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黑暗硬币谜题 – 译学馆
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黑暗硬币谜题

Can you solve the dark coin riddle? - Lisa Winer

你听说了旅行家的传说
You heard the traveler’s tales,
你跟随破碎的地图的指引
you followed the crumbling maps,
现在 在经历漫长而危险的探寻后
and now, after a long and dangerous quest,
你得到了一些好消息和一些坏消息
you have some good news and some bad news.
好消息是 你成功地找到了传说中的地牢的位置
The good news is you’ve managed to locate the legendary dungeon
地牢里贮藏着古老的斯泰吉亚钱币
containing the stash of ancient Stygian coins
城堡的主人是一个古怪的巫师
and the eccentric wizard who owns the castle
他甚至慷慨地同意给你这些钱币
has even generously agreed to let you have them.
坏消息是 他并不慷慨地允许你
The bad news is that he’s not quite as generous
离开地牢 除非你解开了他的谜题
about letting you leave the dungeon, unless you solve his puzzle.
这个任务听上去很简单
The task sounds simple enough.
每枚硬币的两面有可怕的蝎子装饰
Both faces of each coin bear the fearsome scorpion crest,
一面是银的 一面是金的
one in silver, one in gold.
你要做的就是把它们分成两堆
And all you have to do is separate them into two piles
使得每堆硬币中 银的一面朝上的硬币数量相等
so that each has the same number of coins facing silver side up.
你刚要开始的时候 所有火把忽然全都熄灭了
You’re about to begin when all of the torches suddenly blow out
你处于一片漆黑中
and you’re left in total darkness.
你面前有上百枚硬币
There are hundreds of coins in front of you
每枚硬币的两面摸上去都相同
and each one feels the same on both sides.
你试图回忆银的一面向上的硬币在哪
You try to remember where the silver-facing coins were,
但徒劳无望
but it’s hopeless.
你已经忘记了
You’ve lost track.
但你确定知道一件事
But you do know one thing for certain.
当这里还亮着的时候
When there was still light,
你数了硬币堆里银面朝上的硬币 正好20枚
you counted exactly 20 silver-side-up coins in the pile.
你能怎么办
What can you do?
你注定要和你刚得到的财宝永远留在地牢里?
Are you doomed to remain in the dungeon with your newfound treasure forever?
你想要踢那堆硬币
You’re tempted to kick the pile of coins
诅咒把你带到这里来的好奇心
and curse the curiosity that brought you here.
但是在最后关头 你停了下来
But at the last moment, you stop yourself.
你刚刚意识到有一个非常简单的解决办法
You just realized there’s a surprisingly easy solution.
那是什么?
What is it?
如果你想自己解决的话 在这里暂停
Pause here if you want to figure it out for yourself.
公布答案倒计时:3
Answer in: 3
公布答案倒计时:2
Answer in: 2
公布答案倒计时:1
Answer in: 1
你小心地一个一个地移开了20枚硬币
You carefully move aside 20 coinsone by one.
移开哪些硬币都不要紧 任何硬币都可以
It doesn’t matter which ones: any coins will do,
然后把它们每一枚翻面
and then flip each one of them over.
这就是解决方法的所有步骤
That’s all there is to it.
为什么这么简单的方法是有效的?嗯
Why does such a simple solution work? Well,
开始的时候共有多少枚硬币都不重要
it doesn’t matter how many coins there are to start with.
重要的是 所有硬币中只有20枚是银面朝上
What matters is that only 20 of the total are facing silver side up.
当你在黑暗中拿出20枚硬币时
When you take 20 coins in the darkness,
你没有办法知道这些银面朝上的硬币
you have no way of knowing how many of these silver-facing coins
有多少枚在新的这堆硬币里
have ended up in your new pile.
但我们假设你有7枚银面朝上的硬币
But let’s suppose you got 7 of them.
这意味着剩余13枚银面朝上的硬币在原来的一堆里
This means that there are 13 silver-facing coins left in the original pile.
也意味着新的硬币堆里的另外13枚都是金面朝上
It also means that the other 13 coins in your new pile are facing gold side up.
所以当你把新硬币堆的每枚硬币都翻面后 会发生什么?
So what happens when you flip all of the coins in the new pile over?
7枚金面朝上的硬币和13枚银面朝上的硬币
Seven gold-facing coins and 13 silver-facing coins
银面朝上的硬币数量正好与原硬币堆相同
to match the ones in the original pile.
原来不论你拿了多少银面朝上的硬币 这一结果都成立
