Can you solve the dark coin riddle? - Lisa Winer

Translator: Sylvia He Reviewer: H_L Au

You heard the traveler's tales,

你聽過旅遊人嘅故事

you followed the crumbling maps,

你跟住啲破舊嘅地圖

and now, after a long and dangerous quest,

經過又長又危險嘅探險，嚟到呢度

you have some good news and some bad news.

宜家有好消息同壞消息

The good news is you've managed to locate the legendary dungeon

好消息係，你已經揾到傳說聞中

containing the stash of ancient Stygian coins

有遠古冥河硬幣嘅地牢

and the eccentric wizard who owns the castle

而身為城堡主人嘅巫师

has even generously agreed to let you have them.

會肯將啲硬幣畀你

The bad news is that he's not quite as generous

壞消息就係，其中有景轟

about letting you leave the dungeon, unless you solve his puzzle.

你唔解開條難題，就冇得走

The task sounds simple enough.

個任務好似幾簡單

Both faces of each coin bear the fearsome scorpion crest,

每個硬幣兩邊都有可怕嘅蠍子圖像

one in silver,

一面銀色

one in gold.

一面金色

And all you have to do is separate them into two piles

你要將佢哋分成兩堆

so that each has the same number of coins facing silver side up.

每堆銀面向上嘅數量要一樣

You're about to begin when all of the torches suddenly blow out

喺你啱啱開始嘅時候 啲火炬全部熄晒

and you're left in total darkness.

黑到你乜都睇唔到

There are hundreds of coins in front of you

呢度有幾百個金幣

and each one feels the same on both sides.

硬幣兩面摸落都一樣

You try to remember where the silver-facing coins were,

你嘗試記返起銀色向上嘅硬幣位置

but it's hopeless.

但冇希望

You've lost track.

你咩都唔記得

But you do know one thing for certain.

你唯一肯定嘅就係

When there was still light,

仲有光嘅時候

you counted exactly 20 silver-side-up coins in the pile.

你數到嗰堆入面 銀面向上嘅有 20 個

What can you do?

你可以點做？

Are you doomed to remain in the dungeon with your newfound treasure forever?

你係咪注定要同新發現嘅寶藏 永遠留喺個地牢？

You're tempted to kick the pile of coins

你好想踢啲硬幣

and curse the curiosity that brought you here.

同詛咒累死自己嘅好奇心

But at the last moment, you stop yourself.

卒之， 你停低

You just realized there's a surprisingly easy solution.

你發現，其實有個出奇地容易嘅方法

What is it?

係乜呢？

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

如果你想自己谂下先， 就暫停

Answer in: 3

答案 3 秒後有

Answer in: 2

答案 2 秒後有

Answer in: 1

答案 1 秒後有

You carefully move aside 20 coins one by one.

你好小心咁將 20 個硬幣 逐個移到一邊

It doesn't matter which ones: any coins will do,

邊幾個都冇所謂，係硬幣就得

and then flip each one of them over.

然後將佢哋全部反轉

That's all there is to it.

搞掂

Why does such a simple solution work?

點解咁快搞掂呢？

Well, it doesn't matter how many coins there are to start with.

其實，一開始有多少個硬幣唔重要

What matters is that only 20 of the total are facing silver side up.

最緊要嘅係， 總共有20 個硬幣銀面向上

When you take 20 coins in the darkness,

當你摸黑拎咗 20 個硬幣

you have no way of knowing how many of these silver-facing coins

你冇可能會呢個新堆

have ended up in your new pile.

其中有幾多個係銀面向上

But let's suppose you got 7 of them.

假設你有 7 個係銀面向上

This means that there are 13 silver-facing coins left

既係有 13 個銀面向上嘅硬幣

in the original pile.

喺原來嗰堆硬幣度

It also means that the other 13 coins in your new pile

亦即係，新嗰堆硬幣有 13 個

are facing gold side up.

係金面向上

So what happens when you flip all of the coins in the new pile over?

咁你將 20 個硬幣全部返轉，會點？

Seven gold-facing coins and 13 silver-facing coins

你宜家會有 7 個金面向上 同 13 個銀面向上

to match the ones in the original pile.

