Can you solve the prisoner boxes riddle

你能解決囚箱之謎嗎

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Your favorite band is great at playing music, but not so great at being organized.?

They keep misplacing their instruments on tour, and it's driving their manager mad.?

On the day of the big concert, the band wakes up to find themselves tied up in a windowless, soundproof practice room.

你最喜歡的樂隊(duì)很擅長(zhǎng)玩音樂，但是在組織整理方面 不那么盡人意。

他們?cè)谘不匮莩鰰r(shí) 不斷出現(xiàn)放錯(cuò)樂器的情況，這使他們的經(jīng)理很惱火。

在一個(gè)音樂會(huì)的當(dāng)天，樂隊(duì)成員醒來發(fā)現(xiàn)： 他們被綁在了一個(gè)沒有窗戶 隔音的練習(xí)室

Their manager explains what's happening.?

Outside, there are ten large boxes.

Each contains one of your instruments, but don't be fooled by the pictures - they've been randomly placed.?

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

While you're outside, you can look inside any five boxes before security takes you back to the tour bus.?

You can't touch the instruments or in any way communicate what you find to the others.?

No marking the boxes, shouting, nothing.

If each one of you can find your own instrument, then you can play tonight.?

Otherwise, the label is dropping you.?

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

經(jīng)理向他們解釋了現(xiàn)狀：

在外面，有十個(gè)大箱子。

每一個(gè)箱子里有一個(gè)你們的樂器，但是不要被箱子外面的圖片所迷惑， 這些樂器是隨意擺放在箱子里的。

我將要每次讓你們出去一個(gè)，

當(dāng)你們?cè)谕饷娴臅r(shí)候 可以打開看任意的五個(gè)箱子，然后保安會(huì)將 你們帶回巡回演出大巴。

你們不可以觸摸樂器，或者以任何形式和其他成員溝通 箱子里的內(nèi)容，

禁止在箱子上作記號(hào)，大聲喧嘩，禁止任何行動(dòng)。

如果你們每一個(gè)人 都可以找到你們自己的樂器，那么你們今晚就可以演出，

否則，你們將被禁止出產(chǎn)唱片。

在我們開始之前 你們有3分鐘思考時(shí)間。

The band is in despair.?

After all, each musician only has a 50% chance of finding their instrument by picking five random boxes.?

And the chances that all ten will succeed are even lower - just 1 in 1024.?

But suddenly, the drummer comes up with a valid strategy that has a better than 35% chance of working.?

Can you figure out what it was??

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

Answer in: 3?

Answer in: 2?

Answer in: 1

這個(gè)樂隊(duì)很絕望。

畢竟，每一個(gè)音樂家只有百分之五十 的機(jī)會(huì)通過隨意挑出五個(gè)箱子 找到他們的樂器。

而且他們十個(gè)全部成功的 幾率更低——僅有1024分之1。

但是突然間，鼓手想出了一個(gè) 有效的策略，這個(gè)策略有超過百分之35 有效的幾率，

你能想出是什么嗎？

如果你能自己想出 請(qǐng)暫停下一個(gè)屏幕的錄像。

答案即將揭曉：3

答案即將揭曉：2

答案即將揭曉：1

Here's what the drummer said: Everyone first open the box with the picture of your instrument.?

If your instrument is inside, you're done.?

Otherwise, look at whatever's in there, and then open the box with that picture on it.?

Keep going that way until you find your instrument.

The bandmates are skeptical, but amazingly enough, they all find what they need.?

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

以下是鼓手的主意：每個(gè)人首先打開標(biāo) 有你們使用的樂器的盒子，

如果你的樂器是在這個(gè)盒子里面 那么你們就完成任務(wù)了，

否則，看看盒子里是什么樂器。然后打開有那個(gè)樂器 圖標(biāo)的盒子。

照這樣一直進(jìn)行下去 直到你找到你的樂器。

樂隊(duì)成員對(duì)此起先是一陣質(zhì)疑，但是使人驚訝的是 他們都順利找到了各自的樂器。

幾個(gè)小時(shí)后，他們?cè)诔砂偕锨?惹人喜愛的樂迷面前演出。

So why did the drummer's strategy work??

Each musician follows a linked sequence that starts with the box whose outside matches their instrument and ends with the box actually containing it.?

Note that if they kept going, that would lead them back to the start, so this is a loop.?

