In the jungles of Noway Magic Island there are the following animals: 17

**A**ntelopes, 55

**W**olves and 5

**L**ions.

The following laws of the jungle exist:

**L**ion eats both **W**olves and **A**ntelopes.

**W** eats **A only.**

When **L** eats a **W** he becomes an **A.**

When he eats a **A** he becomes an **W**.

When **W** eats a **A** he becomes an **L**.

What is the maximal possible amount of animals, such that no one can eat anyone?

The only way nobody can eat anybody else is if they are all the same type. Since we are starting with 55 wolves, let's make them all wolves.

1) 5 lions eat 5 antelopes, leaving 12 Antelopes and 60 Wolves

2) Then 6 Wolves eat 6 antelopes (half of the remaining), leaving 6 Antelopes, 54 wolves, and 6 lions

3) Then the lions eat the 6 antelopes, leaving **60 wolves. Final answer**

It is pretty clear that this is optimal. Only 17 animals have been eaten. Getting rid of all of the wolves require at least 55 eatings.

In retrospect, this could have been done in two steps.

1) 6 wolves eat 6 antelopes, leaving 11 Antelopes, 49 wolves, and 11 lions

2) The lions eat all the antelopes.