Can you solve the control room riddle? - Dennis Shasha

Možete li da rešite zagonetku kontrolne sobe? Denis Šaša (Dennis Shasha)

Prevodilac: Marija Kojić Lektor: Mile Živković

As your country's top spy,

Budući da ste najbolji špijun u državi,

you must infiltrate the headquarters of the evil syndicate,

morate da se ušunjate u sedište zlog udruženja,

nađete tajnu kontrolnu tablu,

find the secret control panel,

and deactivate their death ray.

i deaktivirate njihov zrak smrti.

But all you have to go on is the following information

No, sve što znate o tome su sledeće informacije

picked up by your surveillance team.

koje je prikupio vaš tim za prismotru.

The headquarters is a massive pyramid with a single room at the top level,

Sedište je ogromna piramida

sa samo jednom prostorijom na najvišem nivou,

two rooms on the next,

dve prostorije na sledećem nivou,

and so on.

i tako dalje.

The control panel is hidden behind a painting

Kontrolna tabla je sakrivena iza slike

on the highest floor that can satisfy the following conditions:

na najvišem spratu, koji zadovoljava sledeće uslove:

Each room has exactly three doors to other rooms on that floor,

Svaka prostorija ima tačno troje vrata

koje povezuju druge prostorije na tom spratu,

except the control panel room,

osim prostorije sa kontrolnom tablom,

which connects to only one,

koja je povezana samo sa jednim vratima,

there are no hallways,

nema hodnika,

and you can ignore stairs.

stepenice se ne računaju.

Unfortunately, you don't have a floor plan,

Nažalost, nemate plan spratova,

and you'll only have enough time to search a single floor

i imate dovoljno vremena da pretražite samo jedan sprat

before the alarm system reactivates.

pre nego što se sistem za uzbunu ponovo aktivira.

Možete li da odgonetnete na kom spratu se nalazi kontrolna soba?

Can you figure out which floor the control room is on?

Pause now to solve the riddle yourself.

Pauzirajte sada da sami rešite zagonetku.

Answer in: 3

Odgovor za: 3

Answer in: 2

Odgovor za: 2

Answer in: 1

Odgovor za: 1

To solve this problem, we need to visualize it.

Da rešimo ovaj problem moramo da pribegnemo vizualizaciji.

For starters, we know that on the correct floor

Za početak, znamo da je na pravom spratu

there's one room,

jedna soba,

let's call it room A,

nazovimo je soba A,

with one door to the control panel room,

sa jednim vratima koje vode do kontrolne sobe,

plus one door to room B,

uz jedna vrata koja vode do sobe B,

and one to C.

i jedna koja vode do sobe C.

So there must be at least four rooms,

Stoga, mora da postoji najmanje četiri sobe,

which we can represent as circles,

koje možemo predstaviti u vidu krugova,

drawing lines between them for the doorways.

uz linije nacrtane između njih koje predstavljaju dovratke.

But once we connect rooms B and C,

No kada povežemo sobe B i C,

there are no other connections possible,

nema nijedne druge moguće povezanosti,

so the fourth floor down from the top is out.

stoga četvrti sprat od gore otpada sa spiska.

We know the control panel has to be as high up as possible,

Znamo da kontrolna tabla mora da bude na što višem mestu moguće,

so let's make our way down the pyramid.

stoga je najbolje da se spuštamo kroz piramidu.

The fifth highest floor doesn't work either.

peti najviši sprat takođe ne odgovara.

We can figure that out by drawing it,

To možemo da shvatimo kada ga nacrtamo,

but to be sure we haven't missed any possibilities,

no, da budemo sigurni da nismo nešto propustili,

here's another way.

evo još jednog načina.

Every door corresponds to a line in our graph

Svaka vrata odgovaraju jednoj liniji u našem grafikonu

that makes two rooms into neighbors.

koji predstavlja dve povezane sobe.

So in the end, there have to be an even number of neighbors

tako da, na kraju, mora postojati paran broj povezanih soba

no matter how many connections we make.

bez obzira na to koliko povezanih soba označimo.

On the fifth highest floor, to fulfill our starting conditions,

Na petom najvišem spratu, da ispunimo početne uslove,

we'd need four rooms with three neighbors each,

trebalo bi nam četiri sobe sa još tri povezane sobe,

plus the control panel room with one neighbor,

uz kontrolnu sobu koja bi imala još jednu povezanu sobu,

which makes 13 total neighbors.

što ukupno čini 13 povezanih soba.

Since that's an odd number, it's not possible,

Budući da je to neparan broj nije moguće,

and, in fact, this also rules out every floor that has an odd number of rooms.

zapravo, ovo takođe eliminiše svaki sprat koji ima neparan broj soba.

So let's go one more floor down.

Stoga idemo još jedan sprat niže.

When we draw out the rooms,

Kada nacrtamo sobe,

low and behold, we can find an arrangement that works like this.

kako ispada, dobijamo raspored koji izgleda ovako.

Incidentally, the study of such visual models

Sasvim slučajno, ispitivanje ovakvih vizuelnih modela

that show the connections and relationships between different objects

koji pokazuju povezanost i odnos između različitih objekata

is known as graph theory.

poznato je kao teorija grafova.

In a basic graph, the circles representing the objects are known as nodes,

U najobičnijem grafu, krugovi predstavljaju objekte poznate kao čvorovi,

while the connecting lines are called edges.

koji su povezani linijama koje se zovu grane.

Researchers studying such graphs ask questions like,

Istraživanja koja se bave ovakvim grafovima pitaju se:

"How far is this node from that one?"

„Koliko je ovaj čvor udaljen od onog?”

"How many edges does the most popular node have?"

„Koliko grana imaju najpopularniji čvorovi?”

"Is there a route between these two nodes, and if so, how long is it?"

„Da li postoji veza između ova dva čvora, i ako postoji, koliko je dugačka?”

Graphs like this are often used to map communication networks,

Slični grafovi se koriste da se označe mape komunikacionih mreža,

but they can represent almost any kind of network,

no one se mogu koristiti da označe bilo kakvu mrežu,

from transport connections within a city

od povezanosti puteva u gradu

and social relationships among people,

i društvenih veza među ljudima,

to chemical interactions between proteins

do hemijskih reakcija među proteinima

or the spread of an epidemic through different locations.

ili širenja epidemije kroz različite lokacije.

So, armed with these techniques, back to the pyramid.

Dakle, naoružani ovim tehnikama vraćate se u piramidu.

You avoid the guards and security cameras,

Izbegavate stražare i nadzorne kamere,

infiltrate the sixth floor from the top,

infiltrirate na šesti sprat gledano odgore,

find the hidden panel,

nalazite skrivenu tablu,

pull some conspicuous levers,

povlačite par upadljivih poluga,

and send the death ray crashing into the ocean.

i usmeravate zrak smrti ka okeanu.

Now, time to solve the mystery

Sada, vreme je da odgonetnete

of why your surveillance team always gives you cryptic information.

zašto vam vaš nadzorni tim uvek daje šifrovane informacije.

Hi everybody.

Zdravo svima.

If you liked this riddle, try solving these two.

Ako vam se svidela ova zagonetka pokušajte da rešite i ove dve.