I'm so happy I'm here to be able to get to talk about a viral maths problem. I mean when does that happen? Come on. And this is not in the maths community. We're talking about like in the big wide world. This is really exciting. Have you heard of it, Brady? It's got a few names, at the moment. It's like the Singapore maths problem it's a competition maths problem originally from Singapore. it's also "The Cheryl problem" Not saying anything against Cheryl Cheryl's not a problem Cheryls are usually pretty nice So if you've been living under a rock I'll quickly explain what it is It's actually, from a mathematical point of view it's a classic logic problem It involves 3 people Cheryl, Albert, and Bernard Ok So Cheryl is trying to get Albert and Bernard to guess her birthday For what reason, we don't know Maybe she's just trying to play Albert against Bernard Or maybe Albert and Bernard, y'know, are trying to scam Cheryl for like her secret question for a bank account Who knows? But Anyway She gives them a bunch of options Ok so, Cheryl has shared a possible pool of dates But now, what's she's done is she's actually gonna give a piece of information to Albert and a piece of information to Bernard An incomplete piece of information about her birthday so this is how it goes Albert, I'm going to tell you the month, - whisper whisper whisper and Bernard, I'm going to tell you the day, - whisper whisper whisper So now all they know is Bernard knows that Albert knows the month and Albert knows that Bernard knows the day But they don't know it together And so then, they have a little exchange So Albert states I don't know when Cheryl's birthday is But I know that Bernard does not know too then Berard replies at first I didn't know when Cheyrl's birthday is, but I know now. So now suddenly, Bernard knows But what happens? Is Albert left the in dark? No Somehow, Albert is then able to deduce then I also know when Cheryl's birthday is. So now they both know. And presumably, Cheryl is either happy or upset Or her bank account has been broken into. Something like that. We don't know exactly. The question is how can you find out the information Nothing is explicit, is it Brady? it just seems like they playing games Are they Jedis? What's going on? Are they reading each other's minds? and this is the nature of these logic problems Believe it or not, this isn't the first time I've been faced with a problem like this As mathematicians, we get asked these problems all the time And so the way to answer this Is to actually break it down and try and attack it logically because otherwise you're not going to get anywhere. I am now going to rearrange this information here Because this is really important we need to have something to focus on So what I'm going to do is I'm actually going to split out the dates at the top here I'm going to..I'm going to put 14 uh... 15 The dates there in columns and in rows I'm going to place the months So here is May So now, what I'm going to do there is I'm just going to have a look at this so May 15 A cross is just basically, this is an option. This could be it. 16 or 19 Yeah, these are also contenders. What I'm going to do is actually give us a bit of understanding here because once we get into the logic we could get lost Let's look at the options for this column. For the day or the date 14 how many different options do we have? We've got 2 ok 15 we have 2 16 we have 2 17 we have 2 18 we have 1 and 19 we have 1 as well. Ok, now let's have a look for months. So now for months how many options do we have for each month? So we have 1,2,3 for May 2 for June 2 for July and 3 for August See where I'm going with this, Brady? So now what's going on here is that I've actually just, I've just spread out the information Before I start bringing in the weird conversation they had The weird terse conversation that they had so now Albert says I don't know, I don't know what the birthday is. OK. (Brady: Of course he doesn't.) Yeah, but that's a weird thing to say. Can I just say that? It is a weird thing to say because in a logic problem Obviously you don't. We both know the game here. You've only been told months. There is 3 options, 2 options, 2 options, 3 options. The only way you'd know is if there was 1 month there with only 1 date. Just saying that. I'm just saying that. What's interesting though is Albert says "But I also know that Bernard doesn't know." We've got the information in a way that, ya know, I'm gonna be able to work with, but just looking at this straight away there are some red-hot dates. Here June 18 Well if you have a look at it it's only one 18 that applies to any of the months It happens to be June. In actual fact the same for May there's 19 19's not anywhere else Can you see that, Brady? There's nothing around there What this means is if Cheryl went over and said to Bernard "18" or "19" *smooch* What that means is straight away Bernard would be in. It's like a gimme. It's like "Bang". I know exactly what it is. You give me the information. It can only be 1 thing. But see, Albert in sort of a gloating way, I mean really Albert needs a bit of emotional intelligence I think because he's basically gloating