It turns out this works no matter how many of the silver-facing coins you grab,
不论是全部 几个 还是没有银面朝上的硬币
whether it’s all of them, a few, or none at all.
这是由于一种被叫做对立事件的现象
That’s because of what’s known as complementary events.
我们知道 每枚硬币都只有两种可能选择
We know that each coin only has two possible options.
如果不是银面朝上
If it’s not facing silver side up,
就一定是金面朝上
it must be gold side up,
反之亦然
and vice versa,
在20枚硬币的所有组合中
and in any combination of 20 coins,
金面朝上和银面朝上的硬币数量之和必为20
the number of gold-facing and silver-facing coins must add up to 20.
我们可以利用代数在数学上证明
We can prove this mathematically using algebra.
原硬币堆中的银面朝上的硬币的数量
The number of silver-facing coins remaining in the original pile
总是20减去你移到新硬币堆的数量 无论你移了多少
will always be 20 minus however many you moved to the new pile.
由于你的新硬币堆的硬币总数也是20
And since your new pile also has a total of 20 coins,
所以其中金面朝上的硬币数量
its number of gold-facing coins will be
是20减去你移动的银面朝上的硬币数量
20 minus the amount of silver-facing coins you moved.
当新硬币堆的所有硬币都被翻面后
When all the coins in the new pileare flipped,
这些金面朝上的硬币变为了银面朝上
these gold-facing coins becomesilver-facing coins,
所以现在两堆中银面朝上的硬币数量相等
so now the number of silver-facing coins in both piles is the same.
大门旋转打开 你带着财宝匆匆离开
The gate swings open and you hurry away with your treasure
趁着巫师还没改变主意
before the wizard changes his mind.
在下一个十字路口 你掷一枚辛苦得来的硬币
At the next crossroads, you flip one of your hard-earned coins
以决定去哪里进行下一次冒险
to determine the way to your next adventure.
但在你走之前
But before you go,
我们还给你准备了另一个硬币谜题
we have another quick coin riddle for you –
这一谜题来自于这个视频的赞助者的优秀网站
one that comes from this videosponsor’s excellent website.
我们这里有硬币的8种排列
Here we have 8 arrangements of coins.
你可以翻转两个相邻的硬币 想翻几次都可以
You can flip over adjacent pairs of coins as many times as you like.
一次翻转总会把金变为银 把银变为金
A flip always changes gold to silver,and silver to gold.
瞥一眼 你能想出怎么判断
Can you figure out how to tell, at a glance,
哪种排列能够变成全都是金的?
which arrangements can be made all gold?
你可以在Brilliant的网站上
You can try an interactive version
尝试这个谜题的交互版本
of this puzzle and confirm your solution
并确定你的解决方案
on Brilliant’s website.
我们爱Brilliant.com网站 因为这个网站
We love Brilliant.org because the sitegives you tools
给你工具 来用我们最喜欢的方式之一解决问题
to approach problem-solving inone of our favorite ways—
这种方式就是把谜题分成小一些的部分 或者是有限的情况
by breaking puzzles into smaller pieces or limited cases,
然后从那里开始努力解决
and working your way up from there.
用这种方式 你建立了问题解决的框架
This way, you’re building up aframework for problem solving,
而不仅仅是记忆公式
instead of just memorizing formulas.
你可以免费注册Brilliant网站
You can sign up for Brilliant for free,
如果你喜欢谜题
and if you like riddles
Brilliant.com的高级会员资格
a Brilliant.org premium membershipwill get you access
能让你接触到数不尽的交互式谜题
to countless more interactive puzzles.
今天就来尝试吧 访问brilliant.org/TedEd
Try it out today by visitingbrilliant.org/TedEd
用这个链接 然后他们就知道这是我们发给你的
and use that link so they knowwe sent you.
访问这个链接的前833人
The first 833 of you to visit that link
将会有高级会员订阅费用的八折优惠
will receive 20% off the annual premium subscription fee.

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视频概述

本视频以动画的形式讲解了黑暗硬币谜题的解决方法。黑暗硬币谜题就是指,每枚硬币都有金和银两面;开始时,共有20枚硬币银面朝上,其他硬币金面朝上:问在一片漆黑、看不见颜色的时候,如何将硬币分成两堆,使得每堆硬币中,银面朝上的硬币数量相同?

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视频来源

https://www.youtube.com/watch?v=pnSw8g3DPHw

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