The original tigers and sheep brain teaser is : hundred tigers and one sheep are put on a magic island that only has grass. Tigers can live on grass, but they want to eat sheep. If a Tiger bites the Sheep then it will become a sheep itself. If 2 tigers attack a sheep, only the first tiger to bite converts into a sheep. Tigers don't mind being a sheep, but they have a risk of getting eaten by another tiger. All tigers are intelligent and want to survive. Will the sheep survive?

Follow up questions:

1. When a tiger bites the sheep, there will be a probability p that the tiger becomes a sheep. Considering such a reward rule: when eating a sheep, gets 1 point, when being eaten, gets -2 point. What will the solution goes?