Can you solve the birthday cake riddle? - Marie Brodsky

Translator: Azizmurod Murodov Reviewer: Nazarbek Nazarov

Your friend’s birthday is tomorrow, and he’s turning...

Ertaga do’stingizning tug’ilgan kuni, va u...

well... the issue is that you’ve forgotten.

yaqinda... muammo esa buni unutganligingizda.

He’s older than 1, but beyond that, he looks timeless.

U 1 yoshdan katta, ammo umriboqiydek ko’rinadi.

You’d believe it if he was 2 or 200.

Siz ishonishingiz mumkin bo’lgan yosh 2 va 200 orasida.

The birthday boy is a giant,

tug’ilgan kuni bo’layotgan do’stingiz - gigant,

and you're afraid that if your forgetfulness becomes known,

va siz bu haqida unutganingizni kimdir bilib qoladigan bo’lsa,

you'll become part of the feast.

siz bazmning bir qismiga aylanasiz.

The baker has meticulously prepared a small mountain range of a cake,

Novvoy puxtalik bilan tog’dek keladigan tort tayyorladi

and your job is to sculpt the giant’s age as the chocolate centerpiece.

va sizning vazifangiz gigantning yoshini tort markazida shokolad bilan tasvirlash

You would love to just count the candles on the cake,

Siz tort ustidagi shamlarni sanashni yoqtirasiz,

but you're much too small to see the top of it.

ammo siz bu uchun juda kichkinalik qilasiz

Then you remember: the baker made an interior tunnel

Keyin eslaysiz: novvoy tortning ichidan o’tadigan tunel yaratgan

to activate the candles from below.

va u yerdan shamlarni yoqadi.

While the giant is asleep, you can sneak in,

Gigant uxlab yotganda, siz yashirincha kirib,

count the candles and escape undetected.

bildirmasdan shamlarni sanab chiqishingiz mumkin.

As night sets, you pull on a full bodysuit and brace yourself for vanilla cream.

Kech tushishi bilan kiymingizni kiyasiz, vanilli kremga sho’ng’iysiz.

Anywhere in the tunnel, you can see whether the candle above you is lit,

Tunnelning istalgan joyida, siz ustingizda sham yoqilganligini ko’rishingiz mumkin,

and can switch it on or off.

va uni yoqishingiz yoki o’chirishingiz mumkin.

Some are currently on, and others off, in no discernible pattern.

Ular hech qanaqa qonuniyatsiz, yoqib yoki o’chirib qo’yilgan.

The tunnel is a single loop, and in the dark you can’t tell its shape or size.

Tunnel bitta halqa bo’lib, qorong’ida siz uning shakli yoki hajmini ayta olmaysiz.

You aren’t carrying anything with you, and any marks you make will disappear.

Siz o’zingiz bilan hech narsa olmadingiz va qo’ygan barcha belgilaringiz yo’qoladi.

You need a strategy.

Sizga strategiya kerak.

How can you count the candles?

Qanday qilib shamlarni sanash mumkin?

Pause here to figure it out for yourself. Answer in 3

Tushinib olish uchun videoni to’xtating. Javob 3 soniyada

Answer in 2

Javob 2 soniyada

Answer in 1

Javob 1 soniyada

There are a few ways to solve this problem.

Muammoni yechishning bir necha usullari mavjud.

Let's start with the most straightforward.

Keling, eng oddiysidan boshlaylik.

There’s exactly one way to mark a location in the tunnel:

Tunneldagi joylashuvni belgilashning aniq bir usuli mavjud:

the state of the candle.

shamning holati.

You can mark the first candle you reach by lighting it or keeping it on.

Birinchi shamni uni yoqish yoki yoniq qoldirish orqali belgilaysiz

If you walk forward, you’ll eventually find another lit candle—

Agar siz oldinga yursangiz, oxir-oqibat boshqa yonayotgan shamni topasiz —

either a new one or you’re starting one.

yoki avvalgisi yoki boshqasi.

The question is: how could you know which?

Savol: siz qaysiligini qanday bilasiz?

Here’s one approach: turn it off and backtrack to the start

Mana bir yondashuv: uni o’chiring va boshiga qayting, bunda

by passing the same number of candles you passed on the way there.

yo’lda bir xil miqdordagi shamlardan o’tish orqali.

If the starting candle is now off,

Agarda boshidagi sham o’chirilgan bo’lsa

you’ve completed the loop and know the giant’s age!

siz aylanib chiqdingiz va gigantning yoshini bilib oldingiz!

