Can you solve the prisoner boxes riddle? - Yossi Elran

翻译人员: Chen Zou 校对人员: Xu Junqing

Your favorite band is great at playing music,

你最喜欢的乐队很擅长玩音乐，

但是在组织整理方面 不那么尽人意。

but not so great at being organized.

They keep misplacing their instruments on tour,

他们在巡回演出时 不断出现放错乐器的情况，

and it's driving their manager mad.

这使他们的经理很恼火。

On the day of the big concert,

在一个音乐会的当天，

the band wakes up to find themselves tied up

乐队成员醒来发现： 他们被绑在了

in a windowless, soundproof practice room.

一个没有窗户 隔音的练习室，

Their manager explains what's happening.

经理向他们解释了现状：

Outside, there are ten large boxes.

在外面，有十个大箱子。

每一个箱子里有一个你们的乐器，

Each contains one of your instruments,

but don't be fooled by the pictures - they've been randomly placed.

但是不要被箱子外面的图片所迷惑， 这些乐器是随意摆放在箱子里的。

I'm going to let you out one at a time.

我将要每次让你们出去一个，

While you're outside, you can look inside any five boxes

当你们在外面的时候 可以打开看任意的五个箱子，

before security takes you back to the tour bus.

然后保安会将 你们带回巡回演出大巴。

You can't touch the instruments

你们不可以触摸乐器，

or in any way communicate what you find to the others.

或者以任何形式和其他成员沟通 箱子里的内容，

No marking the boxes, shouting, nothing.

禁止在箱子上作记号，大声喧哗，禁止任何行动。

If each one of you can find your own instrument,

如果你们每一个人 都可以找到你们自己的乐器，

then you can play tonight.

那么你们今晚就可以演出，

否则，你们将被禁止出产唱片。

Otherwise, the label is dropping you.

在我们开始之前 你们有3分钟思考时间。

You have three minutes to think about it before we start.

The band is in despair.

这个乐队很绝望。

After all, each musician only has a 50% chance of finding their instrument

毕竟，每一个音乐家只有百分之五十 的机会

by picking five random boxes.

通过随意挑出五个箱子 找到他们的乐器。

And the chances that all ten will succeed are even lower -

而且他们十个全部成功的 几率更低——

just 1 in 1024.

仅有1024分之1。

But suddenly, the drummer comes up with a valid strategy

但是突然间，鼓手想出了一个 有效的策略，

that has a better than 35% chance of working.

这个策略有超过百分之35 有效的几率，

你能想出是什么吗？

Can you figure out what it was?

Pause the video on the next screen if you want to figure it out for yourself!

如果你能自己想出 请暂停下一个屏幕的录像。

Answer in: 3

答案即将揭晓：3

答案即将揭晓：2

Answer in: 2

Answer in: 1

答案即将揭晓：1

Here's what the drummer said:

以下是鼓手的主意：

Everyone first open the box with the picture of your instrument.

每个人首先打开标 有你们使用的乐器的盒子，

If your instrument is inside, you're done.

如果你的乐器是在这个盒子里面 那么你们就完成任务了，

Otherwise, look at whatever's in there,

否则，看看盒子里是什么乐器。

and then open the box with that picture on it.

然后打开有那个乐器 图标的盒子。

Keep going that way until you find your instrument.

照这样一直进行下去 直到你找到你的乐器。

The bandmates are skeptical,

乐队成员对此起先是一阵质疑，

but amazingly enough, they all find what they need.

但是使人惊讶的是 他们都顺利找到了各自的乐器。

And a few hours later, they're playing to thousands of adoring fans.

几个小时后，他们在成百上千 惹人喜爱的乐迷面前演出。

So why did the drummer's strategy work?

那么，为什么鼓手的策略有效？

Each musician follows a linked sequence

试想，每个音乐家处在一条直线的程序上。

that starts with the box whose outside matches their instrument

程序开始于盒子外面的标签 和他们使用的乐器相符

and ends with the box actually containing it.

结束于找到那个真正装有他们乐器的盒子

Note that if they kept going, that would lead them back to the start,

注意，如果他们一直这样做下去的话 那将导致他们回到起点，

so this is a loop.

所以，这是一个回路。

For example, if the boxes are arranged like so,

比如，假如盒子被 这样安排，

the singer would open the first box to find the drums,

歌手会打开第一个盒子 发现鼓乐器在里面，

go to the eighth box to find the bass,

然后走到第八个盒子发现贝斯在里面，

and find her microphone in the third box,

然后在第三个盒子里 找到她的麦克风，

which would point back to the first.

这将会导致他回到第一个盒子。

This works much better than random guessing

这个方案比随意猜测 来的有效得多。

because by starting with the box with the picture of their instrument,

因为通过开始于标有属于他们 乐器的盒子，

each musician restricts their search to the loop that contains their instrument,

每一个音乐家将他们的寻找范围 限制在含有他们乐器的回路中，

and there are decent odds, about 35%,

那么这将大大提高找到乐器的几率。

that all of the loops will be of length five or less.

大约有35%的几率使得此回路 保持在5个回合以内。

How do we calculate those odds?

那么这个概率又是如何计算得到的呢？

For the sake of simplicity, we'll demonstrate with a simplified case,

为了使事情简单化 我们将用一个简单的例子来解释：

four instruments and no more than two guesses allowed for each musician.

对于每个音乐家来说 有4个乐器和不超过2次的猜测几率。

Let's start by finding the odds of failure,

让我们从找到失败的机率开始，

the chance that someone will need to open three or four boxes

也就是在找到他们的乐器之前 他们将会需要打开

before they find their instrument.

3个或者4个盒子的机会。

There are six distinct four-box loops.

这里有6个明显的每4个盒子一组的回路，

One fun way to count them is to make a square,

通过一个有趣的方法去数它们 是将它们摆成方形，

put an instrument at each corner,

在每一个角落里摆上一个乐器，

and draw the diagonals.

然后画对角线，

See how many unique loops you can find,

看你可以找到多少个特殊的回路，

and keep in mind that these two are considered the same,

而且记住这两个 被认为是一样的，

they just start at different points.

它们仅仅是在不同的点开始，

These two, however, are different.

然而，这两个，是不同的。

We can visualize the eight distinct three-box loops using triangles.

我们可以用三角形来 使8个明显的由3个盒子组成的回路明显化，

You'll find four possible triangles

你将会找到4个可能的三角形，

depending on which instrument you leave out,

根据哪个乐器你不包括在里面，

and two distinct paths on each.

2个明显的道路在每一个回路上。

So of the 24 possible combinations of boxes,

所以，在有24种 盒子组成的可能性中

there are 14 that lead to faliure,

14种是会失败的，

and ten that result in success.

10种是会成功的，

That computational strategy works for any even number of musicians,

这个计算策略对任何 偶数个音乐家都有效。

but if you want a shortcut,

但是如果你想要一个捷径，

it generalizes to a handy equation.

它会导致出一个很方便的等式

Plug in ten musicians, and we get odds of about 35%.

如果我们将10放到这个等式中 我们得到的几率是35%，

What if there were 1,000 musicians?

如果我们有1000个音乐家呢？

1,000,000?

1百万个呢？

As n increases, the odds approach about 30%.

随着个数的增加 机率接近到大约30%。

Not a guarantee, but with a bit of musician's luck, it's far from hopeless.

这并不能绝对的保证成功，但是如果 音乐家运气还算不错的话，还是很有希望的。

Hi everybody, if you liked this riddle, try solving these two.

大家注意了，如果你喜欢这个谜语 尝试解决这两个。