The Theft Protection

Myths and Facts About Identity Theft

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. "You and nine other individuals have been captured by super intelligent alien overlords"

    Alien with the ray gun pants

    Me: Sounds accurate 🤷

  2. nowadays, this riddle is so famous that not only do i remember doing this in a class once, but one day i saw my mom do this in her class too.

  3. You didnt mention in the beginning that they have bonus one wrong answer . Next time explain the rules well before making a riddle.

  4. i mean, what if the aliens didn’t say who was right or wrong right away? was that specified? they could simply tell the humans if they passed the test or not in the end

  5. Speak in accents, discuses a accent to match each colour in hat and then when it is your turn to guess speak with the accent that matches the hat in front of you

  6. I would have suggested to do a trick.
    When alien comes to you for your answer, say your answer in the following format:
    “<next person’s actual hat color> no, sorry, sorry, let me guess again….<previous person’s first answer>”😎

  7. Simple, they create a simple code. The person guessing will actually state the color of the hat that the person in front is wearing (in code). Everyone will know their hat color except for the tallest guy. OR they could use a pocket mirror and pass it around. They're not turning around to look the other way so they're not breaking any rules.

  8. Just say anything if you have one wrong answer lets say you have a white hat then say anything and f its wrong say the other coler

  9. I'd just say, this is a bad time to see if we qualify for intelligence, maybe come back in another 100 years… assuming we haven't blown up the planet with nuclear weapons or something..

  10. Я по-другому решил: делать паузу в ответе) никто ж не говорил, что нужно отвечать сразу? Первый называет цвет шляпы следующего. Далее Если цвет шляпы перед тобой такой же как у тебя, сразу называешь свой цвет, а если другой, делаешь длинную паузу)
    Ответ неверный, но условиям не противоречит)

  11. Also, why would you and 10 other people an even length apart on height when put in order tallest to smallest be “coincidentally” upducted by “aLiEnS”??

  12. Ok but how are they certain this was going to be the puzzle and how would they interpret the signal without knowing the intentions of the last person?

  13. or the person behind you calls out your hat colour and you call out the person in front of you’s hat colour

  14. 1) The tallest guy says the color he sees in front of him.
    2) The second tall person knows the color of his/her hat immediately.
    3) Then, if the second tall person sees the same color hat in front of him/her, he says his hat color loud.
    4) If the second tall person sees a different color hat in front of him/her, he says his hat color not so loud.
    5) Now, the third tallest person knows his hat color.
    6) Everyone follows this pattern.

  15. 87.5 % About people making puns
    12.5 % People solving this riddle
    100 % About people making comments about Prisoner 1 flipping and Prisoner 4 looking behind.

  16. And how, in 5 minutes with the use of only 2 words, is the 1 person who figured this out suppose to communicate this solution to a group for cooperation?

  17. If you get two guesses and there’s only two options doesn’t that defeat the whole purpose?

  18. Challenging so hard means the alliens are very hungry and will eat them anyway. Take the time to plan a breakout

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