TedTest

From the Ted Talk by Yossi Elran: Can you solve the prisoner boxes riddle?

Unscramble the Blue Letters

Your favorite band is great at playing music, but not so great at being oeirganzd. They keep misplacing their instruments on tour, and it's diivnrg 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. Their manager explains what's happening. Outside, there are ten large beoxs. Each contains one of your irneusmtnts, 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 cmnimutacoe what you find to the others. No mirnkag the boxes, shouting, nothing. If each one of you can find your own instrument, then you can play tgiohnt. Otherwise, the label is dropping you. You have three mniuets to think about it before we start. The band is in despair. After all, each musician only has a 50% chance of finding their instrument by picking five rdonam boxes. And the chances that all ten will succeed are even lower - just 1 in 1024. But suddenly, the dmemrur comes up with a valid strategy that has a better than 35% chance of working. Can you fgiure 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 ansewr in: 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 bdnaemtas are skeptical, but amazingly enough, they all find what they need. And a few hours later, they're pyinlag to tdauoshns of adoring fans. 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 senigr 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 ptrciue of their instrument, each musician restricts their sarceh to the loop that contains their instrument, and there are decent odds, about 35%, that all of the lopos will be of length five or less. How do we calculate those odds? For the sake of simplicity, we'll demonstrate with a siipfliemd case, four instruments and no more than two guesses allowed for each musician. Let's start by fnidnig the odds of failure, the chance that someone will need to open three or four boxes before they find their itmensrnut. There are six distinct four-box loops. One fun way to cnuot them is to make a square, put an instrument at each cnoerr, and draw the diagonals. See how many uqiune 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. We can viizaulse the eight distinct three-box loops using tglrinaes. 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 citumapaoontl strategy wroks 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.

Open Cloze

Your favorite band is great at playing music, but not so great at being _________. They keep misplacing their instruments on tour, and it's _______ 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. Their manager explains what's happening. Outside, there are ten large _____. Each contains one of your ___________, 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 ___________ what you find to the others. No _______ the boxes, shouting, nothing. If each one of you can find your own instrument, then you can play _______. Otherwise, the label is dropping you. You have three _______ to think about it before we start. The band is in despair. After all, each musician only has a 50% chance of finding their instrument by picking five ______ boxes. And the chances that all ten will succeed are even lower - just 1 in 1024. But suddenly, the _______ comes up with a valid strategy that has a better than 35% chance of working. Can you ______ 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 ______ in: 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 _________ are skeptical, but amazingly enough, they all find what they need. And a few hours later, they're _______ to _________ of adoring fans. 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 ______ 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 _______ of their instrument, each musician restricts their ______ to the loop that contains their instrument, and there are decent odds, about 35%, that all of the _____ will be of length five or less. How do we calculate those odds? For the sake of simplicity, we'll demonstrate with a __________ case, four instruments and no more than two guesses allowed for each musician. Let's start by _______ the odds of failure, the chance that someone will need to open three or four boxes before they find their __________. There are six distinct four-box loops. One fun way to _____ them is to make a square, put an instrument at each ______, and draw the diagonals. See how many ______ 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. We can _________ the eight distinct three-box loops using _________. 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 _____________ strategy _____ 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.

Solution

organized
triangles
bandmates
computational
answer
tonight
playing
thousands
boxes
search
simplified
instrument
figure
works
visualize
marking
picture
drummer
instruments
loops
unique
finding
random
singer
count
minutes
corner
communicate
driving

Original Text

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. 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. 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 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. 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. 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. 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.

Frequently Occurring Word Combinations

Important Words

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