Name: 【TED-Ed】Can you solve the prisoner boxes riddle? - Yossi Elran
Uploaded: 2016-10-06T00:14:09.000Z
Duration: 4 min 53 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Your favorite band is great at playing music,

Adverbs of degree

They keep misplacing  their instruments on tour,

the band wakes up  to find themselves tied up

in a windowless,  soundproof practice room.

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

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

before security takes you back to the tour bus.

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

If each one of you  can find your own instrument,

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

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

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

But suddenly, the drummer comes up with a valid strategy

that has a better than 35% chance of working.

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

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

If your instrument is inside, you're done.

and then open the box  with that picture on it.

Keep going that way until you find your instrument.

but amazingly enough, they all find what they need.

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

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,

For example, if the boxes  are arranged like so,

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

and find her microphone in the third box,

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,

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

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

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

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

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

depending on which instrument  you leave out,

So of the 24 possible  combinations of boxes,

That computational strategy works for any even number of musicians,

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

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.