Can you solve the dark coin riddle

你能解決黑暗硬幣之謎嗎

來源視頻

Stick around after this episode for a bonus riddle.?

You heard the traveler's tales, you followed the crumbling maps, and now, after a long and dangerous quest, you have some good news and some bad news.

The good news is you've managed to locate the legendary dungeon containing the stash of ancient Stygian coins and the eccentric wizard who owns the castle has even generously agreed to let you have them.

The bad news is that he's not quite as generous about letting you leave the dungeon, unless you solve his puzzle.

正片結(jié)束后后請(qǐng)繼續(xù)觀看?會(huì)有一個(gè)額外的謎題。

你聽說過探險(xiǎn)者的傳說，你循著那張皺巴巴的地圖，現(xiàn)在，經(jīng)過悠長(zhǎng)又危險(xiǎn)的探險(xiǎn)后，你有一些好消息和一些壞消息。

好消息是你成功找到了傳說中的的地窖，那兒存放著古希臘冥河的錢幣，而那位擁有這座城堡的古怪巫師竟然慷慨地同意讓你?帶走這些錢幣。

但是壞消息是他?卻并非如此大方地讓你離開地窖，?除非你解開他的謎題。

The task sounds simple enough.?

Both faces of each coin bear the fearsome scorpion crest, one in silver, one in gold.?

And all you have to do is separate them into two piles so that each has the same number of coins facing silver side up.

You're about to begin when all of the torches suddenly blow out and you're left in total darkness.?

There are hundreds of coins in front of you and each one feels the same on both sides.?

You try to remember where the silver-facing coins were, but it's hopeless.

任務(wù)看似簡(jiǎn)單。

錢幣每一面都鑄有?令人生畏的蝎子飾章，一面是銀的，另一面是金的。

你只需要把它們分為兩堆好讓每一堆中銀面向上的?都有相同的數(shù)目。

當(dāng)你想開始時(shí)，突然?所有的火炬都滅了你完全陷入漆黑中。

你的面前堆放著上百枚錢幣，每一枚的兩面都有相同的質(zhì)感。

你嘗試回想起銀面向上?的錢幣的所在位置，但都徒勞無功。

You've lost track.?

But you do know one thing for certain.

When there was still light, you counted exactly 20 silver-side-up coins in the pile.?

What can you do?

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

You're tempted to kick the pile of coins and curse the curiosity that brought you here.?

But at the last moment, you stop yourself.?

You just realized there's a surprisingly easy solution.?

What is it?

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

Answer in: 3?

Answer in: 2

Answer in: 1

你毫無頭緒了。

但是你很確定一件事兒。

當(dāng)火炬還亮著時(shí)，你準(zhǔn)確地算到那堆錢幣中?有20枚銀面向上的。

你可以怎么做呢？

你是否注定永遠(yuǎn)地跟你 新發(fā)現(xiàn)的寶藏留在地窖里？

你激怒得想踢那堆錢幣一腳以及咒罵帶你到此地的好奇心。

但那一瞬間，你停下來。

你剛意識(shí)到有個(gè)相當(dāng) 簡(jiǎn)單的解決方案。

那是什么呢？

如果你想要自己解開， 請(qǐng)?jiān)谶@里暫停視頻。

答案在?3?秒內(nèi)出現(xiàn)

答案：2

答案：1

You carefully move aside 20 coins one by one.

It doesn't matter which ones: any coins will do, and then flip each one of them over.?

That's all there is to it.?

Why does such a simple solution work??

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.

你小心翼翼地拿出20枚錢幣。

哪些錢幣不重要： 那堆中任何錢幣都行，然后你把每一枚都翻轉(zhuǎn)過來。

你僅需這么做。

為什么簡(jiǎn)單的解決方案行得通？

其實(shí)，開始時(shí)有多少枚 錢幣并不重要。

最重要的是全部錢幣中 有20枚是銀面向上的。

When you take 20 coins in the darkness, you have no way of knowing how many of these silver-facing coins have ended up in your new pile.

But let's suppose you got 7 of them.?

This means that there are 13 silver-facing coins left in the original pile.

It also means that the other 13 coins in your new pile are facing gold side up.

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

Seven gold-facing coins and 13 silver-facing coins to match the ones in the original pile.?

It turns out this works no matter how many of the silver-facing coins you grab, whether it's all of them, a few, or none at all.

