Name: 【TED-Ed】The famously difficult green-eyed logic puzzle - Alex Gendler
Uploaded: 2015-07-09T04:21:53.000Z
Duration: 4 min 42 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

The imperative

all perfect logicians, are imprisoned by a mad dictator.

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

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

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

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

As it happens,  all 100 prisoners have green eyes,

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

they're not allowed  to communicate among themselves.

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

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

After much pressure  from human rights groups,

the dictator reluctantly agrees to let you visit the island

and speak to the prisoners under the following conditions:

and you cannot tell them  any new information.

What can you say  to help free the prisoners

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

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

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

But on the hundredth morning  after your visit,

each having asked to leave the previous night.

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

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

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

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

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

after concluding the statement  could only refer to himself.

Bill simultaneously realizes  the same thing about Adria.

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

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

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

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

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

Adria and Bill were just  watching each other,

and will now both leave  on the second night."

But when he sees both  of them the third morning,

he realizes they must  have been watching him, too.

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

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

The key is the concept  of common knowledge,

The new information was not contained in your statement itself,

but in telling it to everyone  simultaneously.

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

each prisoner also knows  that everyone else is keeping track

of all the green-eyed people they can see,

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

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

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

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

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

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