Name: 【TED-Ed】你能解出暗黑幣的謎題嗎？ (Can you solve the dark coin riddle? - Lisa Winer)
Uploaded: 2018-01-23T01:41:05.000Z
Duration: 5 min 26 s

and now, after a long and dangerous quest,

而現在，經過漫長而危險的探索，

you have some good news and some bad news.

你有一些好消息和一些壞消息。

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

好消息是你已經成功找到了傳說中的地牢。

containing the stash  of ancient Stygian coins

and the eccentric wizard  who owns the castle

has even generously agreed to let you have them.

甚至慷慨地同意讓你擁有它們。

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

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

讓你離開地牢，除非你解決他的謎題。

Both faces of each coin bear the fearsome scorpion crest,

每枚硬幣的兩面都有可怕的蠍子徽章。

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

而你要做的就是把它們抽成兩堆。

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

使每個人的硬幣數量相同，面向銀色的一面向上。

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

你正準備開始的時候，所有的火把突然都熄滅了。

There are hundreds  of coins in front of you

and each one feels the same on both sides.

而每一個人的兩邊感覺都是一樣的。

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

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

你數了數，正好有20枚銀色邊上的硬幣在堆裡。

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

你是否註定要和你的新發現的寶藏永遠留在地牢裡？

and curse the curiosity  that brought you here.

並詛咒把你帶到這裡的好奇心。

But at the last moment, you stop yourself.

但在最後一刻，你阻止了自己。

You just realized there's  a surprisingly easy solution.

你才發現有一個出人意料的簡單解決方案。

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

如果你想自己想明白的話，請在這裡暫停。

You carefully move aside 20 coins one by one.

你小心翼翼地把20枚硬幣一個個挪到一邊。

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

為什麼這麼簡單的解決方案就能成功？

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

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

重要的是，總共只有20個面向銀色的一面。

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

你無從得知這些銀面錢幣的數量。

This means that there are thirteen silver-facing coins left

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

這也意味著你新的那堆硬幣中的其他13個硬幣

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

那麼，當你把新的一堆硬幣都翻過來的時候，會發生什麼？

Seven gold-facing coins and thirteen silver-facing coins

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

事實證明，無論你搶到多少銀面幣，這都是有效的。

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

We know that each coin only has two possible options.

我們知道，每個硬幣只有兩種可能的選擇。

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

如果不是面向銀色的一面朝上，那一定是金色的一面朝上。

the number of gold-facing and silver-facing coins

We can prove this mathematically using algebra.

我們可以用代數在數學上證明這一點。

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

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

將永遠是20減去多少你移動到新的一堆。

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

由於你的新堆也有總共20個硬幣。

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

When all the coins in the new pile are flipped,

當新堆中的所有硬幣都被翻開時。

these gold-facing coins become silver-facing coins,

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

所以現在兩堆銀面幣的數量是一樣的。

The gate swings open and you hurry away with your treasure

大門一開，你就帶著你的寶藏匆匆離開了

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

在下一個十字路口，你拋出一個你辛苦賺來的硬幣。

to determine the way  to your next adventure.

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

但在你走之前，我們還有一個快速的硬幣謎語給你--------。

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

其中，來自這個視頻贊助商的優秀網站。

這裡我們有8種錢幣的排列方式。

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

你可以隨意翻轉相鄰的硬幣對。

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

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

你能不能想辦法分辨，一目瞭然。

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

您可以嘗試這個謎題的互動版本，並確認您的解決方案

We love Brilliant.org because the site  gives you tools

我們愛Brilliant.org，因為這個網站給你提供了工具。

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

用我們最喜歡的一種方式來解決問題------。

by breaking puzzles into smaller pieces  or limited cases,

通過將謎題分解成小塊或有限的案例。

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

這樣，你就建立了一個解決問題的框架。

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

你可以免費註冊Brilliant，如果你喜歡猜謎語

a Brilliant.org premium membership  will get you access

成為Brilliant.org的高級會員後，您可以獲得以下服務

Try it out today by visiting  brilliant.org/TedEd

今天就來試試吧，訪問 brilliant.org/TedEd。

and use that link so they know  we sent you.

並使用該鏈接，使他們知道我們給你發。