One hundred tigers and one sheep are placed 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.
Will the tigers eat the sheep?
Solution: 100 is a large number, so let’s start with a simplified version of the problem.
If there is only 1 tiger (n =1), surely it will eat the sheep since it does not need
to worry about being eaten.
How about 2 tigers? Since both tigers are perfectly rational, either tiger probably would do some thinking as to what will happen if it eats the sheep.
Both Tigers are probably thinking, if I eat the sheep, I will become a sheep; and then the other tiger will eat me. So to guarantee the highest likelihood of survival, neither tiger will eat the sheep.
If there are 3 tigers, the sheep will be eaten since each tiger will realize that once it changes to a sheep, there will be 2 tigers left and it will not be eaten. Therefore, the first tiger that thinks this through will eat the sheep. If there are 4 tigers, each tiger will understand that if it eats the sheep, it will turn to a sheep. Since there are 3 other tigers, it will be eaten.
So to guarantee the highest likelihood of survival, no tiger will eat the sheep.
Following the same logic, we can naturally show that if the number of tigers is even, the sheep will not be eaten. If the number is odd, the sheep will be eaten. For the case
n =100, the sheep will not be eaten.