可汗学院公开课：脑筋急转弯 13集英中字幕.doc

目 录第1集 诚实人和说谎者2第2集 善变者5第3集 外星人来袭！12第1集 诚实人和说谎者 and I'm sure a bunch of you have heard it before.But I wanted to include this in the brain teaser playlistthat I'm making right now.Because this one is actually a good build up,and a bit of a nice warm up session for a slightly harder brain teaserthat deals with people telling the truth and lying.So this one, we could call it the truth teller and the liar.So we're on some type of adventure quest,and we get to a fork in a road, right?So let's say that there's two doors.That's even better.So there's two doors.And I've gotten to the end of my adventure quest.And I know that my treasure is behind one of these two doors.Unfortunately, behind the other door is slow and painful death,and all of the misery in the world.So I want to pick the door carefully.And beside these doors, there are two people sitting there.There's one guy that looks like this.And then there's another guy that looks like this.And I know for a fact - the gods of brain teasers have come and told me -that both of these guys know which door has the treasure,and both of these guys knowwhich door has the unbelievable despair that would ensueif I opened that door.So both of these guys know which door I should be opening.And I also know, and both of them know,that one of them always tells the truth.One is always honest. And then one of them always lies.And the problem is I don't know who's who.And I only have one chance.Obviously I can't just open a door and close it.If I open the wrong door,the despair will come out and kill.And you know, all of the pain will happen.And I can only ask one question of one of themto decide which door to open.So remember, they both know the correct answer.But one of them always lies.One of them always tells the truth.And I only have one question to ask of one of them.So the brain teaser is: What question do you ask?Who do you ask it to?Do you ask it to the green guy or to the brown guy?And then what do you do based on what they tell you?So that is the problem description.And I will now give you the solution.So if you don't want the solution,and I encourage you not to.I think if you think about this one for maybe 20 or 30 minutes,or at most a day.Sometimes when you sleep on a brain teaserit might come to you.So I encourage you to do that.So pause it, stop it, whatever.Don't listen anymore.Because here is the solution.So what you do is- I mean, you don't know who's who.So it's not like there's a correct answeron who you ask a question of.But what you do is you ask you either of the people,what would the other guy say is the correct door to open?So let's think about this.So I could ask this guy, I'm asking the green guy,what would this guy say is the correct door to open?Now what happens if this guy tells the truth?If this guy tells the truth,then this guy's the liar, right?And so he will actually tell mewhat this guy would tell me to do.So what would the other guy sayis the correct door to open, right?So this guy, if you were to tell him the correct door to open,he would tell you the incorrect door to open.Right?So when you ask this guy what would that guy say,he'll be honest about what this guy would say.And since he's a liar,he would tell you the incorrect door.So the answer to this question,you would get the incorrect door.Incorrect door would be the answer to that questionif this guy's the truth teller and this guy's the liar.Now what happens if it's the other way around?What if I ask this guy and he happens to be the liar?So this guy's the liar, this guy's the truth teller.So the liar, he can't help himself.He will lie.So he knows that this other guyis the truth teller there, right?There's only two of them there.He knows this guy's the truth teller.And he knows that this guy when askedwill say the correct door to open.So if you happened to be luckyand you ask this guy the