Solving the Farmer's Animal Riddle

This riddle involves understanding the meaning of the phrase "all but two" in relation to the total number of animals.

Interpreting the Clues

Let T represent the total number of animals the farmer has.

Let C be the number of cows, H be the number of horses, and P be the number of pigs.

The statement "all but two were cows" means the number of animals that are *not* cows is 2. The animals that are not cows are horses and pigs. So:

• H + P = 2

Similarly, "all but two were horses" means the number of animals that are *not* horses is 2. These are cows and pigs.

• C + P = 2

And "all but two were pigs" means the number of animals that are *not* pigs is 2. These are cows and horses.

• C + H = 2

Solving the Equations

We now have a system of three equations:

1. $ H + P = 2 $
2. $ C + P = 2 $
3. $ C + H = 2 $

From equations (1) and (2), since both equal 2:

$ H + P = C + P $

Subtracting P from both sides gives $ H = C $.

From equations (2) and (3), since both equal 2:

$ C + P = C + H $

Subtracting C from both sides gives $ P = H $.

Therefore, we have $ C = H = P $.

Now substitute $ H = C $ into equation (3):

$ C + C = 2 $

$ 2C = 2 $

$ C = 1 $

Since $ C = H = P $, it means $ H = 1 $ and $ P = 1 $.

Calculating the Total Animals

The total number of animals (T) is the sum of cows, horses, and pigs:

$ T = C + H + P $

$ T = 1 + 1 + 1 $

$ T = 3 $

The farmer had a total of 3 animals.