Can you solve the famously difficult green-eyed logic puzzle? - Alex Gendler

翻译人员: Rebecca Wang 校对人员: Zhuo Wang

Imagine an island where 100 people,

想象在一个岛上，

all perfect logicians, are imprisoned by a mad dictator.

一个疯狂的独裁者囚禁了100个完美的逻辑家

There's no escape, except for one strange rule.

他们没办法逃离，除了一个奇怪的规则

Any prisoner can approach the guards at night and ask to leave.

在晚上任何囚犯都可以请求警卫放他走

If they have green eyes, they'll be released.

若他有绿眼睛，他就会被释放

If not, they'll be tossed into the volcano.

若不是，他就会被扔进火山口

As it happens, all 100 prisoners have green eyes,

实际上，那一百个逻辑家都有绿眼睛

but they've lived there since birth,

但他们从出生起就住在那儿

and the dictator has ensured they can't learn their own eye color.

而且独裁者确保他们不会知道自己眼睛什么颜色

There are no reflective surfaces,

那儿也没有反光表面

all water is in opaque containers,

所有水都装在不透明的容器里

and most importantly,

而且最重要的

they're not allowed to communicate among themselves.

他们不能互相交流

Though they do see each other during each morning's head count.

尽管他们每天早上点人数时都能看到彼此

Nevertheless, they all know no one would ever risk trying to leave

不仅如此，他们都知道 若没有绝对的把握会成功

without absolute certainty of success.

没人会尝试离开

After much pressure from human rights groups,

在人权组织的压力下

the dictator reluctantly agrees to let you visit the island

那个独裁者勉强允许你访问那个岛

and speak to the prisoners under the following conditions:

并且和犯人说话时 要遵从以下条件：

you may only make one statement,

你只可陈述一个声明

and you cannot tell them any new information.

你不能告诉他们新的信息

What can you say to help free the prisoners

你说什么才能帮助这些犯人获得自由

without incurring the dictator's wrath?

而不激怒这位独裁者呢？

After thinking long and hard,

经过深思熟虑

you tell the crowd, "At least one of you has green eyes."

你告诉人群：你们当中 至少有一个人有绿眼睛

The dictator is suspicious

独裁者持有怀疑的态度

but reassures himself that your statement couldn't have changed anything.

但还是告诉自己你的言论不会改变任何事情

You leave, and life on the island seems to go on as before.

你离开了，岛上的生活依然照旧

But on the hundredth morning after your visit,

但在你访问后的第一百天早上

all the prisoners are gone,

所有的犯人都不见了

each having asked to leave the previous night.

每一个人都在前天晚上要求离开

So how did you outsmart the dictator?

所以你是如何智胜独裁者的？

It might help to realize that the amount of prisoners is arbitrary.

意识到犯人的数量不固定也许能帮到你

Let's simplify things by imagining just two, Adria and Bill.

我们来把这个问题简化一下， 假设只有两个犯人，小红和小明

Each sees one person with green eyes,

彼此都能看到对方的绿眼睛

and for all they know, that could be the only one.

他们心里清楚 也许只有对方有绿眼睛

For the first night, each stays put.

所以第一天，谁也没轻举妄动

But when they see each other still there in the morning,

但当他们第二天早上又看到对方时

they gain new information.

他们得到了新的信息

Adria realizes that if Bill had seen a non-green-eyed person next to him,

小红意识到如果小明看到了一个“非绿眼睛”的人在他旁边

he would have left the first night

他就知道自己拥有绿眼睛

after concluding the statement could only refer to himself.

第一天就会离开

Bill simultaneously realizes the same thing about Adria.

小明也同一时间想到了同样的事情

The fact that the other person waited

两个人都在等这个事实

tells each prisoner his or her own eyes must be green.

告诉她或他的眼睛一定是绿色的

And on the second morning, they're both gone.

之后的那天早上，他俩都走了

Now imagine a third prisoner.

现在想象第三个犯人

Adria, Bill and Carl each see two green-eyed people,

小红小明和小刚各看到两个绿眼睛的人

but aren't sure if each of the others is also seeing two green-eyed people,

但不确定另外两人是不是也看到了

or just one.

一个或者两个绿眼睛的人

They wait out the first night as before,

他们第一天也和之前一样等着

but the next morning, they still can't be sure.

到了第二天，他们还是不确定

Carl thinks, "If I have non-green eyes,

小刚想：如果我没有绿眼睛

Adria and Bill were just watching each other,

小红和小明只是看着彼此

and will now both leave on the second night."

那他们第二天早上就会都走了

But when he sees both of them the third morning,

但当他第三天早上看到另外两人时

he realizes they must have been watching him, too.

他意识到那两人肯定也在观察他

Adria and Bill have each been going through the same process,

小红和小明在想同样的事情

and they all leave on the third night.

然后他们三人在第三天晚上都走了

Using this sort of inductive reasoning,

用这种归纳性推理

we can see that the pattern will repeat no matter how many prisoners you add.

我们可以看出这种模式会一直重复， 不论犯人的数量多少

The key is the concept of common knowledge,

关键点是公识的概念

coined by philosopher David Lewis.

来自哲学家David Lewis的创造

The new information was not contained in your statement itself,

新知识不在你的陈述里

but in telling it to everyone simultaneously.

而在于你的声明同时陈述给了所有人

Now, besides knowing at least one of them has green eyes,

现在呢，每个犯人除了知道他们中至少一个有绿眼睛

each prisoner also knows that everyone else is keeping track

也知道其他人都在观察记录

of all the green-eyed people they can see,

他们能看到的所有绿眼睛的人

and that each of them also knows this, and so on.

而且所有人都知道每个人都是这么想的

What any given prisoner doesn't know

每个犯人不知道的是

is whether they themselves are one of the green-eyed people

他们自己是不是别人观察记录的

the others are keeping track of

绿眼睛的人中的一员

until as many nights have passed as the number of prisoners on the island.

直到和犯人数量同等的夜数过去了才能确定

Of course, you could have spared the prisoners 98 days on the island

当然啦，你也可以让犯人早98天离开这岛

by telling them at least 99 of you have green eyes,

告诉他们至少99个人有绿眼睛

but when mad dictators are involved, you're best off with a good headstart.

但当疯狂独裁者在的时候，你最好做出明智的选择