同原來嗰堆一樣嘞

It turns out this works no matter how many of the silver-facing coins you grab,

無論你新嗰堆最先有 幾多硬幣係銀面向上

whether it's all of them, a few, or none at all.

係全部、有啲亦或 一個都冇都好，結果都一樣

That's because of what's known as complementary events.

因為呢個就係一個互補事件

We know that each coin only has two possible options.

我哋知道，每個硬幣只有兩個可能性

If it's not facing silver side up, it must be gold side up,

唔係銀面向上 就係金面向上

and vice versa,

調返轉都一樣

and in any combination of 20 coins,

無論喺 20 個硬幣係乜組合

the number of gold-facing and silver-facing coins

銀面向上同金面向上嘅硬幣嘅數量

must add up to 20.

加埋都肯定係 20

We can prove this mathematically using algebra.

我哋可以用代數證明

The number of silver-facing coins remaining in the original pile

喺舊堆嘅銀面向上嘅硬幣數量

will always be 20 minus however many you moved to the new pile.

無論點，都會係 20 減去 你移幾多去新堆嘅數量

And since your new pile also has a total of 20 coins,

既然你會移總共 20 個硬幣去新堆

its number of gold-facing coins will be

新堆裡邊金面向上嘅硬幣

20 minus the amount of silver-facing coins you moved.

會係 20 減去 銀面向上嘅硬幣嘅數量

When all the coins in the new pile are flipped,

新堆嘅硬幣全部都反轉時

these gold-facing coins become silver-facing coins,

嗰啲金面向上嘅硬幣就變成銀面向上

so now the number of silver-facing coins in both piles is the same.

所以宜家， 兩個堆裡邊 銀面向上嘅硬幣嘅數量都一樣

The gate swings open and you hurry away with your treasure

大門開咗， 你好快啲喺魔法師改變主意之前

before the wizard changes his mind.

攞住啲財寶走佬

At the next crossroads, you flip one of your hard-earned coins

喺十字路口， 你拋你 千辛萬苦賺到嘅硬幣中嘅一個

to determine the way to your next adventure.

來決定下一步

But before you go, we have another quick coin riddle for you –

你走之前， 我哋仲有一個謎語畀你

one that comes from this video sponsor’s excellent website.

係贊助我哋嘅網站提供嘅

Here we have 8 arrangements of coins.

我哋有 8 個金幣

You can flip over adjacent pairs of coins as many times as you like.

你可以將兩個相鄰嘅 金幣反轉，幾次都得

A flip always changes gold to silver, and silver to gold.

從金轉銀，從銀轉金

Can you figure out how to tell, at a glance,

你得唔得，瞄一眼

which arrangements can be made all gold?

就講出邊個排列 可以反轉到全部金面向上

You can try an interactive version of this puzzle and confirm your solution

你可以喺 Brilliant 網站 玩呢個謎語嘅互動版

on Brilliant’s website.

同查答案

We love Brilliant.org because the site gives you tools

我哋好鍾意 Brilliant 網站

to approach problem-solving in one of our favorite ways—

因為我哋有同樣嘅 解決問題嘅哲學

by breaking puzzles into smaller pieces or limited cases,

就係將問題分成 幾舊仔

and working your way up from there.

然後 一 一 解決

This way, you're building up a framework for problem solving,

咁樣，你就建立到 解決問題嘅框架

instead of just memorizing formulas.

就唔使背公式啦

You can sign up for Brilliant for free, and if you like riddles

你可以喺 Brilliant 網站上註冊

a Brilliant.org premium membership will get you access

升級嘅會員可以喺網站上

to countless more interactive puzzles.

玩無數嘅謎題

Try it out today by visiting brilliant.org/TedEd

喺 brilliant.org/TedEd 度試下啦

and use that link so they know we sent you.

記住用呢個網連 咁佢哋先會知你係我哋送去

The first 833 of you to visit that link

嘅前 833 個用戶

will receive 20% off the annual premium subscription fee.

就會畀你 20% 嘅升級會員年費 折扣