Can you solve the Alice in Wonderland riddle? - Alex Gendler

Prevoditelj: Sanja Srbljnović Čuček Recezent: Sanda Liker

After many adventures in Wonderland,

Nakon mnogih pustolovina u Zemlji čudesa,

Alice has once again found herself in the court

Alisa se ponovno našla na dvoru

of the temperamental Queen of Hearts.

temperamentne Kraljice Srca.

She’s about to pass through the garden undetected,

Dok pokušava neopaženo proći kroz vrt,

when she overhears the king and queen arguing.

začuje kralja i kraljicu kako se prepiru.

“It’s quite simple,” says the queen. “64 is the same as 65, and that’s that.”

"Vrlo jednostavno", kaže kraljica. "64 je isto što i 65, i to je to."

Without thinking, Alice interjects. “Nonsense,” she says.

Bez razmišljanja, Alisa upadne u riječ. "Glupost.

“If 64 were the same as 65, then it would be 65 and not 64 at all.”

Da je 64 isto što i 65, tada bi bilo 65, a nikako ne 64."

“What? How dare you!” the queen huffs.

"Što? Kako se usuđuješ!" plane kraljica.

“I’ll prove it right now, and then it’s off with your head!”

"To ću odmah dokazati, a onda ti ode glava!"

Before she can protest,

Alisa se nije stigla ni pobuniti,

Alice is dragged toward a field with two chessboard patterns—

i već je odvučena na travnjak s dvije šahovske ploče --

an 8 by 8 square and a 5 by 13 rectangle.

s kvadratom 8 x 8 i pravokutnikom 5 x 13.

As the queen claps her hands, four odd-looking soldiers approach

Dok kraljica plješće rukama, četiri stražara čudnog izgleda prilaze

and lie down next to each other, covering the first chessboard.

i legnu jedan do drugoga, prekrivajući prvu šahovnicu.

Alice sees that two of them are trapezoids with non-diagonal sides measuring 5x5x3,

Alisa vidi da dvojica od njih, trapezoidi nedijagonalnih stranica, mjere 5x5x3,

while the other two are long triangles with non-diagonal sides measuring 8x3.

dok su druga dva dugački trokuti s nedijagonalnim stranicama mjera 8x3.

“See, this is 64.”

"Vidiš, ovo je 64."

The queen claps her hands again.

Kraljica ponovno pljesne rukama.

The card soldiers get up, rearrange themselves,

Stražari karte ustaju, preslože se

and lie down atop the second chessboard.

i legnu na drugu šahovsku ploču.

“And that is 65."

"A to je 65."

Alice gasps. She’s certain the soldiers didn’t change size or shape

Alisa je zgranuta. Stražari sigurno nisu promijenili veličinu ni oblik

moving from one board to the other.

prelazeći s jedne ploče na drugu.

But it’s a mathematical certainty that the queen must be cheating somehow.

Ali matematički je sigurno da kraljica mora nekako varati.

Can Alice wrap her head around what’s wrong— before she loses it?

Može li Alisa odgonetnuti što nije u redu - prije no što izgubi glavu?

Pause the video to figure it out yourself. Answer in 3.

Pauzirajte video da biste sami shvatili. Odgovor u 3,

Answer in 2

2,

Answer in 1

1.

Just as things aren’t looking too good for Alice, she remembers her geometry,

I baš kad stvari ne idu Alisi u prilog, ona se sjeti svoje geometrije,

and looks again at the trapezoid and triangle soldier

i ponovno pogleda trapezoidnog i trokutastog stražara

lying next to each other.

polegnute jedan uz drugog.

They look like they cover exactly half of the rectangle,

Čini se kao da pokrivaju točno pola pravokutnika,

their edges forming one long line running from corner to corner.

a njihove stranice tvore jednu dugu crtu koja prolazi od kuta do kuta.

If that’s true, then the slopes of their diagonal sides

Ako je to istina, tada bi nagibi njihovih dijagonalnih stranica

should be the same.

trebali biti jednaki.

But when she calculates these slopes

Ali kad izračuna te nagibe

using the tried and true formula "rise over run,"

koristeći provjerenu formulu "rast kroz put",

a most curious thing happens.

dogodi se najčudnovatija stvar.

The trapezoid soldier’s diagonal side goes up 2 and over 5,

Dijagonalna stranica trapezoidnog stražara raste za 2 i pomiče se za 5,

giving it a slope of two fifths, or 0.4.

dajući nagib od dvije petine ili 0,4.

The triangle soldier’s diagonal, however, goes up 3 and over 8,

Dijagonala trokutnog stražara, međutim, raste za 3 i pomiče se za 8,

making its slope three eights, or 0.375.

dajući nagib od tri osmine ili 0,375.

They’re not the same at all!

Oni uopće nisu isti!

Before the queen’s guards can stop her,

Prije nego što je stražari mogu zaustaviti,

Alice drinks a bit of her shrinking potion to go in for a closer look.

Alisa otpije malo napitka za smanjivanje da to pobliže pogleda.

Sure enough, there’s a miniscule gap between the triangles and trapezoids,

Svakako, postoji mali razmak između trokuta i trapeza,

forming a parallelogram that stretches the entire length of the board

i tvori paralelogram koji se proteže cijelom duljinom ploče

and accounts for the missing square.

i vrijedi za kvadrat koji nedostaje.

There’s something even more curious about these numbers:

Još je nešto čudnovatije u vezi s tim brojevima:

they’re all part of the Fibonacci series,

svi su oni dio Fibonaccijevog niza,

where each number is the sum of the two preceding ones.

gdje je svaki sljedeći broj zbroj dvaju prethodnih.

Fibonacci numbers have two properties that factor in here:

Fibonaccijevi brojevi imaju dva svojstva koja ovdje igraju ulogu:

first, squaring a Fibonacci number gives you a value

prvo, kvadrat Fibonaccijevog broja daje vam vrijednost

that’s one more or one less

koja je za jedan više ili jedan manje različiita

than the product of the Fibonacci numbers on either side of it.

od umnoška Fibonaccijevih brojeva s obje njegove strane.

In other words, 8 squared is one less than 5 times 13,

Drugim riječima, 8 na kvadrat je jedan manje od 5 puta 13,

while 5 squared is one more than 3 times 8.

dok je 5 na kvadrat za jedan više od 3 puta 8.

And second, the ratio between successive Fibonacci numbers is quite similar.

I drugo, omjer između uzastopnih Fibonaccijevih brojeva prilično je sličan.

So similar, in fact, that it eventually converges on the golden ratio.

Toliko sličan da se na kraju pretapa u zlatni rez.

That’s what allows devious royals to construct slopes

To je ono što omogućuje nepoštenim vladarima

da grade varljivo slične nagibe.

that look deceptively similar.

In fact, the Queen of Hearts could cobble together an analogous conundrum

Zapravo, Kraljica Srca mogla bi skovati sličnu zagonetku

out of any four consecutive Fibonacci numbers.

od bilo koja četiri uzastopna Fibonaccijeva broja.

The higher they go, the more it seems like the impossible is true.

Što su ti brojevi veći, to ono nemoguće više liči na istinu.

But in the words of Lewis Carroll— author of Alice in Wonderland

Ali riječima Lewisa Carrolla -- autora knjige Alisa u Zemlji čudesa

and an accomplished mathematician who studied this very puzzle—

i vrsnog matematičara koji je proučavao upravo ovu zagonetku --

one can’t believe impossible things.

ne može se vjerovati u nemoguće stvari.