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.

Author: Kennedi Daugherty

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

  1. 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

  2. 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

  3. 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!

  4. 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

  5. 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 😂

  6. 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.

  7. 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

  8. 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..

  9. 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

  10. 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?

  11. 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…"

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

  13. What happens if they decide on the suggested code but the tallest person only sees white hats in front of them? What would they say?

  14. Aliens: let’s eat this one
    Aliens: DIES 20 SECONDS LATER TO REALISE IM 98% SUGER AND GUARANTEED TO GIVE HEART ATTACKS FROM EATING ME

  15. WHAT!? How is no one seeing this: THE GUY IN THE BACK JUST TELLS THE PERSON IN FRONT WHAT COLOR THEIR HAT IS IN THE FIRST PLACE, AND SO ON DOWN THE LINE! Or the opposite color! Did i fast-forward too much and miss something?!

  16. I understand the idea, but in a world full of idiots, they’d all be dead. Counting on the intellectual deduction of a group of people is foolishish. Honestly, I’d just try and make a run for it.

  17. internet MAGNA CARTA for banks & regulations transparency and facts/ Getting the Barons to agreed/ / the charter is done. 👽 EVEN the UN needs a MAGNA CARTA FOR THE WEB/ / MAGNA CARTA/ benefit to police & plotters/ search engines dispute, from Bing to bing & google & Bing/ all on the google store / 🐣🐣/ a good gesture for clean air/ a philosophical change of climate on practical terms 😇 the amazons of information & applications/ edge DEV/ 👽.

  18. If i were the last one and it was all up to me, I would probably panic and shout "Uhh… uhh. WHITE!" and doom us all.

  19. imagine if you want to relax in your swimming pool, but flesh-eating aliens want to make you guess hat colors with other people.
    now THATS relatable

  20. Im confused… why couldn’t the person behind you let you know your color? So only the last guy in line will fail as no one will tell him. But the person in front will have hinted the person in front and so on…

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