Can you solve the dark coin riddle? - Lisa Winer

翻译人员: Chien Yet Chong 校对人员: Sylvia He

正片结束后后请继续观看 会有一个额外的谜题。

You heard the traveler's tales,

你听说过探险者的传说，

you followed the crumbling maps,

你循着那张皱巴巴的地图，

and now, after a long and dangerous quest,

现在，经过悠长又危险的探险后，

you have some good news and some bad news.

你有一些好消息和一些坏消息。

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

好消息是你成功找到了传说中的的地窖

containing the stash of ancient Stygian coins

那儿存放着古希腊冥河的钱币

and the eccentric wizard who owns the castle

而那位拥有这座城堡的古怪巫师

has even generously agreed to let you have them.

竟然慷慨地同意让你 带走这些钱币。

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

但是坏消息是他 却并非如此大方地

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

让你离开地窖， 除非你解开他的谜题。

The task sounds simple enough.

任务看似简单。

Both faces of each coin bear the fearsome scorpion crest,

钱币每一面都铸有 令人生畏的蝎子饰章，

one in silver,

一面是银的，

one in gold.

另一面是金的。

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

你只需要把它们分为两堆

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

好让每一堆中银面向上的 都有相同的数目。

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

当你想开始时，突然 所有的火炬都灭了

and you're left in total darkness.

你完全陷入漆黑中。

There are hundreds of coins in front of you

你的面前堆放着上百枚钱币，

and each one feels the same on both sides.

每一枚的两面都有相同的质感。

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

你尝试回想起银面向上 的钱币的所在位置，

but it's hopeless.

但都徒劳无功。

You've lost track.

你毫无头绪了。

But you do know one thing for certain.

但是你很确定一件事儿。

When there was still light,

当火炬还亮着时，

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

你准确地算到那堆钱币中 有20枚银面向上的。

What can you do?

你可以怎么做呢？

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

你是否注定永远地跟你 新发现的宝藏留在地窖里？

You're tempted to kick the pile of coins

你激怒得想踢那堆钱币一脚

and curse the curiosity that brought you here.

以及咒骂带你到此地的好奇心。

But at the last moment, you stop yourself.

但那一瞬间，你停下来。

You just realized there's a surprisingly easy solution.

你刚意识到有个相当 简单的解决方案。

What is it?

那是什么呢？

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

如果你想要自己解开， 请在这里暂停视频。

Answer in: 3

答案在 3 秒內出現

Answer in: 2

答案：2

Answer in: 1

答案：1

You carefully move aside 20 coins one by one.

你小心翼翼地拿出20枚钱币。

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

哪些钱币不重要： 那堆中任何钱币都行，

and then flip each one of them over.

然后你把每一枚都翻转过来。

That's all there is to it.

你仅需这么做。

Why does such a simple solution work?

为什么简单的解决方案行得通？

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

其实，开始时有多少枚 钱币并不重要。

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

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,

当你从黑暗中抽取20枚钱币，

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

你没办法知道那些银面 向上的钱币哪些最终

have ended up in your new pile.

属于这新的一堆钱币中。

But let's suppose you got 7 of them.

但是假设你拿到7枚银面向上的。

This means that there are 13 silver-facing coins left

这表示还有13枚银面向上的

in the original pile.

留在原本那一堆里。

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

这也表示新的一堆里 有13枚钱币

are facing gold side up.

是金面向上的。

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

当你把新的这堆全部都 翻转过来，那会发生什么事呢？

Seven gold-facing coins and 13 silver-facing coins

最终会有七枚金面向上 和13枚银面向上

to match the ones in the original pile.

跟原本那堆银面向上的数目一样。

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

结果是不论你从原本那堆 拿了多少枚银面向上的，

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

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.

那是因为“互补事件。”

We know that each coin only has two possible options.

我们知道每一枚钱币 只有两种可能性。

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

如果不是银面向上， 那肯定就是金面向上，

and vice versa,

反过来也一样，

and in any combination of 20 coins,

任何20枚钱币的组合，

the number of gold-facing and silver-facing coins

金面向上和 银面向上的总和

must add up to 20.

一定要等于20.

We can prove this mathematically using algebra.

我们可以使用数学中的 代数来证明。

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

原本那堆中所剩下的 银面向上钱币

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

永远是20减去你放到 新的那堆中银面向上的数目。

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

既然新的那堆钱币的 总和也是20，

its number of gold-facing coins will be

新的那堆金面向上的数目

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

就是20减去你所抽到 银面向上的数目。

When all the coins in the new pile are flipped,

当新的那堆中所有的 钱币都翻转过来，

these gold-facing coins become silver-facing coins,

本来金面向上的就会 变成银面向上的，

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

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

闸门打开了，你急忙地 带着你的宝藏离开

before the wizard changes his mind.

以免那位巫师改变主意。

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

当你来到下一个岔口时， 你掷一枚辛苦取得的钱币

to determine the way to your next adventure.

决定你接下来探险旅程 该走的路。

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

在你离开前，我们还有另外 一个简短的钱币谜题给你 ——

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

这题来自这段视频 赞助者的杰出网站。

Here we have 8 arrangements of coins.

我们这儿有8种钱币组合。

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

你可以无数次地翻转 两个相邻的硬币。

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

每次翻转就会把金的变成银的， 和银的变成金的。

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

你可以着看一眼就知道

which arrangements can be made all gold?

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

如果你要尝试这个互动性 谜题以及确认你的答案，

on Brilliant’s website.

你可上Brilliant的网站。

We love Brilliant.org because the site gives you tools

我们喜爱Brilliant.org因为 这网站给你工具

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

以我们最喜欢的方式 来解决问题 ——

by breaking puzzles into smaller pieces or limited cases,

把谜题分解成小部分 或有限的事例，

and working your way up from there.

然后从中慢慢解答问题。

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

这样，你正在建立一个 解决问题的结构，

instead of just memorizing formulas.

而不是单单牢记公式。

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

你可以免费注册Brilliant账户， 如果你喜欢谜题

a Brilliant.org premium membership will get you access

Brilliant.org的高级会员 让你应用

to countless more interactive puzzles.

更多互动性的谜题。

Try it out today by visiting brilliant.org/TedEd

今天就尝试使用， 你可浏览brilliant.org/TedEd

and use that link so they know we sent you.

并使用以上链接好让 他们知道你是我们推荐的。

The first 833 of you to visit that link

首833位点入以上链接的人

will receive 20% off the annual premium subscription fee.

可享有20%的每年高级 会员费折扣。