Can you solve the dark coin riddle

你能解决黑暗硬币之谜吗

来源视频

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.

正片结束后后请继续观看 会有一个额外的谜题。

你听说过探险者的传说，你循着那张皱巴巴的地图，现在，经过悠长又危险的探险后，你有一些好消息和一些坏消息。

好消息是你成功找到了传说中的的地窖，那儿存放着古希腊冥河的钱币，而那位拥有这座城堡的古怪巫师竟然慷慨地同意让你 带走这些钱币。

但是坏消息是他 却并非如此大方地让你离开地窖， 除非你解开他的谜题。

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.

任务看似简单。

钱币每一面都铸有 令人生畏的蝎子饰章，一面是银的，另一面是金的。

你只需要把它们分为两堆好让每一堆中银面向上的 都有相同的数目。

当你想开始时，突然 所有的火炬都灭了你完全陷入漆黑中。

你的面前堆放着上百枚钱币，每一枚的两面都有相同的质感。

你尝试回想起银面向上 的钱币的所在位置，但都徒劳无功。

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

你毫无头绪了。

但是你很确定一件事儿。

当火炬还亮着时，你准确地算到那堆钱币中 有20枚银面向上的。

你可以怎么做呢？

你是否注定永远地跟你 新发现的宝藏留在地窖里？

你激怒得想踢那堆钱币一脚以及咒骂带你到此地的好奇心。

但那一瞬间，你停下来。

你刚意识到有个相当 简单的解决方案。

那是什么呢？

如果你想要自己解开， 请在这里暂停视频。

答案在 3 秒內出現

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枚钱币。

哪些钱币不重要： 那堆中任何钱币都行，然后你把每一枚都翻转过来。

你仅需这么做。

为什么简单的解决方案行得通？

其实，开始时有多少枚 钱币并不重要。

最重要的是全部钱币中 有20枚是银面向上的。

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.

当你从黑暗中抽取20枚钱币，你没办法知道那些银面 向上的钱币哪些最终属于这新的一堆钱币中。

但是假设你拿到7枚银面向上的。

这表示还有13枚银面向上的留在原本那一堆里。

这也表示新的一堆里 有13枚钱币是金面向上的。

当你把新的这堆全部都 翻转过来，那会发生什么事呢？

最终会有七枚金面向上 和13枚银面向上跟原本那堆银面向上的数目一样。

结果是不论你从原本那堆 拿了多少枚银面向上的，要么全部银面向上的， 一些或完全没有。

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.

那是因为“互补事件”

我们知道每一枚钱币 只有两种可能性。

如果不是银面向上， 那肯定就是金面向上，反过来也一样，任何20枚钱币的组合，金面向上和 银面向上的总和一定要等于20。

我们可以使用数学中的 代数来证明。

原本那堆中所剩下的 银面向上钱币永远是20减去你放到 新的那堆中银面向上的数目。

既然新的那堆钱币的 总和也是20，新的那堆金面向上的数目就是20减去你所抽到 银面向上的数目。

当新的那堆中所有的 钱币都翻转过来，本来金面向上的就会 变成银面向上的，所以现在银面向上的数目 会跟原本那堆的一样。

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?

闸门打开了，你急忙地 带着你的宝藏离开以免那位巫师改变主意。

当你来到下一个岔口时， 你掷一枚辛苦取得的钱币决定你接下来探险旅程 该走的路。

在你离开前，我们还有另外 一个简短的钱币谜题给你 ——这题来自这段视频 赞助者的杰出网站。

我们这儿有8种钱币组合。

你可以无数次地翻转 两个相邻的硬币。

每次翻转就会把金的变成银的， 和银的变成金的。

你可以着看一眼就知道哪些组合可以全部变成金的吗？

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.

如果你要尝试这个互动性 谜题以及确认你的答案，你可上Brilliant的网站。

我们喜爱Brilliant.org因为 这网站给你工具以我们最喜欢的方式 来解决问题 ——把谜题分解成小部分 或有限的事例，然后从中慢慢解答问题。

这样，你正在建立一个 解决问题的结构，而不是单单牢记公式。

你可以免费注册Brilliant账户， 如果你喜欢谜题Brilliant.org的高级会员 让你应用更多互动性的谜题。

今天就尝试使用， 你可浏览brilliant.org/TedEd并使用以上链接好让 他们知道你是我们推荐的。

首833位点入以上链接的人可享有20%的每年高级 会员费折扣。