# Brain Teasers | Tiger and Sheep

**Question:**

One hundred tigers and one sheep arc are put on a magic island that only has grass. Tigers can eat grass, but they would rather eat sheep.

**Assume:**

A. Each time only one tiger can eat one sheep, and that tiger itself will become a sheep after it cats the sheep.

B. All tigers are smart and perfectly rational and they want to survive. So will the sheep be eaten?

*Solution:*

Let no of tigers = n

Let’s start with 1 tiger(n=1).

Since there is only one tiger it will definitely eat the sheep as there will be no more tigers to eat him once he becomes a sheep.

With n=2 tigers,

If any of the tigers eat the sheep, it will become a sheep itself so the other tiger who is left will definitely eat him. So none of the tigers will eat the sheep.

With n=3 tigers,

The sheep will be eaten since each tiger realizes that once it becomes a sheep there will be two tigers left and none of the two tigers will eat the sheep. So the first tiger to realize this will eat the sheep.

With n=4 tigers,

Each tiger realizes that once it becomes a sheep it will be eaten as three tigers will be left. So none of the tigers will eat the sheep.

**In general:**

When n = odd, the sheep will be eaten

When n = even, the sheep will not be eaten.

For the given question where n= 100, the sheep will not be eaten.

https://quantifiers101.blogspot.com/2021/10/puzzle-tiger-and-sheep.html