The Wolves and Sheep Dilemma
On an island in a far away country there is a population of 100 wolves and 1 sheep. They are the only two living species on the island. The following facts are known to be true:
- There is grass covering the whole island (grass is not considered as a living species for the purposes of the problem).
- The sheep can survive just by eating grass throughout its lifespan.
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As the grass is being eaten, it instantaneously grows back. No matter how many times it gets eaten, it will always grow back. It is therefore suitable to state that the island has an infinite supply of grass.
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The wolves themselves, unlike the sheep, are part of a very rare and intelligent species. They are actually perfectly rational beings, and can be considered as being infinitely intelligent.
- Similarly to the sheep, the wolves can also survive by eating grass throughout their whole lifespan.
- As one might imagine, the wolves prefer eating sheep than eating grass.
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If the sheep were to be eaten, it could only be eaten by a single wolf (the wolves cannot share their prey). However, there is catch:
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In this faraway land it is known that after a wolf eats a sheep, the wolf itself will become a sheep and it will therefore be in danger of being eaten by other wolves.
- All wolves are perfectly aware of this.
- If a wolf knows for sure that eating the sheep will cause him to be eaten by another wolf, then it prefers to eat grass instead.
- In the same way, if the wolf knows that eating the sheep will not put him in danger, it will eat the sheep.
Given all these facts and given the scenario from the very beginning, the question which must be answered is the following:
Will the sheep be eaten?
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This is more of an induction problem as it is easier to figure out what is going on for a smaller number of wolves. Let's consider several cases:
This logic can go on for any number of wolves and it soon becomes apparent that if the number of wolves on the island is odd, the sheep will be eaten, and if the number of wolves is even the sheep will be safe. Consequently, for the original problem where there are 100 wolves (even number), the sheep will NOT be eaten.