Can you solve the prisoner hat riddle? – Alex Gendler

Can you solve the prisoner hat riddle? – Alex Gendler


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.

100 thoughts on “Can you solve the prisoner hat riddle? – Alex Gendler”

  1. I have a hard riddle that’s really easy (???):

    Bob had 9000 chocolate bars
    He has many different flavors in different colors.
    What colors are they?

  2. When that alien was waving the cutlery, I thought that this would be another piece of evidence that the Rakshasa demins of Hindu mythology had evolved into aliens

  3. they could just have the guy in the back say what the color of the third persons hat is and second person names 4th and so on

  4. Take the hat from the person in front of you, see which hat was on your head, best guess is you'll win? Or die. Who cares anyway

  5. There's an easier solution: Starting from the back of the line each says what colour he / she sees in front of him / her during the discussion time…

  6. the correct answer:
    have the tallest person step on the aliens

    4:13 plot twist: the cow is albert einstein reincarnated

  7. "Their civilization forbids them to eat highly logical beings and they arent sure if you qualify"
    I dont know if i should be offended by that or not…

  8. Try to get them to empathize and set you free by telling them your fate with imaginary aliens is caused by the white supremacists in white hoods in the USA.

  9. Why dont the people say the colour from the one after him, he will see the strategy and go on. We gonna make 9 people that know after all. Am i breaking any of the rules?

  10. That's a lot of faith you have in humanity. You do realize that antivaxxers and flatearthers are a thing, right?

  11. Hi im a med student in italy, what if…i told you the medical admission test in italy has these kinds of riddles?😂😂

  12. Prisoners 4 and 10 is exception to the rule can you even make em understand the scenario in 5 min so i guess its not rlly 100% accuratr for them

  13. But you have to remember everything the first person up to the person before you have said (and in order) to make a correct guess. So imagine if you are the last person in a line of 100. 😳

  14. My guess is, that the first tallest one will say a color, which he see has odd number of people in front of him (always will be odd only one color, because there is 9 people he see). And the others will always know their color from the information what colors have taller people behind and what he see in front and with knowing, which color from 9 (without the tallest one) is odd.
    Edit: I love myself 😀

  15. Solution 2: the biggest person say the colour of the persons hat in front of him. The next say his colour. If he's saying it with a high voice the person in front of him got the same colour, but if he speak with a low voice the next person got the opposite colour. and so one…

  16. Couldn’t you just say the colour of the persons hat in front of you, then guess ur own? Number 1 could be wrong but this is easier to understand

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