Otherwise, depart again, continuing until the next lit candle,

Aks holda, keyingi sham yonguncha davom etib, yana yo’lga chiqing,

testing if it’s your starting one and so on.

bu birinchisi ekanligini tekshiring va hokazo.

This will work... eventually.

Bu ishlaydi... Oxir-oqibat.

But if the giant isn’t young, and many candles are on,

Lekin gigant yosh emas va ko’p shamlar yoniq bo’lsa,

you might have a marathon to run between now and sunrise.

Sizda quyosh chiqishigacha yugurish marafoni bo’lishi mumkin.

And you definitely don’t want to be in the cake when he starts digging in.

U yeyishni boshlaganida, siz, albatta, tortda bo’lishni xohlamaysiz.

So let’s look for a more efficient solution.

Shunday ekan, boshqa samaraliroq usulga qaraymiz.

How about testing a series of hypotheses about the giant's age?

Gigantning yoshi haqidagi farazlarni ko’rib chiqishga nima deysiz?

Suppose you guess he’s turning 10.

You could light the starting candle, walk forward 10,

Siz birinchi shamni yoqasiz, oldinga 10 qadam yurasiz,

switch or leave the destination candle off, and return.

Belgilangan sahmni o’chiring va orqaga qayting.

If the starting candle’s still on, 10 isn’t the answer.

Agar boshlang’ich sham yoniq bo’lsa, demak to’gri javob 10 emas.

If it’s off, 10 could be right, but you may have made multiple loops—

U o’chiq bo’lsa, javob 10 bo’lishi mumkin, ammo bir nechta aylanishingiz ham mumkin.

so 10′s factors 5 and 2 are also possibilities.

Shuning uchun 10ning ko’paytuvchilari - 5 va 2 ham javob bo’lishi mumkin.

Then you would have passed a repeating pattern—

Bir necha marta aylanganingizda,

but that could have just been the starting arrangement.

lekin bu faqat boshlang’ich tartib bo’lishi mumkin edi.

So what if you changed the candles on the way?

Shunda yo’lda shamlarni adashtirib qo’ygan bo’lsangizchi?

If you turned them all on while walking from candle 1 to 11,

Agar siz 1-shamdan 11-shamgacha hammasini aylanish davomida yoqqan bo’lsangiz,

switch that off, then turn back,

uni o’chiring, keyin orqaga qayting,

the first unlit candle you find would tell you the exact candle count.

birinchi o’chirilgan sham sizga shamning aniq sonini aytib beradi.

And if you don't hit any extinguished candles,

Va agar siz o’chirilgan shamni uchratmasangiz,

you'll know that the total must be higher than 10.

siz shamlar soni 10tadan ko’pligini bilib olasiz.

You could then pick a larger guess and try again.

Shunda kattaroq sonni taxmin qilib, qaytadan urinib ko’ra olasiz.

To be systematic, you could increase your guess

Tizimli bo’lish uchun siz taxminlaringizni

by the same number each time, say 4.

aniq bir songa oshirib borishingiz mumkin, aytaylik 4ga.

If there were 99 candles,

Agar jami shamlar 99ta bo’lganida,

this method would take 24 roundtrips and involve visiting nearly 2,700 candles.

usul davomida 24ta aylanish, 2,700 shamni ko’rib chiqishingizga to’g’ri keladi

But you don’t have to increase your guess linearly.

Ammo, siz taxminlaringizni tezlikda oshirishingiz kerak emas.

For instance, you could double it, from 10 to 20 to 40,

Masalan, siz ikki barobarga oshirishingiz mumkin, 10 dan 20 dan 40 gacha,

and discover the true number on your 5th trip after around 560 candles.

va taxminan 560 shamdan keyin, 5-sayohatingizda haqiqiy raqamni topasiz.

Doubling allows you to reach high numbers quickly,

Ikki barobar oshirib, siz katta raqamlarni osonlik bilan topasiz,

while starting with small intervals in case there are only a few candles.

kam sham bo’lgan holatda, kichik oraliqlar boshlaganda.

After expecting a lengthy trek,

Uzoq sayohat kutilgan bir vaqtda,

you’re pleased to discover the giant is only turning 12.

siz gigant bor yo’gi 12ga kirayotganidan hayratga tushasiz.

You hurry to change into slightly more inconspicuous clothing;

Siz biroz ko’zga tashlanmaydigan kiyimga o’tishga shoshilasiz;

chisel up some enormous chocolate numbers; and at the party, make your own wish:

ulkan shokoladli sonni yaratasiz; va bazmda o’z istagingizni aytasiz:

that you’re not downwind when your friend blows out his candles.

do’stingiz shamni o’chirganda siz shamol tomonda turmaslikni tilaysiz.