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Current time:0:00Total duration:11:12

Video transcript

this brings teaser this video is once again not one that I made up I actually don't remember the first time that I heard it I think it was in the back of a magazine I want to say Scientific American and and me and a bunch of buddies we were traveling through Europe and it kind of became our pastime to do these brain teasers in the back of magazines and just so you know I think a lot of people think that you know these type of brain teasers you can just read them and solve them and if you can't solve them then you're not good at this type of thing this brain teaser I'm about to give you I just kind of sat and thought about it and I mean my buddies we argued about it for literally about a day and then I just slept on it and then the first thing in the morning I like woke up all my friend that's like I figured it out so this isn't some kind of easy thing and and I encourage you know just listen to the statement understand it and then you know pause the video and then think about it for 24 hours and then come back to it and one you'll probably solve it yourself and if you don't in 24 or 48 hours and you'll probably find the solution that much more satisfying so this is the problem of the toddlers toddlers not toddlers toddlers I have a well I have an infant so words like toddler are in my brain but this is the problem of the toddler so there are five guys in front of you and that's one of them two three or five they don't have to be guys they could be of any gender and four of them are what we called toddlers and what a toddler so four of them for toddlers for toddlers and what a toddler does is they the first time you ask them a question they're either going to tell the truth and they're going to lie so truth or a lie but then the second time that you ask them they're going to toggle they're going to switch so the second time you ask them a question if they told the truth the first time then the next time you ask that same person a question they're going to switch to lying but if they lied the first time you ask them a question then they're gonna switch to telling the truth and then it goes on and so on and so forth so if you ask the same person the third question if they told the truth the first time then they'll lie the second time you ask them a question and then the third time they'll tell them the truth it's like if I was a toddler and you said hey you what is your name and if I said oh my name is Bill then clearly I'm lying that first time and then you say you point it to me again and you say what is your name them say oh my name is Sal and then if you were asking me again what is your name I would say oh my name is Susan and if you ask me again my name is Sal so this is so the first time I just decided to lie but I just as easy just as easily I could have decided to tell the truth the first time you might have you know said hey you what's your name I still hadn't said Sal and then you asked me what's your name again and I would have said Elizabeth and then you asked me what's my name again I would say oh with my name is Sal and then again what's your name and I would say you know George Washington or something arbitrary but I think you get the idea a toddler the first you know I don't know who's the target let's say that this is a toddler the first time you ask some question they might lie they might tell the truth but if they lie the next time you ask the same person a question they're gonna tell the truth but if the first time you ask them a question and they did tell the truth the next time you ask the same personal question he or she is going to lie so that's a toddler so you can already imagine this is I mean I don't know the first time that I read the problem it kind of made my brain hurt this notion of a toddler it's much easier when there's a reality where people only lie or only tell the truth it's much harder when they toggle and not only they toggle but their initial state whether they start telling the truth or they start off lying you don't know that's arbitrary there's no way of predicting whether this person first of all we don't know if this person is a toddler because I said there's only four toddlers but even if they are a toddler I don't even know if the first time I asked them a question whether they're going to tell the truth or whether they're going to lie so for our more toddlers what's the fifth well you probably could guess because this is how these brain teasers go the fifth is the truth teller and he's much simpler or he or she I don't want to give any clues on who it might be is a truth teller and a truth teller always tells the truth always tells the truth so this brain teaser or the goal of this brain teaser is to figure out who is the truth teller so you want to know which of these five people is the solicited goal whose truth teller and as you can imagine you don't have infinite questions to do this with you have exactly two questions to do this with and you have two questions and those two questions they can be you know one question to this guy and then another question to this guy both questions could be to this guy both questions could be to her right over there so the questions don't have to be the same person although they can be the same person or they could be kind of to two different people so you have two questions any question to ask of any cop you know any combination of either two questions to one person or two questions to two people to figure and by the end of those two questions you should know for sure who is the truth teller and that is the the brainteaser statement so pause it now if you don't want any hints or the solution or anything else so you know I encourage you to pause it and think about it for at least for at least a day and you know sleep on it because a lot of you know although the real math problems or logic problems that are worth solving aren't the ones that you can solve right when you see them they're the ones that you kind of sit and let your brain do a little background processing while you sleep so with that said hopefully you've stopped it and now you've resumed it after after really struggling with this for a long period not eating and sleeping and and all the things that normal people do and now you're ready for the solution or even better you're ready to confirm your solution so first I'll give you a hint I mean you know it's a tough question I struggled with this at first I was just like you know how do you know when you ask someone a question how do you know if they're lying or not how do you know if they're the truth teller how do you know if they're a toddler you don't have any information so the crux of this problem is to it's essentially it doesn't matter who you're asking the question to the first time around and actually the solution is it doesn't matter who you're asking to the question the second time around you want to ask a question so that no matter what they say you know what they're going to do the second time around you know whether they're going to tell the truth the second time around or you know whether they're going to lie the second time around and that's a hint and if you just want a hint if they keep thinking about it pause it again because I'm about to give you a solution so question one so question one and you can pick any of the five people to ask this question to and that's kind of the nature of one of these solutions there's no reason for you to pick one of the five over the other they're all equally likely to be the truth teller so you ask them are you the truth teller are you the truth teller truth teller so let's think about a couple of of citizens well first of all they're either gonna answer to this yes or no right so the either gonna say there's going to be two situations they either gonna say yes or they're going to say no so if someone says yes - are they the truth teller it means that they are either that they they they are the truth teller telling the truth truth teller telling truth telling truth or they are a lying toddler a lying toddler if they say that they are not the truth teller they clearly cannot be the truth teller because the truth teller cannot lie about not being the truth teller and so they have to be a toddler and they be an honest toddler being a toddler who's telling the truth right so it would be a truthful toddler truthful truthful toddler right remember I asked anybody any of these five people right here said are you the truth teller if they say yes I immediately know that they're either the truth teller telling the truth or they're a lying toddler if they say no I know that they are a truthful toddler now what's interesting is in this scenario if they say yes what do I know that they're going to do next so if this is a if this is the truth telling if this is a the truth teller and they told the truth that this on the second question they're going to tell the truth again they're gonna tell the truth on on question number two if they're the lying toddler what are they gonna do when you ask him another question well they toggle if they lie the first time you ask them they're gonna tell the truth the second time you ask them so they're going to tell the truth on question number two right so if the person says yes - are you the truth teller you immediately know no matter who they are that they're gonna tell the truth on question number two so if you can know for a fact that the person gonna tell the truth on question number two you - you ask them who is the truth teller who so this is number two who is the truth teller so it's kind of weird you go to someone and say are you the truth teller and and they'll say yes and then you ask them again who is the truth teller and then because they have to tell the truth they will actually they'll either say if it was this case they say I am the truth teller or if it's this case they'll say no that dude over there is the truth teller and then you'll know who the truth teller is now what happens in this situation that they're truthful toggler well then on the second question what are they going to do they're going to lie they're gonna lie on the second question right on cue on question number two so if you know for a fact that someone's going to lie how can you phrase a question so you can figure out who the truth teller is well if they say no to this first question and you know they're gonna lie on the second one your second question should just be who is not the truth teller not the truth teller so the only way to lie on this question right the only way to lie on this question this person has to lie now is to tell you who the truth teller is and so using these two questions we essentially using the first question are you the truth teller we can immediately predict what the person is going to do on the second question and then we can phrase the second question depending on that response to definitely know who the truth teller is anyway I thought you would enjoy that and I hopefully you see why the the the liar game show brain teaser was a bit of a warm up for this one see you in the next video