TedTest

From the Ted Talk by Alex Gendler: Can you solve the prisoner hat riddle?

Unscramble the Blue Letters

You and nine other individuals have been captured by suepr intelligent aeiln overlords. The aliens think humans look quite tasty, but their civilization forbids eating hhilgy logical and ciropeaovte beings. Unfortunately, they're not sure whether you qfilauy, so they decdie to give you all a test. Through its universal translator, the alien guarding you tlels you the following: You will be placed in a single-file line facing forward in size order so that each of you can see everyone lined up ahead of you. You will not be able to look behind you or step out of line. Each of you will have either a bcalk or a white hat on your head assigned rdnmoaly, and I won't tell you how many of each color there are. When I say to begin, each of you must guess the color of your hat starting with the pseorn in the back and moving up the line. And don't even try saying words other than black or wthie or signaling some other way, like intonation or volume; you'll all be eaten immediately. If at least nine of you gesus correctly, you'll all be srpaed. You have five minutes to discuss and come up with a plan, and then I'll line you up, assign your hats, and we'll begin. Can you think of a strategy guaranteed to save everyone? Pause the video now to figure it out for yourself. Answer in: 3 Answer in: 2 Answer in: 1 The key is that the person at the back of the line who can see everyone else's hats can use the words "black" or "white" to communicate some cedod information. So what meaning can be assigned to those words that will allow everyone else to dcudee their hat colros? It can't be the total number of black or white hats. There are more than two possible values, but what does have two possible values is that number's parity, that is whether it's odd or even. So the solution is to agree that whoever goes first will, for example, say "black" if he sees an odd number of black hats and "white" if he sees an even number of black hats. Let's see how it would play out if the hats were distributed like this. The tallest captive sees three black hats in front of him, so he says "black," telling everyone else he sees an odd number of black hats. He gets his own hat color wrong, but that's okay since you're collectively allweod to have one wrong answer. Prisoner two also sees an odd nemubr of black hats, so she knows hers is white, and answers correctly. ponriser three sees an even number of black hats, so he knows that his must be one of the black hats the first two prisoners saw. Prisoner four hears that and knows that she should be looking for an even number of black hats since one was behind her. But she only sees one, so she deduces that her hat is also black. prseirnos five through nine are each looking for an odd number of black hats, which they see, so they fiugre out that their hats are white. Now it all comes down to you at the front of the line. If the ninth prisoner saw an odd number of black hats, that can only mean one thing. You'll find that this strategy wkros for any possible arrangement of the hats. The first prisoner has a 50% chance of giving a wrong awsner about his own hat, but the parity information he conveys allows everyone else to guess theirs with absolute certainty. Each begins by expecting to see an odd or even number of hats of the specified color. If what they count doesn't match, that mneas their own hat is that color. And everytime this happens, the next person in line will switch the pirtay they expect to see. So that's it, you're free to go. It looks like these aliens will have to go hungry, or find some less logical osmgianrs to abduct.

Open Cloze

You and nine other individuals have been captured by _____ intelligent _____ overlords. The aliens think humans look quite tasty, but their civilization forbids eating ______ logical and ___________ beings. Unfortunately, they're not sure whether you _______, so they ______ to give you all a test. Through its universal translator, the alien guarding you _____ you the following: You will be placed in a single-file line facing forward in size order so that each of you can see everyone lined up ahead of you. You will not be able to look behind you or step out of line. Each of you will have either a _____ or a white hat on your head assigned ________, and I won't tell you how many of each color there are. When I say to begin, each of you must guess the color of your hat starting with the ______ in the back and moving up the line. And don't even try saying words other than black or _____ or signaling some other way, like intonation or volume; you'll all be eaten immediately. If at least nine of you _____ correctly, you'll all be ______. You have five minutes to discuss and come up with a plan, and then I'll line you up, assign your hats, and we'll begin. Can you think of a strategy guaranteed to save everyone? Pause the video now to figure it out for yourself. Answer in: 3 Answer in: 2 Answer in: 1 The key is that the person at the back of the line who can see everyone else's hats can use the words "black" or "white" to communicate some _____ information. So what meaning can be assigned to those words that will allow everyone else to ______ their hat ______? It can't be the total number of black or white hats. There are more than two possible values, but what does have two possible values is that number's parity, that is whether it's odd or even. So the solution is to agree that whoever goes first will, for example, say "black" if he sees an odd number of black hats and "white" if he sees an even number of black hats. Let's see how it would play out if the hats were distributed like this. The tallest captive sees three black hats in front of him, so he says "black," telling everyone else he sees an odd number of black hats. He gets his own hat color wrong, but that's okay since you're collectively _______ to have one wrong answer. Prisoner two also sees an odd ______ of black hats, so she knows hers is white, and answers correctly. ________ three sees an even number of black hats, so he knows that his must be one of the black hats the first two prisoners saw. Prisoner four hears that and knows that she should be looking for an even number of black hats since one was behind her. But she only sees one, so she deduces that her hat is also black. _________ five through nine are each looking for an odd number of black hats, which they see, so they ______ out that their hats are white. Now it all comes down to you at the front of the line. If the ninth prisoner saw an odd number of black hats, that can only mean one thing. You'll find that this strategy _____ for any possible arrangement of the hats. The first prisoner has a 50% chance of giving a wrong ______ about his own hat, but the parity information he conveys allows everyone else to guess theirs with absolute certainty. Each begins by expecting to see an odd or even number of hats of the specified color. If what they count doesn't match, that _____ their own hat is that color. And everytime this happens, the next person in line will switch the ______ they expect to see. So that's it, you're free to go. It looks like these aliens will have to go hungry, or find some less logical _________ to abduct.

