How can you tell each type of animal?

Question

On a farm they keep black and white goats and black and white sheep. Two shipyards take 50 animals out of them to the meadow. On the way there, one of the sheppards counts the number of white animals, and the other sheppard counts the number of sheep. From these two numbers they want to know how many black goats and white goats and how many black sheep and white sheep are there with them. Give an example when they can, and give an example when they cannot do it.

Answer 1

There are 50 animals.

Let's say there are S sheep and G goats.

S + G = 50

Let's say there are B black animals and W white animals.

B + W = 50

If the shepherd who counts the sheep counts either 50 sheep or 0 sheep then they CAN do it.

If the shepherd who counts the number of white animals counts either 50 white animals or Zero white animals then they CAN do it.

However, if neither shepherd counts either 50 or Zero then they CANNOT do it. You cannot solve the simultaneous equations

S + G = 50

B + W = 50

unless either S, G, B, or W are Zero, OR you know the colour proportions of one of the species.