Can you solve the prisoner hat riddle? - Alex Gendler

Prevodilac: Ivana Krivokuća Lektor: Tijana Mihajlović

You and nine other individuals have been captured

Vas i devet drugih osoba su zarobili

by super intelligent alien overlords.

superinteligentni vanzemaljci.

The aliens think humans look quite tasty,

Vanzemaljci misle da ljudi izgledaju prilično ukusno,

but their civilization forbids eating highly logical and cooperative beings.

ali njihova civilizacija im zabranjuje da jedu

izuzetno smislena bića koja sarađuju.

Nažalost, nisu sigurni da vi ispunjavate taj uslov,

Unfortunately, they're not sure whether you qualify,

so they decide to give you all a test.

pa su rešili da svima vama zadaju test.

Through its universal translator,

Preko svog univerzalnog prevodioca,

the alien guarding you tells you the following:

vanzemaljac koji vas čuva saopštava vam sledeće:

You will be placed in a single-file line facing forward in size order

bićete smešteni u redu jedan iza drugog okrenuti ka napred, po svojoj visini,

so that each of you can see everyone lined up ahead of you.

tako da svako od vas može da vidi svakog ko je ispred vas u redu.

You will not be able to look behind you or step out of line.

Nećete moći da gledate iza sebe niti da iskoračite iz reda.

Each of you will have either a black or a white hat on your head

Svako od vas će na glavi imati ili crni ili beli šešir,

assigned randomly,

nasumično dodeljen,

and I won't tell you how many of each color there are.

a neću vam reći koliko ima šešira svake boje.

When I say to begin, each of you must guess the color of your hat

Kada kažem da počnete, svako od vas mora da pogodi boju svog šešira

starting with the person in the back and moving up the line.

počevši od osobe na začelju, krećući se ka početku reda.

And don't even try saying words other than black or white

Nemojte ni da pokušate da izgovorite drugu reč osim „crno“ i „belo“

or signaling some other way, like intonation or volume;

ili da date znak na neki drugi način, na primer, intonacijom ili jačinom;

you'll all be eaten immediately.

odmah ćete svi biti pojedeni.

If at least nine of you guess correctly, you'll all be spared.

Ako makar devet vas tačno pogodi, svi ćete biti pošteđeni.

Imate pet minuta da diskutujete i da osmislite plan,

You have five minutes to discuss and come up with a plan,

and then I'll line you up, assign your hats, and we'll begin.

a zatim ću vas poređati, dodeliti vam šešire i počećemo.

Can you think of a strategy guaranteed to save everyone?

Da li se se možete dosetiti strategije koja će garantovano spasiti sve?

Pause the video now to figure it out for yourself.

Pauzirajte video kako biste otkrili sami.

Odgovor za: 3.

Answer in: 3

Odgovor za: 2.

Answer in: 2

Answer in: 1

Odgovor za: 1.

Ključ je da osoba na začelju reda

The key is that the person at the back of the line

who can see everyone else's hats can use the words "black" or "white"

koja vidi svačije šešire može da koristi reči „crno“ ili „belo“

to communicate some coded information.

da bi prenela šifrovane informacije.

So what meaning can be assigned to those words

Dakle, koje značenje se može dodeliti tim rečima

that will allow everyone else to deduce their hat colors?

koje će svima ostalima omogućiti da donesu zaključak o boji svog šešira?

It can't be the total number of black or white hats.

To ne može biti ukupan broj crnih ili belih šešira.

There are more than two possible values,

Postoji više od dve moguće vrednosti,

but what does have two possible values is that number's parity,

ali ono što ima dve moguće vrednosti je paritet tog broja,

that is whether it's odd or even.

odnosno, da li je paran ili neparan.

So the solution is to agree that whoever goes first will,

Dakle, rešenje je složiti se oko toga da onaj ko kreće prvi,

for example, say "black" if he sees an odd number of black hats

na primer, kaže „crno“ ako vidi neparan broj crnih šešira

and "white" if he sees an even number of black hats.

i „belo“ ako vidi paran broj crnih šešira.

Let's see how it would play out if the hats were distributed like this.

Hajde da vidimo kako bi se to odvijalo kada bi šeširi bili ovako raspodeljeni.

The tallest captive sees three black hats in front of him,

Najviši zarobljenik vidi tri crna šešira ispred sebe,

so he says "black," telling everyone else he sees an odd number of black hats.

tako da kaže „crno“, rekavši ostalima da vidi neparan broj crnih šešira.

He gets his own hat color wrong, but that's okay

Nije pogodio boju svog šešira, ali to je u redu

since you're collectively allowed to have one wrong answer.

jer vam je dozvoljeno da zajedno imate jedan pogrešan odgovor.

Prisoner two also sees an odd number of black hats,

Drugi zatvorenik takođe vidi neparan broj crnih šešira,

so she knows hers is white, and answers correctly.

tako da zna da je njen beo, i daje tačan odgovor.

Prisoner three sees an even number of black hats,

Treći zatvorenih vidi paran broj crnih šešira,

so he knows that his must be one of the black hats

tako da zna da njegov šešir mora biti jedan od crnih šešira

the first two prisoners saw.

koje su videla prva dva zatvorenika.

Prisoner four hears that and knows

Četvrti zatvorenik to čuje i zna

that she should be looking for an even number of black hats

da treba da traži paran broj crnih šešira

since one was behind her.

jer je jedan bio iza nje.

But she only sees one, so she deduces that her hat is also black.

Međutim, ona vidi samo jedan, tako da zaključuje da je i njen šešir crn.

Prisoners five through nine are each looking for an odd number of black hats,

Svako od petog do devetog zatvorenika traži neparan broj crnih šešira,

which they see, so they figure out that their hats are white.

što i vide, tako da zaključuju da su njihovi šeširi beli.

Now it all comes down to you at the front of the line.

Sada sve ostaje na vama na početku reda.

Ako je deveti zatvorenik video neparan broj crnih šešira,

If the ninth prisoner saw an odd number of black hats,

that can only mean one thing.

to može da znači samo jedno.

Videćete da ova strategija funkcioniše za bilo koji raspored šešira.

You'll find that this strategy works for any possible arrangement of the hats.

The first prisoner has a 50% chance of giving a wrong answer about his own hat,

Prvi zatvorenik ima 50% šanse da da pogrešan odgovor o svom šeširu,

but the parity information he conveys

ali informacija o paritetu koju on saopštava

allows everyone else to guess theirs with absolute certainty.

omogućava svima ostalima da pogode svoj sa apsolutnom sigurnošću.

Each begins by expecting to see an odd or even number of hats

Svako započinje očekujući da vidi neparan ili paran broj šešira

of the specified color.

određene boje.

If what they count doesn't match, that means their own hat is that color.

Ako se ono što izbroje ne uklapa, to znači da je njihov šešir te boje.

And everytime this happens,

I svaki put kada se to dogodi,

the next person in line will switch the parity they expect to see.

sledeća osoba u redu će promeniti paritet koji očekuje da vidi.

So that's it, you're free to go.

Dakle, to je to, možete da idete.

It looks like these aliens will have to go hungry,

Izgleda da će ovi vanzemaljci morati da ostanu gladni,

or find some less logical organisms to abduct.

ili da nađu da otmu neke manje smislene organizme.