Can you solve the egg drop riddle? - Yossi Elran

Prevoditelj: Ivan Stamenković Recezent: Senzos Osijek

The city has just opened its one-of-a-kind Fabergé Egg Museum

Grad je upravo otvorio svoj jedinstveni Muzej Fabergé jaja

with a single egg displayed on each floor of a 100-story building.

sa jednim jajetom izloženim na svakom katu zgrade sa sto katova.

And the world's most notorious jewel thief already has her eyes on the prize.

I najpoznatija kradljivica dragulja već gleda svoju lovinu.

Because security is tight and the eggs are so large,

jer je osiguranje jako a jaja su tako velika,

she'll only get the chance to steal one

imat će šansu ukrasti samo jedno

by dropping it out the window into her waiting truck

bacajući ga kroz prozor u kamion koji čeka

and repelling down before the police can arrive.

i spustiti se dolje prije nego policija dođe.

All eggs are identical in weight and construction,

Sva jaja su identične težine i konstrukcije,

but each floor's egg is more rare and valuable than the one below it.

ali jaje na svakom katu je vrednije od onog ispod.

While the thief would naturally like to take the priceless egg at the top,

Iako bi kradljivica najviše voljela ukrasti jaje s vrha,

she suspects it won't survive a 100-story drop.

sumnja kako neće preživjeti pad sa stotinu katova visine.

Being pragmatic, she decides to settle for the most expensive egg she can get.

Kako je praktična, odlučuje se za najskuplje jaje koje može uzeti.

In the museum's gift shop, she finds two souvenir eggs,

U muzejskoj trgovini nalazi dva jaja suvenira,

perfect replicas that are perfectly worthless.

savršene replike koje su savršeno bezvrijedne.

The plan is to test drop them

Plan je bio baciti ih i testirati

to find the highest floor at which an egg will survive the fall

kako bi utvrdila koji je najviši kat s kojeg jaje može preživjeti pad

without breaking.

bez lomljenja.

Of course, the experiment can only be repeated

Naravno, eksperiment se može ponavljati

until both replica eggs are smashed.

dokle god oba lažna jaja nisu slomljena.

And throwing souvenirs out the window too many times

A bacanje suvenira kroz prozor previše puta

is probably going to draw the guards' attention.

vjerojatno će privući pažnju čuvara.

What's the least number of tries it would take

Koji je najmanji broj pokušaja

to guarantee that she find the right floor?

koji će garantirati da nađe pravi kat?

Pause here if you want to figure it out for yourself!

Pauzirajte ovdje ako želite pronaći odgovor!

Answer in: 3

Odgovor za: 3

Answer in: 2

Odgovor za: 2

Answer in: 1

Odgovor za: 1

If you're having trouble getting started on the solution,

Ako imate problema sa započinjanjem rada na rješenju,

it might help to start with a simpler scenario.

možda će vam pomoći početi s jednostavnijim scenarijem.

Imagine our thief only had one replica egg.

Zamislite da naš lopov ima samo jedno jaje repliku.

She'd have a single option:

Imala bi jednu opciju:

To start by dropping it from the first floor

Baciti ga s prvog kata

and go up one by one until it breaks.

i penjati se jedan po jedan dok ne pukne.

Then she'd know that the floor below that

Onda bi znala da je kat ispod

is the one she needs to target for the real heist.

onaj na kojem treba izvesti pravu pljačku.

But this could require as many as 100 tries.

Ali ovo bi moglo tražiti i stotinu pokušaja.

Having an additional replica egg gives the thief a better option.

Budući da ima još jedno jaje daje lopovu bolju opciju.

She can drop the first egg from different floors at larger intervals

Može bacati prvo jaje s različitih katova u većim intervalima

in order to narrow down the range where the critical floor can be found.

kako bi suzila raspon gdje se može naći kritični kat.

And once the first breaks,

I kada se prvo jaje razbije,

she can use the second egg to explore that interval floor by floor.

može koristiti drugo da istraži taj interval kat po kat.

Large floor intervals don't work great.

Veliki intervali između katova nisu baš najbolji.

In the worst case scenario, they require many tests with the second egg.

U najgorem scenariju, traže puno testova sa drugim jajetom.

Smaller intervals work much better.

Manji intervali rade puno bolje.

For example, if she starts by dropping the first egg from every 10th floor,

Na primjer, ako počne bacati prvo jaje sa svakog desetog kata,

once it breaks, she'll only have to test the nine floors below.

kada se razbije, mora testirati samo devet katova ispod.

That means it'll take at most 19 tries to find the right floor.

To znači da će joj trebti samo 19 pokušaja da nađe pravi kat.

But can she do even better?

Ali može li bolje?

After all, there's no reason every interval has to be the same size.

Ipak, ne postoji razlog da svi intervali budu iste veličine.

Let's say there were only ten floors.

Recimo da je samo deset katova.

The thief could test this whole building with just four total throws

Lopov može testirati čitavu zgradu sa samo četiri bacanja

by dropping the first egg at floors four,

bacajući prvo jaje na četvrtom,

seven,

sedmom,

and nine.

i devetom katu.

If it broke at floor four, it would take up to three throws of the second egg

Ako se razbije na četvrtom katu, trebat će tri pokušaja s drugim jajetom

to find the exact floor.

da bi se pronašao pravi kat.

If it broke at seven,

Ako se razbije na sedmom,

it would take up to two throws with the second egg.

trebat će dva bacanja drugog jajeta.

And if it broke at floor nine,

A ako se razbije na devetom,

it would take just one more throw of the second egg.

trebat će samo jedan pokušaj s drugim jajetom.

Intuitively, what we're trying to do here is divide the building into sections

Intuitivno, pokušavamo zgradu podijeliti na sekcije

where no matter which floor is correct,

gdje bez obzira na koji kat je ispravan,

it takes up to the same number of throws to find it.

treba isti broj bacanja da se pronađe.

We want each interval to be one floor smaller than the last.

Želimo da svaki interval bude manji od prethodnog.

This equation can help us solve for the first floor we need to start with

Ova jednadžba nam može pomoći riješti na kojem katu trebamo početi

in the 100 floor building.

u zgradi od 100 katova.

There are several ways to solve this equation,

Postoji nekoliko načina da riješimo jednadžbu,

including trial and error.

uključujući pokušaje i pogreške.

If we plug in two for n, that equation would look like this.

Ako stavimo dva za n, ta jednadžba bi izgledala ovako.

If we plug in three, we get this.

Ako stavimo tri, dobijemo ovo.

So we can find the first n to pass 100

Tako da možemo naći prvi n koji će proći 100

by adding more terms until we get to our answer,

dodajući još uvjeta dok ne dobijemo naš odgovor,

which is 14.

koji je 14.

And so our thief starts on the 14th floor,

Tako da ako naš lopov počne na 14. katu,

moving up to the 27th,

penjući se na 27.,

the 39th,

39.,

and so on,

i tako dalje,

for a maximum of 14 drops.

sa maksimalno 14 bacanja.

Like the old saying goes, you can't pull a heist without breaking a few eggs.

Stara izreka kaže da ne možete izvesti pljačku bez da razbijete par jaja.