correct door, he would tell it to you.This guy will lie.Let's say that this is the correct door,door number two is the correct door.So let's say that door number two is the correct door.If you ask this guy directly,he'll say oh yeah, door number two.You'll find all your happiness behind door number two.Now if this guy's a liar,he knows that the truth teller will say door number two.But he's a liar, so he'll tell you door number one.So once again, if I ask the same question of the liar,I still get the incorrect door. Right?So no matter who I ask this question to,their answer will be the wrong door,the incorrect door, or the door that I get all of the pain from.So what you do is you ask this question,what would the other guy say is the correct door to open?And no matter who you ask that to,they're going to answer the incorrect door.And so you do the opposite.So I ask this guy, mister green guy,what would mister brown guy say is the correct door to open?And green guy will saybrown guy will tell you to open door number one.Well green guy says that brown guy will tell me to open door number one,then I should open up door number two.And likewise, if green guy says brown guy will sayto open door number two, then I should open door number one.Anyway that's a nice warm up brain teaserfor the next one I'm going to give you.E01 下面这个脑筋急转弯很经典我相信你有些人可能听过但我还是希望可以把它放到当前的视频教程里面因为它是个很好的开始对于更高难度的脑筋急转弯来说 它是个好热身关于如何应对实话和谎话的我们不妨称之为“诚实人和说谎者”假如我们在征途上遇到了岔道 对吧？还是假设有两扇门吧那好一点有两扇门假如我到达了征途的终点宝藏就藏在其中一扇门后面不幸的是 另一扇门后面是“万劫不复”是世上所有的不幸所以我要小心地选择门旁边 坐着两个人一个人长得像这样另一个长得像这样我知道的是。“脑筋急转弯世界”的上帝透露了这两个人都知道哪扇门后有宝藏也都知道哪扇门后面是难以置信的苦难开门则厄难降临他们都知道 我应该打开哪扇门我也知道 他俩都知道其中某人总是讲真话一个人是诚实的 另一个人总是说谎问题是我不知道谁是谁我只有一次机会显然 我不能打开门然后关上如果开错了门 那些苦难就会涌出来杀了我你懂的 万劫不复的痛苦我只能向他们中的一个人 问一个问题来决定开哪扇门记住 他们都知道正确的答案但是其中一个总是撒谎其中一个总是说真话我只能问他们其中一个人一个问题此脑筋急转弯问的是你会问什么问题？你又会问谁呢？你会问绿色的人 还是棕色的呢？然后根据他们的回答 怎么做呢？问题叙述完了下面我告诉你们答案如果你不想知道我也鼓励你这样自己思考个二三十分钟顶多一天吧有时你睡着睡着就迎刃而解了我鼓励你这么做暂停视频 停下来 怎样都好不再往下听了因为下面就是答案了要做的是. 你并不知道谁是谁现在不是你问谁他就会告诉你正确答案你所要做的就是 问其中一个人“如果我问另一个人该开哪扇门 他会怎么回答？”我们来琢磨琢磨如果我问这个绿色人“这个人会告诉我 应该打开哪扇门呢？”如果他告诉我真相 之后呢？如果这人说了实话另一个就是说谎者 对吧？所以他会如实地告诉我这人会怎么指导我要问的是 “另一个人会指出那扇门是正确的门” 对吧？这个人 如果你问哪扇门是正确的他会回答你那扇错误的门对吧？当你问这个人 “另一个会如何回答？”他会诚实地告诉你因为他是个骗子他告诉你的是错误的门对于你的提问 得到的结果是那扇错误的门答案会是那扇错误的门假设了这个人诚实人 这个人是说谎者现在调换一下 看会发生什么呢？如果我问这个人 这个是说谎者他是说谎者 他是诚实人说谎者 他无法控制自己他总骗人他也知道 另一个人是一个诚实人 对吧？这里只有两个人他知道另一个人是诚实人并且他知道 这个人会告诉我哪扇是正确的门如果你足够幸运的话你问这人哪扇是正确的门 他会如实回答的但这个人会撒谎我们假设这扇是正确的门2号门是正确的2号门是正确的门如果你直接问他他会说 2号门啊你会发现 人间极乐就在它后面如果这人是说谎者他知道诚实人说告诉你2号门的但是他是骗子 所以他会告诉你 1号门所以 如果我问骗子同样的问题他告诉我的答案 也是不正确的 对吧？所以无论我问谁这个问题他们的答案 都是指向错误的门不正确的门 万劫不复的门所以你做的就是 问这个问题问“另一个人会说哪扇门是正确的呢？”不管你问谁他们都会说那扇错误的门所以你要反其道而行之我会这人 绿先生啊棕先生会告诉我哪扇门是正确的呢？绿色人会说棕色人会告诉你是一号门如果绿色人说“棕色人会告诉我 应该开1号门”那我应该开的就是2号门如果绿色人说 “棕色人会告诉我应该开2号门” 那我要开的就应该是1号门无论如何 这对于之后的脑筋急转弯来说这是一个很不错的热身第2集 善变者 E02 This brain teaser in this videois 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 me and a bunch of buddies,we were traveling through Europe.And it kind of became our pastimeto do these brain teasers in the back of magazines.And just so you know,I think a lot of you think that 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 me and my buddies,we argued about it for literally about a day.And then I just slept on it.And then first thing in the morning,I woke up all my friends, I was like, I figured it out!So this isn't some kind of easy thing.And I encourage you, just listen to the statement,understand it, and then pause the video.And then think about it for 24 hours.And then come back to it.One, you'll probably solve it yourself.And if you don't, in 24 or 48 hours,then you'll probably find the solution that much more satisfying.So this is the problem of the togglers.Not toddlers.Togglers.I have an infant, so words like toddler are in my brain.But this is the problem of the togglers.So there are five guys in front of you.That's one of them.Two.Three.Four.Five.They don't have to be guys.They can be of any gender.And four