Can you solve the prisoner hat riddle? - Alex Gendler

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Welp, it's been a good run. I guess I'm being eaten by aliens.

πŸ‘οΈŽ︎ 12 πŸ‘€οΈŽ︎ u/PartyBusGaming πŸ“…οΈŽ︎ Dec 14 2015 πŸ—«︎ replies

I'm sad that even if you had the correct solution he explained, you would still be eaten because of that one guy not paying attention during the explanation

πŸ‘οΈŽ︎ 7 πŸ‘€οΈŽ︎ u/abucketofpuppies πŸ“…οΈŽ︎ Dec 14 2015 πŸ—«︎ replies

You could also use the way you say your colour to communicate the colour of person's hat directly in front of you. If I thought my hat was black and the person in front's was also black, I could say black in a deep tone, but if there was white I'd say black in a squeaky tone. Easier to know what's going on, and we don't need to keep track of even numbers or odd numbers of anything.

πŸ‘οΈŽ︎ 2 πŸ‘€οΈŽ︎ u/FlyingSwords πŸ“…οΈŽ︎ Dec 15 2015 πŸ—«︎ replies

no.

πŸ‘οΈŽ︎ 1 πŸ‘€οΈŽ︎ u/BePassionate πŸ“…οΈŽ︎ Dec 14 2015 πŸ—«︎ replies
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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.
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Channel: TED-Ed
Views: 27,360,104
Rating: undefined out of 5
Keywords: Logic, Riddle, Puzzle, TED, TED-Ed, TED Education, TEDx, Alex Gendler, Hat riddle, Creativity, Problem solving, Critical thinking
Id: N5vJSNXPEwA
Channel Id: undefined
Length: 4min 34sec (274 seconds)
Published: Mon Oct 05 2015
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