Cheryl's birthday

- [Voiceover] So, this is a fun deductive reasoning problem that's being forwarded around the Internet. Several people have actually forwarded it to me, and so, I thought it would be a fun thing to work through. The grammar isn't perfect, but the problem is a fun one. So, it says Albert and Bernard just, it should say became friends with Cheryl and they wanted to know when her birthday is. Cheryl gives them a list of 10 possible dates and we have our 10 dates here. Cheryl then tells Albert and Bernard separately the month and the day of her birthday, respectively. So, just to make sure we're parsing that sentence correctly, she gives Albert, she tells Albert the month of her birthday. And she gives Bernard, she gives Bernard, the day of her birthday. And, I think we, it's fair to assume that Albert knows, he's been given the month and he knows that Bernard's been given the day. And Bernard's been given the day and he knows that Albert has been given the month. And we should also assume that they are good logicians. That they are going to do very logical things. And then, we have this dialogue. Albert says, I don't know when Cheryl's birthday is, but I know that Bernard does not know too. That's fascinating. And then, Bernard says, at first I didn't know when Cheryl's birthday is, but now I know, but now I know. Fascinating, and then Albert says, then I also know when Cheryl's birthday is. So, when is Cheryl's birthday? So like always, pause the video. See if you can work through this on your own. It's a fun problem to tackle, and I'll give you a little bit of a hint. Diagram out, write the information that each, that Albert knows and how does the world look from Albert's point of view. And then, write out how the world looks from Bernard's point of view and then tell us, and then think about what these, what you can deduce from these sentences. So, I'm assuming you've had a go at it, so let's just do what I just said. Let's diagram out the world from each of their points of view. First, from Albert's point of view, A for Albert. So, he's been given the month. so he's been given either May, and if it's May, he says, well then if it's May it's gonna be, the actual day is gonna be 15, 16, or 7, the 15th, 16th or 19th, 15th, 16th or 19th. He was told, or he was told the month June. And if he was told the month of June, then he says, well I don't know if the date is 17 or 18, 17 or 18. If he was told the month of July, if he was told July, he'd say, well I don't know whether the date is the 14th or the 16th. And if he was told the month August, if he was told the month August, he'd be thinking to himself, well, the date's either gonna be the 14th, the 15th, or the 17th. Now, let's think about the world from Bernard's point of view. >From Bernard's point of view, he's been given the date. So, if he's been given the date the 14th, if he was told the 14th, then he would say, all right, let's see, May's not an option. June wouldn't be an option, July would be an option and August would be an option, 'cause there's a July 14. and an August 14. There's no May 14th or June 14th. So he would say, well, I'm not sure. If he was told it was the 14th, then it's either gonna be July or August. If he was told the 15th, then it would be, let's see, May would be an option, there's a May 15th here, or August would be an option, there's no June 15th or July 15th here. So, May, May or August. If he was told the 16th, let's see what are the options? It could be May, there's a May 16th as one of the options. There's no June 16th, there is a July 16th. So he'd say maybe it's July. And there's no August 16th either. If he was told, it's a 17th, if he was told it's the 17th, he could say, well it's not gonna be in May, there's no May 17th. There is a June 17th. There is a June 17th. There's no July 17th, but there is an August 17th. So, there is an August, there is, I'll just write Aug for short. There is an August 17th. And then, if he was told an 18th, he would say, let's see, there's no May 18th, there is a June 18th, and I think that's the only 18th that we have here. So, if he was told that the day is the 18th, then he would know, he would know that the month is June. And, if he was told that the day is the 19th, then up here, the only 19th here is May 19th, May, May 19th. So, if Bernard, Bernard's interesting. If he was told the 18th or the 19th, then he would know what the month is. So, with this out of the way, and if you're getting inspired, I encourage you to pause the video again and see if you could work through these statements, but now let's work through the statements. So, Albert says, I don't know when Cheryl's birthday is, which makes sense 'cause no matter what month he's been given here, there's multiple options for each of those months, so it makes sense that he doesn't know when Cheryl's birthday is. But, I know, I know that Bernard does not know too. So how could he be so confident that Bernard does not know too? Well, Albert has the same information that we have right over here and Albert says well look, if the date, if Bernard was given an 18 or a 19, then he would know for sure that Bernard does know the date. So, the only way that he can feel confident, the only way that he can feel confident that Bernard, the only way he could say, I know that Bernard does not know too, means that Albert knows that Bernard did not get an 18th or 19th. So, another way to translate this statement is, Bernard did not get an 18th or 19th. Bernard not get 18th or 19th. Now how can Albert be so confident that Bernard did not get an 18th or 19th? Well, Albert knows, Albert knows the month, Albert knows the month. And if he's so confident that Bernard did not get an 18th or 19th, that's because he knows it's not May or June. If the month that Albert got was May, then he would say, oh maybe he did get an 19th here, in which I can't, couldn't make the statement. Or, if the month was June, well then 18th would've been a possibility for what Bernard got. And so, he wouldn't have been able to make this statement here. But because he says, I know that Bernard does not know too, the reason why he can say that is because he knows it's not May or June. So we can rule out, we can rule out May or June. So we can rule out, we can rule out the 18th, the 19th here, and we can also rule out May or June now from Bernard. Now from Bernard's point of view, we can say look, Albert was, the only reason why he was able to make that statement is because Albert knows that the month is not May or June. So, let me rule out all of the Mays and Junes. So, let me rule out June here. Let me rule out, let me rule out May over here. Now I think you see where this is going. Now Bernard, and once again, at any point, if you get so inspired, please pause the video and continue on with the deductive reasoning that we have started. All right, now Bernard says, At first, I didn't know when Cheryl's birthday is. Which is fair because it wasn't the 18th or 19th which Albert already knew. But now I know. So, now I know. So before he didn't know, but now he knows. So, if now he knows, what are the possibilities? What are the possibilities going on here? So he knows if the date he was given is the 17th, we've been able to, then he could deduce that, hey, the month is now August. If the date he was given was the 16th, the month that he could now deduce is July. If the date he was given was the 15th, he could deduce August. But if the date he was given was 14th, he still wouldn't know what the month is. It could still be July or August. So we could rule out the 14th, 'cause if the date he was given was the 14th he still wouldn't know. But he says, now I do know. So we could rule out the 14th. And once again, we're assuming Albert is hearing everything. Albert and Bernard, they both could kind of draw these diagrams out. And so Albert could now say, okay, look, if he now knows, then the date couldn't have been the 14th. So then he rules out the 14th. He rules out the 14th. So the stuff in orange that I just did I got from this statement there. And then Albert says, then I also know when Cheryl's birthday is. So, from Albert's point of view, the only way that he now knows what the birthday is if the month he was given was August he still has two options there. But he says he now knows when Cheryl's birthday is. So it can't be August because all the deductive reasoning we've just now done, if he was given August then he would still not know whether it was the 15th or 16th. But now that he knows, it must be July. Because if he was given the month July, there's only one option now for the date. So therefore, the date must be July 16th. Albert must have been given July, Albert must have been given July. And Bernard must have been given, must have been given the 16th. So Cheryl was born on July 16th. Lots of fun.