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. Easier approach: if you see the next person wearing a white hat, answer it quick (like after 1s)
    otherwise, answer your hat color slower (like after 10s).
    For the first person, 50%, from the next one 100% chance. LOL

  2. Unfortunately, I've met my fair share of humans and… AT LEAST 1 in 10 is not smart enough to follow these directions, even IF someone in the line came up with this "foolproof solution."

  3. More like a guessing game rather than a riddle. I thought there was an actual trick to know the definitive answer to which hat one has on…Disappointed

  4. I thought of a more simple solution that the first person could say the color of the next person's hat and so on until the end and they would get the same result.

  5. I feel like the challenge isn’t the riddle but rather how to convince 9 other people to agree with your plan or screw up in the process.

  6. It's a good thing this vid is less than 5 minutes.
    Should this happen, show this video, if you can't explain it yourself

  7. Simply tell the colour of a hat a person wearing, who is standing ahead of you.Chances are minimum 9 person guess their hat colour right.

  8. I'm the type of person that sighs often, so after I get the color right I would probably sigh, and the aliens would think I was making a signal, and we would all get eaten lmao

  9. humans while the aliens are using the translator: so, u know we have a bunch of other animals for consumption?
    THE END

    ALSO

    that one person who speaks a different language has screwed us all

  10. Isn’t it possible to just say the hat colour of the person in front of you so 9 people would be correct. Since no one knows their own hat colour you could tell the aliens you were just guessing your own.

  11. yeah, that would work if everyone of those 10 people was intelligent enough to properly understand the plan… unfortunately, 1 of 10 random people has IQ low enough to get the rest eaten… if it takes 10% of idiots to exterminate human species than we're done, cause this percentage is much higher ;]

  12. Or.. the first person can say the hat color of the person standing in front of him and so on .. they’ll get 9 answers correctly this way

  13. What if first person would say the colour he is seing in front and the next person will say twice the colour if the next is the same and if isn't he will say once.

  14. Prisoner 1 : Let’s storm Area 51!
    (All prisoners gets abducted)
    Prisoner 10 : No need to storm…We got taken by aliens.

  15. oh man, relying on everyone understanding the plan after it's been decided&codified and the aliens not using the translator to pop in and learn the trick or someone not fudging it all up LOL >_>

  16. honestly these videos are so interesting and cool compared to the riddle videos with titles like 99.999% OF PEOPLE WILL NOT SOLVE THESE RIDDLES!!!! thnx ted.

  17. as confusing and wound up the riddle was..

    the comments were very logical too as well as hilarious..

    so they wouldn't be eaten by puny aliens too.. i gz

  18. I might have another answer, couldn't the tallest say the colours in order from closest person to the furthest away person and guess his hat because you can only get 1 colour wrong as a group

  19. Isn’t this as simple as: the tallest guy says the color of the hat in front of him, then the next guy says the color of the hat in front of him as well and so on. Then the shortestt guy would have to guess the color of the hat of the tallest guy and also has a 50% chance of getting it correctly, but at least 9 of the answers are correct!

  20. It's called deductive reasoning… even if you have a plan like this you should have a great sense of accountability and coordination otherwise use the theory of quantum entanglement

  21. My soultion was the tallest guy(#10) in the back says the color of the persons hat in front of him(#9). If #9 sees that the person in front of them has the same hat color they say their hat color loud, if it’s the opposite they whisper it. And then you keep going down the line. 10 might get his color wrong but you only need 9 correct so you’re good, they never said anything bout how loud you can say the words 😂

  22. cows are most emotional closest animal to human, if someone dies in home they shed a tear, you can eat other like fish they dont feel same. or maybe wicked cat. im kidding.

  23. Why didn’t they yet say what coulee the person in front of them had ?? It’s way more simple and works every time two duhhhhhhhhhhhhhh

  24. Sadly, in reality it would simply NOT work. Ok, lets suppose someone is really smart and manages to figure out the plan you descrobe at the video, it would be really rare for the rest to be at least smart enough to understand how the plan will go and obey..

  25. it would rather be way easier for the first person on the line to say the colour of the person right ahead of him. ggwp

  26. But wouldn't signalling to the others show that you're intelligent and cooroporative and therefore the aliens wouldn't be allowed to eat you?

  27. Wait, I've been watching this video for a long time & only just considered if one of them is mute. What if another is blind, deaf, or what!?!?!? What do you do then?!
    "Well, boss, this one's not answering. What should we do?"

    "EaT tHeM…"

  28. Would have never guessed that one, im more of a right brainer, this seems more for left brainers 😂😂 thats my excuse haha

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