Tiger And Sheep

Problem

One hundred tigers and one sheep 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 eats the sheep.

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

Hint 1

Again. Think about smaller cases like n=1,2,... for n denoting the number of tigers.

Hint 2

There are only 2 patterns that affect the result.

Hint 3

Take a look at whether n being even or odd.

Show Solution

Consider the smaller cases

Case $n=1$

There is only 1 tiger.
It will eat the sheep immediately, because after becoming a sheep, there are no other tigers left to threaten it.
So the sheep is eaten.

Case $n=2$

Suppose Tiger A considers eating the sheep and turning into a sheep.
After this, there will be 1 tiger left and 1 new sheep (Tiger A as a sheep).
From the $n=1$ subproblem, the remaining tiger would then eat Tiger A (who is now a sheep).
Hence, Tiger A does not eat, and neither does the other tiger.
The sheep survives.

Case $n=3$

Tiger A considers eating the sheep.
After becoming a sheep, there will be 2 tigers left and 1 new sheep (Tiger A as a sheep).
From the $n=2$ subproblem, we know two tigers will not eat a sheep, since they fear retaliation.
Therefore, once Tiger A has eaten and turned into a sheep, no tiger will eat Tiger A.
So the sheep is eaten.

Case $n=4$

General Pattern:

Answer Summary:

In this problem, $n=100$ then no tiger dares to eat the sheep.