Can you solve the prisoner boxes riddle? - Yossi Elran

Prevoditelj: Tomas Kurbanović Recezent: Sanda L

Your favorite band is great at playing music,

Tvoj omiljeni bend je odličan u sviranju,

but not so great at being organized.

ali ne tako dobar kada se treba organizirati.

They keep misplacing their instruments on tour,

Stalno zameću svoje instrumente na turneji,

and it's driving their manager mad.

a to izluđuje njihovog menadžera.

On the day of the big concert,

Na dan velikog koncerta,

the band wakes up to find themselves tied up

članovi benda probude se zatočeni

in a windowless, soundproof practice room.

u zvučno izoliranoj sobi za probe bez prozora.

Their manager explains what's happening.

Njihov menadžer objasni im što se događa.

Outside, there are ten large boxes.

Vani je deset velikih kutija.

Svaka sadrži jedan od vaših instrumenata,

Each contains one of your instruments,

but don't be fooled by the pictures - they've been randomly placed.

ali ne dajte da vas slike zavaraju; postavljene su nasumično.

I'm going to let you out one at a time.

Puštat ću vas jednog po jednog.

While you're outside, you can look inside any five boxes

Dok ste vani, možete pogledati u bilo kojih pet kutija,

before security takes you back to the tour bus.

prije nego vas zaštitari vrate u autobus.

You can't touch the instruments

Ne smijete dirati instrumente

or in any way communicate what you find to the others.

ili na neki način drugima pokušati reći što ste našli.

No marking the boxes, shouting, nothing.

Nema označavanja kutija, vikanja, ničega.

If each one of you can find your own instrument,

Ako svatko od vas uspije naći svoj instrument,

then you can play tonight.

večeras možete svirati.

Otherwise, the label is dropping you.

U suprotnom, diskografska kuća raskida ugovor s vama.

You have three minutes to think about it before we start.

Imate tri minute za razmišljanje prije početka.

The band is in despair.

Bend je u očaju.

After all, each musician only has a 50% chance of finding their instrument

Svaki glazbenik ima samo 50% šanse za pronalaženje svog instrumenta,

by picking five random boxes.

bude li birao pet nasumičnih kutija.

And the chances that all ten will succeed are even lower -

Šanse da svi uspiju čak su i manje;

just 1 in 1024.

samo 1 : 1024.

But suddenly, the drummer comes up with a valid strategy

Iznenada, bubnjar je iznio razumnu strategiju

that has a better than 35% chance of working.

koja ima više od 35% šanse za uspjeh.

Možeš li shvatiti što je predložio?

Can you figure out what it was?

Pause the video on the next screen if you want to figure it out for yourself!

Pauziraj video na idućem zaslonu ako želiš sam riješiti zagonetku.

Answer in: 3

Odgovor za: 3

Answer in: 2

Odgovor za: 2

Answer in: 1

Odgovor za: 1

Here's what the drummer said:

Bubnjar je rekao sljedeće:

Everyone first open the box with the picture of your instrument.

Svatko neka prvo otvori kutiju sa slikom svojeg instrumenta.

If your instrument is inside, you're done.

Ako je unutra tvoj instrument, gotov si.

Otherwise, look at whatever's in there,

U suprotnom, pogledaj što je u kutiji

and then open the box with that picture on it.

i zatim otvori kutiju koja ima sliku tog instrumenta.

Keep going that way until you find your instrument.

Nastavi dok ne nađeš svoj instrument.

The bandmates are skeptical,

Članovi benda su skeptični,

but amazingly enough, they all find what they need.

no, začuđujuće, svi nađu što trebaju.

And a few hours later, they're playing to thousands of adoring fans.

Nekoliko sati kasnije, sviraju za tisuće svojih obožavatelja.

So why did the drummer's strategy work?

Zašto je bubnjarova strategija djelovala?

Each musician follows a linked sequence

Svaki glazbenik prati povezani niz

that starts with the box whose outside matches their instrument

koji počinje kutijom čija slika odgovara njihovom instrumentu

and ends with the box actually containing it.

i završava kutijom koja ga sadrži.

