Survival of the Sheep Puzzle

[mskavi]

Survival of the Sheep Puzzle


There is an island filled with grass and trees and plants. The only inhabitants are 100 lions and 1 sheep.
The lions are special :
1) They are infinitely logical, smart, and completely aware of their surroundings.
2) They can survive by just eating grass (and there is an infinite amount of grass on the island).
3) They prefer of course to eat sheep.
4) Their only food options are grass or sheep.

Now, here's the kicker:

5) If a lion eats a sheep he TURNS into a sheep (and could then be eaten by
other lions).
6) A lion would rather eat grass all his life than be eaten by another lion (after he turned into a sheep).

Assumptions :
1) Assume that one lion is closest to the sheep and will get to it before
all others. Assume that there is never an issue with who gets to the sheep
first. The issue is whether the first lion will get eaten by other lions
afterwards or not.
2) The sheep cannot get away from the lion if the lion decides to eat it.
3) Do not assume anything that hasn't been stated above.

So now the question:

Will that one sheep get eaten or not and why?

---

[Admin]

The sheep wont get eaten in its lifetime. The lions are intelligent and will refrain from eating the sheep.
So the only choice is that the sheep dies natural death.

Will the lions still turn to eating a dead sheep?

[Admin]

Ans: The sheep will not get eaten.
Reason:
1. If there was only 1 lion, it would definitely eat the sheep.
2. If there were 2 lions, each one would think if it eats the sheep, the other one would eat him and hence both wouldnt eat the sheep.
3. If there were 3 lions, the first lion thats gonna eat the sheep knows that after it eats the sheep there will be only 2 lions left and both wouldnt eat him (by case 2).
4. In case there were 4 lions, all the lions know that the first one thats gonna eat the sheep will be eaten by one more (by case 3, since only 3 will be left) and hence none would dare to eat it.

Thus if there were odd number of lions, the sheep would have been eaten.. but since there are even number of lions, the sheep is safe.