of cows and calves, that each calf should go with his mother, that each child should receive at least one cow of each color and that each son should not own more than half of cows of the same color.

How is it possible to make the cast?

#### Solution

The distribution must be done as follows:

The first child corresponds:

• 3 white cows and their 9 calves
• 4 black cows and their 8 calves
• 3 brown cows and their 3 calves

In total 10 cows and 20 calves

The second child corresponds:

• 3 white cows and their 9 calves
• 4 black cows and their 8 calves
• 3 brown cows and their 3 calves

In total 10 cows and 20 calves

And the third child corresponds:

• 4 white cows and their 12 calves
• 2 black cows and their 4 calves
• 4 brown cows and their 4 calves

In total 10 cows and 20 calves.

With this distribution all the conditions of the will are fulfilled.