### Brain Teasers

# Survival of the Sheep

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?

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?

### Hint

There are two hints. The first one will really be just that - a small hint. The second one is a BIG one, and could very well give it away, so don't read it if you don't want to:Hint 1) Use math induction.

Hint 2) Consider the scenario where there is only one lion and one sheep. What would happen? Now take the next step.

### Answer

The sheep would remain untouched.In fact, the sheep would remain untouched if there is an even number of lions on the island, and would be eaten immediately if there is an odd number of lions on the island.

Here's the reasoning:

Consider a scenario with just one lion and one sheep: The lion will eat the sheep. Why? Because after he eats it and turns into a sheep himself, there aren't any lions on the island to eat him, so he is happy.

Now look at a scenario with 2 lions and 1 sheep. Here the sheep would remain unharmed. Why? Because if any one of them eats it, and turns into a sheep himself, he knows that he awaits certain death because he will then be a sheep and the other lion will be the only lion on the island and nothing will stop him from eating the sheep.

So now we know for a fact 1 lion and 1 sheep - sheep gets eaten. 2 lions and 1 sheep - sheep doesn't get eaten.

We can now make a conclusion about 3 lions and 1 sheep: the sheep will definitely be eaten, because the lion that eats it will know that by eating he leaves behind 2 lions and 1 sheep (himself). And as we already know 2 lions and 1 sheep is a situation where the sheep survives.

You can use the same logic to go on to 4 lions and 1 sheep, and then all the way to 100 or 1000, but it will always be true that with an odd number of lions the sheep gets eaten and with an even number the sheep doesn't.

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