Solution

alien
colors
prisoner
parity
works
coded
tells
spared
qualify
number
highly
decide
white
super
guess
cooperative
prisoners
answer
black
figure
randomly
allowed
person
organisms
means
deduce

Original Text

You and nine other individuals have been captured by super intelligent alien overlords. The aliens think humans look quite tasty, but their civilization forbids eating highly logical and cooperative beings. Unfortunately, they're not sure whether you qualify, so they decide to give you all a test. Through its universal translator, the alien guarding you tells you the following: You will be placed in a single-file line facing forward in size order so that each of you can see everyone lined up ahead of you. You will not be able to look behind you or step out of line. Each of you will have either a black or a white hat on your head assigned randomly, and I won't tell you how many of each color there are. When I say to begin, each of you must guess the color of your hat starting with the person in the back and moving up the line. And don't even try saying words other than black or white or signaling some other way, like intonation or volume; you'll all be eaten immediately. If at least nine of you guess correctly, you'll all be spared. You have five minutes to discuss and come up with a plan, and then I'll line you up, assign your hats, and we'll begin. Can you think of a strategy guaranteed to save everyone? Pause the video now to figure it out for yourself. Answer in: 3 Answer in: 2 Answer in: 1 The key is that the person at the back of the line who can see everyone else's hats can use the words "black" or "white" to communicate some coded information. So what meaning can be assigned to those words that will allow everyone else to deduce their hat colors? It can't be the total number of black or white hats. There are more than two possible values, but what does have two possible values is that number's parity, that is whether it's odd or even. So the solution is to agree that whoever goes first will, for example, say "black" if he sees an odd number of black hats and "white" if he sees an even number of black hats. Let's see how it would play out if the hats were distributed like this. The tallest captive sees three black hats in front of him, so he says "black," telling everyone else he sees an odd number of black hats. He gets his own hat color wrong, but that's okay since you're collectively allowed to have one wrong answer. Prisoner two also sees an odd number of black hats, so she knows hers is white, and answers correctly. Prisoner three sees an even number of black hats, so he knows that his must be one of the black hats the first two prisoners saw. Prisoner four hears that and knows that she should be looking for an even number of black hats since one was behind her. But she only sees one, so she deduces that her hat is also black. Prisoners five through nine are each looking for an odd number of black hats, which they see, so they figure out that their hats are white. Now it all comes down to you at the front of the line. If the ninth prisoner saw an odd number of black hats, that can only mean one thing. You'll find that this strategy works for any possible arrangement of the hats. The first prisoner has a 50% chance of giving a wrong answer about his own hat, but the parity information he conveys allows everyone else to guess theirs with absolute certainty. Each begins by expecting to see an odd or even number of hats of the specified color. If what they count doesn't match, that means their own hat is that color. And everytime this happens, the next person in line will switch the parity they expect to see. So that's it, you're free to go. It looks like these aliens will have to go hungry, or find some less logical organisms to abduct.

Frequently Occurring Word Combinations

ngrams of length 2

collocation	frequency
black hats	6
odd number	5
wrong answer	2

Important Words

abduct
absolute
agree
alien
aliens
allowed
answer
answers
arrangement
assign
assigned
begins
beings
black
captive
captured
certainty
chance
civilization
coded
collectively
color
colors
communicate
conveys
cooperative
correctly
count
decide
deduce
deduces
discuss
distributed
eaten
eating
everytime
expect
expecting
facing
figure
find
forbids
free
front
give
giving
guaranteed
guarding
guess
hat
hats
head
hears
highly
humans
hungry
immediately
individuals
information
intelligent
intonation
key
line
lined
logical
match
meaning
means
minutes
moving
ninth
number
odd
order
organisms
overlords
parity
pause
person
plan
play
prisoner
prisoners
qualify
randomly
save
sees
signaling
size
solution
spared
starting
step
strategy
super
switch
tallest
tasty
telling
tells
test
total
translator
universal
values
video
white
words
works
wrong