Tiger & Sheep Puzzle..Will Sheep Survive or Not

Hundred tigers and one sheep are put on a magic island that only has grass. Tigers can live on grass, but they would rather eat sheep. Its a Magic Iceland because if a Tiger eats the Sheep then it will become a sheep itself (and hence can be eaten up by another tiger).

Tigers don’t mind being a sheep, but they would never want themselves to be eaten up. All tigers are intelligent and they want to survive. They however, don’t care of survival of others.

Will the sheep survive or will it be eaten up?

Solution:

This problem and the problem of pirates belong to the same family of Puzzles, where the puzzle is solved by simplification. Lets Consider the case when there are less Tigers

If there is 1 tiger, then he will eat the sheep because he does not need to worry about being eaten. Sheep will Not survive.

If there are 2 tigers, Both of them knows that if he eats the Sheep, the other tiger will eat him. So, The Sheep will Survive.

If there are 3 tigers, then they each of them knows that if he eats up the Sheep, then Iceland will be left with 1 sheep and 2 Tigers and as shown in the previous case, the Sheep will survive. Hence each tiger will try to eat up the sheep. The sheep will Not Survive.

If there are 4 Tigers, then the sheep will Survive.

And so on….

So, If there are even number of tigers the sheep will Survive, else it will die. Hence, if there are 100 tigers the sheep will Survive.