This one weird trick will get you infinite gold - Dan Finkel

Translator: Ilkhomiddin Nabijonov Reviewer: Sevara Pulatova

Well, you're in a real pickle.

Xo’sh, sen juda mushkul muammodasan.

You see, a few years ago, the king decided your life would be forfeit

Agar qirol xazinasini ko’paytirmasang

unless you tripled the gold coins in his treasury.

qirol seni o’lishingni qaror qilgan.

Fortunately for you, a strange little man appeared

Baxtga ko’ra, gnom paydo bo’lgan,

and magically performed the feat.

va buni sehr yordamida amalga oshirgan.

U sehrli xalta ichiga tillalar soldi,

He placed handfuls of coins in and out of a magical bag,

and sang a strange rhyme:

va g’alati bir qo’shiq kuyladi: aminmanki

“The more gold goes in and more comes out, as sure as I am me.

“Qancha ko’p tilla, shuncha ko’p tilla.

And in again, and out again, and now it’s it times three!”

Kirib, chiqib tillalar, mana 3 barobar!”

Incredibly, that tripled the coins and saved your life.

Ajablanarlisi, u hayotingni asrab qoldi.

Were you grateful? Yes. Were you desperate? Yes.

Xursandmisan? Ha. Muhtojmiding? Ha.

Did you promise him your first-born child in exchange for his help? Yes.

Evaziga birinchi bolangni va’da berding.

Fast forward to today.

Hozirga kelsak.

No sooner have you given birth to a beautiful baby boy

Go’dakni dunyoga keltirishing bilan,

than the little man shows up to claim his prize.

Gnom sovg’ani olish uchun paydo bo’ldi.

You cry and beg him not to take the baby.

Yig’lab undan bolani olmasligini so’rading

Softening, he begins, “If you can guess my name—”

Ohista, “agar ismimni aytsang__”

“Banach-Tarski?” you say. “It’s on the front of your shirt.”

“Banak-Tarski”. “U kiyimingda turibdi.”

“What! That won’t do. Aha. My bag,” he explains,

“Nima! Bo’lishi mumkinmas. Qopim,” dedi u,

“increases the number of gold coins placed inside it in a very special way.

ichidagi tillalarni noodatiy ko’paytiradi.

If I take any number of coins and place them in, more will come out.

Solgan tillalaring ko’proq bo’lib chiqadi.

And if I place those in the bag again,

Va agar ularni yana solsam, umumiy soni

the total that comes out will be three times whatever I began with.”

boshida solganimdan 3 martaga ko’payadi.

He takes 13 coins and places them in the bag,

U 13 ta tillani qopga soladi. Va

then removes the contents.

chiqqanini oladi. Va u deydi,

“I’ve used the magic once, not twice,” he says.

“Men 1 marta sehr qildim, 2 marta emas.”

“Tell me how many coins are in my hand and I’ll have mercy.”

“Nechta tillam bor va men shafqat qilaman”

How many coins is he holding?

Unda nechta tilla bor?

Pause here to figure it out yourself. Answer in 3

Shu joyda to’xtab, nechtaligini ayting. 3

Answer in 2

2

Answer in 1

1

The bag’s magic works just like what in mathematics is called a “function,”

Qop sehri xuddi “funksiya” tushunchasidek,

and it’s convenient in both cases to use an arrow to denote the transformation.

Ko’payishni ko’rsatgich orqali belgilaymiz

We can write what we know like this.

Bilganimizni shunday yozsak bo’ladi.

We want to know what goes in this particular blank.

Bosh joyga nima kerakligini bilib olamiz.

Maybe the bag just multiplies the number of coins by some number.

Qop tillalarni qaysidir songa ko’paytirar.

In that case, multiplying by that number twice

Bunda, o’sha songa 2 marta ko’paytirish

would be the same as multiplying by 3,

xuddi 3ga ko’paytirishdek bo’ladi,

which means the multiplier would be the square root of 3.

ya’ni ko’paytiruvchi 3ning ildizi bo’ladi.

That’s not a whole number, though.

Ammo, bu butun son emas. Va tillalar

And we don’t have bits of gold coins coming out of the bag.

bo’laklarga bo’linib qopdan chiqmayapti.

Something else is going on.

Yana nimadir sodir bo’lyapti. Xo’sh, agar

Well, if filling in the blank between 13 and 39 is too hard,

bo’sh joyni 13 bilan 39 orasida to’ldirish

maybe we can start with something easier.

qiyin bo’lsa, boshqa osonroq yo’l tutamiz.

Can we figure out what’ll happen to 1 coin?

1 ta tillaga nima bo’lishini bilasizmi?

If you use the bag on a single coin twice, you end up with triple;

Agar 1 ta tillani 2 martda solsez, 3 ta

that’s three gold pieces.

bo’ladi: bu 3 tillalar degani. Chunki

Because the bag always increases the number of gold coins,

qop tillarni sonini doim oshiradi, bo’sh

the blank must be between 1 and 3, so 2.

joydagi son 1 va 3 orasida, shu uchun 2.

It’s a start. What’s next?

Bu boshlanishi. Keyinchi?

Let’s think about a few other possible starting places.

Qani boshqa boshlanish joylarini o’ylaymiz

We already know 2 becomes 3

Allaqachon bilamizki, 2 soni 3ga aylanadi

and that lets us fill in the next blank as well.

va bu keyingi bo’shliqni to’ldiradi.

Now we’re getting somewhere!

Mana endi, javoblarni topyapmiz.

We just need to extend this out to 13.

Buni shunchaki 13gacha cho’zishimiz kerak.

Remember the other rule, though:

Ammo, qoida yodda tursin:

when you put more coins in, you get more coins out.

ko’proq tilla solsang, ko’proq olasan.

That means the numbers in every column must go in increasing order as well.

Bu degani, har ustundagi son o’sishi kerak

In other words, because 6 coins become 9,

Ya’ni, chunki 6 ta tilla 9 ta bo’ladi,

it’s not possible for 4 coins to become 10.

4 ta tilla 10 ta bo’lishi mumkinmas.

Nor could 4 become 5, since 3 becomes 6.

4 5 bo’la olmaydi, chunki 3 6 bo’ladi.

So 7 and 8 fill those blanks on the right of 4 and 5,

Demak, 7 va 8, 4 va 5 ning yonida bo’ladi,

which in turn gives the answer for two more blanks.

bu boshqa 2 ta bosh joyga sonlar beradi.

Knowing that the numbers go in increasing order in every column,

Hamma son o’sishini hisobga olgan holda,

the only choices for the remaining blanks are 19, 20, 22, and 23.

19, 20, 22, va 23 javob sifatida qolyapti.

And look! We have our answer!

Va qara! Javoblar tayyor!

There must be 22 gold coins in his hand.

Uning qo’lida 22 ta tilla bo’lishi kerak.

“I’ll give you three guesses,” the little man begins to say.

“3ta imkon beraman,” dedi gnom.

“22 coins,” you respond.

“22 ta” deding.

“What?! How did you know?”

“Nima? Qanday bilding?”

“I enjoy a good riddle,” you say. “Also, it’s on the back of your shirt.”

“Topishmoq yoqdi. Javob kiyiming orqasida”