For example, if the boxes are arranged like so, the singer would open the first box to find the drums, go to the eighth box to find the bass, and find her microphone in the third box, which would point back to the first.?

This works much better than random guessing because by starting with the box with the picture of their instrument, each musician restricts their search to the loop that contains their instrument, and there are decent odds, about 35%, that all of the loops will be of length five or less.

那么，為什么鼓手的策略有效？

試想，每個(gè)音樂家處在一條直線的程序上。程序開始于盒子外面的標(biāo)簽 和他們使用的樂器相符結(jié)束于找到那個(gè)真正裝有他們樂器的盒子注意，

如果他們一直這樣做下去的話 那將導(dǎo)致他們回到起點(diǎn)，所以，這是一個(gè)回路。

比如，假如盒子被 這樣安排，歌手會(huì)打開第一個(gè)盒子 發(fā)現(xiàn)鼓樂器在里面，然后走到第八個(gè)盒子發(fā)現(xiàn)貝斯在里面，然后在第三個(gè)盒子里 找到她的麥克風(fēng)，這將會(huì)導(dǎo)致他回到第一個(gè)盒子。

這個(gè)方案比隨意猜測(cè) 來的有效得多。因?yàn)橥ㄟ^開始于標(biāo)有屬于他們 樂器的盒子，每一個(gè)音樂家將他們的尋找范圍 限制在含有他們樂器的回路中，那么這將大大提高找到樂器的幾率。大約有35%的幾率使得此回路 保持在5個(gè)回合以內(nèi)。

How do we calculate those odds??

For the sake of simplicity, we'll demonstrate with a simplified case, four instruments and no more than two guesses allowed for each musician.?

Let's start by finding the odds of failure, the chance that someone will need to open three or four boxes before they find their instrument.?

There are six distinct four-box loops.?

One fun way to count them is to make a square, put an instrument at each corner, and draw the diagonals.?

See how many unique loops you can find, and keep in mind that these two are considered the same, they just start at different points.?

These two, however, are different.

那么這個(gè)概率又是如何計(jì)算得到的呢？

為了使事情簡(jiǎn)單化 我們將用一個(gè)簡(jiǎn)單的例子來解釋：對(duì)于每個(gè)音樂家來說 有4個(gè)樂器和不超過2次的猜測(cè)幾率。

讓我們從找到失敗的機(jī)率開始，也就是在找到他們的樂器之前 他們將會(huì)需要打開3個(gè)或者4個(gè)盒子的機(jī)會(huì)。

這里有6個(gè)明顯的每4個(gè)盒子一組的回路，

通過一個(gè)有趣的方法去數(shù)它們 是將它們擺成方形，在每一個(gè)角落里擺上一個(gè)樂器，然后畫對(duì)角線，

看你可以找到多少個(gè)特殊的回路，而且記住這兩個(gè) 被認(rèn)為是一樣的，它們僅僅是在不同的點(diǎn)開始，

然而，這兩個(gè)，是不同的。

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

You'll find four possible triangles depending on which instrument you leave out, and two distinct paths on each.?

So of the 24 possible combinations of boxes, there are 14 that lead to faliure, and ten that result in success.?

That computational strategy works for any even number of musicians, but if you want a shortcut, it generalizes to a handy equation.?

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

What if there were 1,000 musicians? 1,000,000??

As n increases, the odds approach about 30%.?

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

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

我們可以用三角形來 使8個(gè)明顯的由3個(gè)盒子組成的回路明顯化，

你將會(huì)找到4個(gè)可能的三角形，根據(jù)哪個(gè)樂器你不包括在里面，2個(gè)明顯的道路在每一個(gè)回路上。

所以，在有24種 盒子組成的可能性中14種是會(huì)失敗的，10種是會(huì)成功的，

這個(gè)計(jì)算策略對(duì)任何 偶數(shù)個(gè)音樂家都有效。但是如果你想要一個(gè)捷徑，它會(huì)導(dǎo)致出一個(gè)很方便的等式

如果我們將10放到這個(gè)等式中 我們得到的幾率是35%，

如果我們有1000個(gè)音樂家呢？1百萬個(gè)呢？

隨著個(gè)數(shù)的增加 機(jī)率接近到大約30%。

這并不能絕對(duì)的保證成功，但是如果 音樂家運(yùn)氣還算不錯(cuò)的話，還是很有希望的。

大家注意了，如果你喜歡這個(gè)謎語 嘗試解決這兩個(gè)。