Opazi da bi se vratili na početak kada bi nastavili,

Note that if they kept going, that would lead them back to the start,

so this is a loop.

dakle, ovo je petlja.

For example, if the boxes are arranged like so,

Na primjer, da su kutije ovako poslagane,

the singer would open the first box to find the drums,

pjevačica bi otvorila prvu kutiju i našla bubnjeve,

go to the eighth box to find the bass,

otišla do osme kutije i našla bas gitaru

and find her microphone in the third box,

i našla mikrofon u trećoj kutiji,

which would point back to the first.

koja bi je vodila natrag do prve.

This works much better than random guessing

Ovo djeluje puno bolje od nasumičnog pogađanja,

because by starting with the box with the picture of their instrument,

jer ako započne kutijom sa slikom svojeg instrumenta,

each musician restricts their search to the loop that contains their instrument,

svaki glazbenik ograničava potragu na petlju koja sadrži njihov instrument

and there are decent odds, about 35%,

i postoji pristojna mogućnost, oko 35%,

that all of the loops will be of length five or less.

da će sve petlje biti duge pet ili manje koraka.

How do we calculate those odds?

Kako smo izračunali tu mogućnost?

For the sake of simplicity, we'll demonstrate with a simplified case,

U svrhu jednostavnosti, demonstrirat ćemo na pojednostavljenom slučaju;

four instruments and no more than two guesses allowed for each musician.

četiri instrumenta i ne više od dva pokušaja po glazbeniku.

Let's start by finding the odds of failure,

Počnimo pronalaženjem mogućnosti neuspjeha,

the chance that someone will need to open three or four boxes

slučajem da će netko morati otvoriti tri ili četiri kutije,

before they find their instrument.

prije nego pronađe svoj instrument.

There are six distinct four-box loops.

Postoji šest jedinstvenih petlji s četiri kutije.

One fun way to count them is to make a square,

Jedan zabavan način da ih izbrojiš jest da napraviš kvadrat.

put an instrument at each corner,

Stavi po jedan instrument u svaki kut

and draw the diagonals.

i povuci dijagonale.

See how many unique loops you can find,

Vidi koliko jedinstvenih petlji možeš naći,

and keep in mind that these two are considered the same,

ali imaj na umu da se ove dvije smatraju jednakima,

they just start at different points.

samo kreću iz različite točke.

These two, however, are different.

Međutim, ove su dvije različite.

We can visualize the eight distinct three-box loops using triangles.

Možemo si predočiti osam različitih petlji s tri kutije koristeći trokute.

You'll find four possible triangles

Naći ćeš četiri moguća trokuta,

depending on which instrument you leave out,

ovisno o instrumentu kojeg izostaviš,

and two distinct paths on each.

i dva različita puta na svakom.

So of the 24 possible combinations of boxes,

Dakle, od 24 mogućih kombinacija kutija,

there are 14 that lead to faliure,

14 ih vodi k neuspjehu,

and ten that result in success.

a 10 rezultira uspjehom.

That computational strategy works for any even number of musicians,

Ta računska strategija vrijedi za sve parne brojeve glazbenika,

but if you want a shortcut,

no, ako želiš kraticu,

it generalizes to a handy equation.

može se svesti na korisnu jednadžbu.

Plug in ten musicians, and we get odds of about 35%.

Uključi deset glazbenika i dobit ćemo šanse od oko 35%.

What if there were 1,000 musicians?

Što kada bismo imali tisuću glazbenika?

1,000,000?

Milijun?

As n increases, the odds approach about 30%.

Kako se n povećava, šanse se približavaju 30-ak posto.

Not a guarantee, but with a bit of musician's luck, it's far from hopeless.

Nije garancija za uspjeh, no uz malo sreće, stvar je daleko od beznadne.

Hi everybody, if you liked this riddle, try solving these two.

Ako vam se svidjela ova zagonetka, pokušajte riješiti ove dvije.