of them are what we call togglers.So four of them.Four togglers.And what a toggler does is, the first time you ask them a question,they're either going to tell the truth or 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 asked them a question,then they're going to 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 the truth again.It's like, if I was a toggler 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 pointed to me again,and you say, what is your name?And I say, oh my name is Sal.And if you ask 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 the first time, I just decided to lie.But just as easily,I could've decided to tell the truth the first time.You might have said, hey you, what's your name?I would have said, Sal.And then you ask me, what's your name again?And I would have said Elizabeth.And then you ask me, what's my name again?I would say, oh, 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 toggler- I don't know who's a toggler.Let's say that this is a toggler.The first time you ask them a 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 going to tell the truth.But the first time you ask them a question,and they did tell the truth,the next time you ask the same person a question,he or she is going to lie. So that's a toggler.So you can already imagine, this is- I don't know.The first time that I read the problemit kind of made my brain hurt.This notion of a toggler.It's much easier when there's a realitywhere people only lie or only tell the truth.It's much harder when they toggle.And not only do 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 toggler,because I said there's only four togglers.But even if they are toggler,I don't even know if the first time I ask them a questionwhether they're going to tell the truth or whether they're going to lie.So four of them are togglers.What's the fifth?Well, you probably could guessbecause this is how these brain teasers go.The fifth is a truth teller.And he is 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.So the goal of this brain teaser is to figure outwho is the truth teller.So you want to know which of these five people is- So let's say, goal.Who's 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 one question to this guy and 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 to the same person,although they can be to the same person.Or they could be to two different people.So you have two questions.Any question to ask of any combination of either two questionsto one person or two questions to two people.And by the end of those two questions,you should know for sure who is the truth teller.And that is the brain teaser statement.So pause it now if you don't want any hints or the solution,or anything else.So I encourage you to pause itand think about it for at least a day.And sleep on it.Because a lot of the real math problems or logic problemsthat are worth solving aren't the onesthat you can solve right when you see them.They're the ones where you kind of sit and let your braindo a little background processing while you sleep.So that said, hopefully you've stopped itand now you've resumed it after really strugglingwith this for a long period.Not eating and sleeping 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, it's a tough question.I struggled with this at first.I was like, when you ask someone a questionhow 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 toggler?You don't have any information.So the crux of this problem is,essentially, it doesn't matter who you're askingthe question to the first time around.And actually the solution is that it doesn't matterwho you're asking the question to 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 totell 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 and then to keep thinking about it,pause it again.Because I'm about to give you the solution.So question one.