Goat and lions

fzy · 发表于 2005-3-9 22:09:05

There are 53 lions and a goat in a cage.

1) Now if a lion eats a goat then the lion becomes a goat.

2) Each and every lion is as intelligent as others.(i.e. they know the
consequences of eating a goat)

3) A lion prefers to eat a goat.....but he does not want himslef to get
killed after becoming a goat.....i.e if he knows that after eating a goat ,
he is gonna get eaten up by other lions then he will not eat it....

Consdering this situation and above 3 knowledge base can you tell me whether the goat will be eaten or not?

Remark by fzy: The problem does not make a lot of real sense because a lion would not want to spend the rest of his life as a goat. But assume he prefers it as long as he will not be eaten. Treat it as a logical problem.

ob · 发表于 2005-3-9 22:59:55

share the goat. If a lion does not eat the whole goat, it may not become a goat. If eat a piece of goat meat will turn a lion to a goat, then try to change every lion into a goat.

One question: will a lion starve to death if it does not eat that goat?

新用户 · 发表于 2005-3-9 23:04:44

我想你错误的理解了题目的原意，

只是一道逻辑题，，所以我的理解是：要么选择吃，要么选择不吃；如果吃了，就的冒着生命危险。

如果知道吃了以后没有关系，自己不会被吃掉，那他一定吃。

我的看法：

只有当一头狮子认为其他的52只狮子不会冒着生命危险吃山羊时，他才会先吃山羊。很显然，他不能确信，所以他不会吃。所有其他的52头狮子想法也一样。所以我认为，山羊不会被吃掉

fzy · 发表于 2005-3-9 23:09:46

You understand the problem correctly. But the solution is more complicated. Remember there are 53 lions? The number is important.

sean9991 · 发表于 2005-3-9 23:14:47

The quickest lion will eat the goat and change to goat. No other lion will dare to eat the goat from that point on. As long as the total number of lions is even, it's a stable situation.

fzy · 发表于 2005-3-9 23:24:51

correct

y · 发表于 2005-3-10 07:00:08

Why no lions will eat the goat if the number of lions is even?

sean9991 · 发表于 2005-3-10 07:25:07

Let L denotes a lion, and G denotes a goat.

consider the case of {L, L, G}, no lion dares to eat the goat and becomes the G of {L, G}, as it will be the victim next.

now consider {L, L, L, G}, since the goat in {L, L, G} is safe, the quickest lion will eat the goat and the situation becomes {L, L, G}, a stable one.

how about {L, L, L, L, G}, no lion wants to eat the goat and becomes the G of {L, L, L, G}.

We can easily extends this to more lions in the samilar vein.

新用户 · 发表于 2005-3-10 07:52:01

谢谢解释，我也明白了。看来这样方法论解决问题很有效：从简单的状况下考虑。

记得21个海盗题也是用这样方法分析的

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Goat and lions

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It is a little more complicated than that.

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