當(dāng)你從黑暗中抽取20枚錢幣，你沒辦法知道那些銀面 向上的錢幣哪些最終屬于這新的一堆錢幣中。

但是假設(shè)你拿到7枚銀面向上的。

這表示還有13枚銀面向上的留在原本那一堆里。

這也表示新的一堆里 有13枚錢幣是金面向上的。

當(dāng)你把新的這堆全部都 翻轉(zhuǎn)過來，那會(huì)發(fā)生什么事呢？

最終會(huì)有七枚金面向上 和13枚銀面向上跟原本那堆銀面向上的數(shù)目一樣。

結(jié)果是不論你從原本那堆 拿了多少枚銀面向上的，要么全部銀面向上的， 一些或完全沒有。

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

We know that each coin only has two possible options.?

If it's not facing silver side up, it must be gold side up, and vice versa, and in any combination of 20 coins, the number of gold-facing and silver-facing coins must add up to 20.?

We can prove this mathematically using algebra.

The number of silver-facing coins remaining in the original pile will always be 20 minus however many you moved to the new pile.

And since your new pile also has a total of 20 coins, its number of gold-facing coins will be 20 minus the amount of silver-facing coins you moved.?

When all the coins in the new pile are flipped, these gold-facing coins become silver-facing coins, so now the number of silver-facing coins in both piles is the same.

那是因?yàn)椤盎パa(bǔ)事件”

我們知道每一枚錢幣 只有兩種可能性。

如果不是銀面向上， 那肯定就是金面向上，反過來也一樣，任何20枚錢幣的組合，金面向上和 銀面向上的總和一定要等于20。

我們可以使用數(shù)學(xué)中的 代數(shù)來證明。

原本那堆中所剩下的 銀面向上錢幣永遠(yuǎn)是20減去你放到 新的那堆中銀面向上的數(shù)目。

既然新的那堆錢幣的 總和也是20，新的那堆金面向上的數(shù)目就是20減去你所抽到 銀面向上的數(shù)目。

當(dāng)新的那堆中所有的 錢幣都翻轉(zhuǎn)過來，本來金面向上的就會(huì) 變成銀面向上的，所以現(xiàn)在銀面向上的數(shù)目 會(huì)跟原本那堆的一樣。

The gate swings open and you hurry away with your treasure before the wizard changes his mind.?

At the next crossroads, you flip one of your hard-earned coins to determine the way to your next adventure.?

But before you go, we have another quick coin riddle for you – one that comes from this video sponsor’s excellent website.?

Here we have 8 arrangements of coins.?

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

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

Can you figure out how to tell, at a glance, which arrangements can be made all gold?

閘門打開了，你急忙地 帶著你的寶藏離開以免那位巫師改變主意。

當(dāng)你來到下一個(gè)岔口時(shí)， 你擲一枚辛苦取得的錢幣決定你接下來探險(xiǎn)旅程 該走的路。

在你離開前，我們還有另外 一個(gè)簡(jiǎn)短的錢幣謎題給你?——這題來自這段視頻 贊助者的杰出網(wǎng)站。

我們這兒有8種錢幣組合。

你可以無數(shù)次地翻轉(zhuǎn) 兩個(gè)相鄰的硬幣。

每次翻轉(zhuǎn)就會(huì)把金的變成銀的， 和銀的變成金的。

你可以著看一眼就知道哪些組合可以全部變成金的嗎？

You can try an interactive version of this puzzle and confirm your solution on Brilliant’s website.?

We love Brilliant.org because the site gives you tools to approach problem-solving in one of our favorite ways— by breaking puzzles into smaller pieces or limited cases, and working your way up from there.?

This way, you're building up a framework for problem solving, instead of just memorizing formulas.

You can sign up for Brilliant for free, and if you like riddles a Brilliant.org premium membership will get you access to countless more interactive puzzles.?

Try it out today by visiting brilliant.org/TedEd and use that link so they know we sent you.?

The first 833 of you to visit that link will receive 20% off the annual premium subscription fee.

如果你要嘗試這個(gè)互動(dòng)性 謎題以及確認(rèn)你的答案，你可上Brilliant的網(wǎng)站。

我們喜愛Brilliant.org因?yàn)?這網(wǎng)站給你工具以我們最喜歡的方式 來解決問題 ——把謎題分解成小部分 或有限的事例，然后從中慢慢解答問題。

這樣，你正在建立一個(gè) 解決問題的結(jié)構(gòu)，而不是單單牢記公式。

你可以免費(fèi)注冊(cè)Brilliant賬戶， 如果你喜歡謎題Brilliant.org的高級(jí)會(huì)員 讓你應(yīng)用更多互動(dòng)性的謎題。

今天就嘗試使用， 你可瀏覽brilliant.org/TedEd并使用以上鏈接好讓 他們知道你是我們推薦的。

首833位點(diǎn)入以上鏈接的人可享有20%的每年高級(jí) 會(huì)員費(fèi)折扣。