and he's going, "<pant> <pant> I've got information that excludes the gimmes" "So I know, Bernard, that you don't have gimmes." But how can he not know? Because he doesn't have the date information. He's only got month information. Ok, what are the months that had potential for gimmes? Well they were June and they were May. And that's the only information that Albert has. He only has month information, yeah, monthly information So. What can we deduce from this? We're mathematicians here. We're all getting mathematical... Albert says, "I don't know the date". Yes, ok, that's a weird thing to say. "But I also know that Bernard doesn't know the date." So logically, what you've got to say is therefore Cheryl didn't whisper May or June in his ear. So, obviously cheryl whispered something like "July" or "August" That's what she did 'Cause if she said May or June, Albert wouldn't be saying that, with conviction. Well that means that this is... no longer an option. And this... is no longer an option. But because Albert has said "I know that 18 and 19 are not an option" the only way Albert would've known that is through monthly information. So, in actual fact, this is gone, this is gone, and this is gone. Basically, everything in May and everything in June is gone This is great because with my prized little chart here, I can actually reduce some numbers here. So now this goes down to 0. This goes down to 0. So now Bernard actually knows.... Oh! An actual fact, because all of May and all of June, all the dates that we had on the table are all gone, that affects the total number of options I have for each day. It doesn't matter about his date. He's actually just looking at all the dates So now for 14... Well, there's still 2 there. That hasn't changed. But for 15, we've just struck out May so now this is only 1 option. For the 16th that was in May and July. May is struck out. So now... there's only 1 standing in this column. For 17 same thing, look at this. There's June 17 and then there's August 17 So this one's getting struck out. And then for 18 and 19 and they turned down to 0 too So Albert's given this information Now Bernard has been able to reduce the options. But to be clear, for Bernard to know the birthday he already has the date. He just needs the month. So now Bernard says... "At first I don't know when Cheyl's birthday is, but I know now." So, from what Albert has said Bernard is now able to say what the month is. Ok, so now, let's put ourselves in Bernard's shoes. So now he's actually discounted May and June. He's reduced the number of options. Really you're only talking about July and August. Now if he did have 14... right? There are still 2 options on the table So... He didn't have 14. If he did have 14... he would have said something like... Uh... yeah, I still don't know. OK? But instead he goes, "I didn't know before", which means he didn't have the gimmes. But now he knows! How does he know? Because there are actually new gimmes on the table, Brady, you wouldn't believe it. Look at this. The new gimmes are 15, 16, and 17 So now, if he's holding onto 15, 16, or 17 in his head, or really, in his heart, because we're dealing with Cheryl here... What's happening here is he's going "Wow, there's only one 15 that applies to August, there's only one 16 that applies to July and there's only one 17 that applies to August." "Look, if I have any of these dates, I will know exactly which month it applies to." So, at this stage of the problem, it could have been 15, 16, or 17. So now, Bernard is going... "Sho sho sho sho sho..." "bup bup bup bup bup" And this one goes down to 0 But not only that because July and August have now lost a date. So that means over here, we need to go bang bang bang... 1. ...and over here.... We need to go: "bang bang bang... 2" Right. So what's the last statement? Albert says, "Then I also know when Cheryl's birthday is." Ok. So that means he's got a gimme. So now if we have a look where the gimmes are... Let's look at the options. He's either got July or August. What options do we have here? Well August is no good because it's got two options. That means it's ambiguous. It means he doesn't have gimmes. It could be either 15 or 17. But because he knows... it has to be July. Do you know what that means, Brady? It means that Albert is going... "Uh-uh, sorry." and Albert's going... "Uh-uh, sorry." So this now goes down to 0. This goes down here. Well Albert's doing it, so I'm doing it in blue. That one goes down to 0 too. So now, look what we end up with. We end up with 1 option for the month and 1 option for the date that they can both get. And that option is July 16. *sighs* Ok, what's really interesting about this problem is the fact that because it's using words it's actually open to interpretation. If this was actually redone in just pure symbolic logic, it would be unambiguous. Because we're using these sentences in actual fact, people have opened them up into interpretation.
Awesome video. Althoough I have never heard of this problem before. I must be living under the rock.
BTW Notch retweeted this video so expect more views than usual. :P
This is my favorite common knowledge problem: https://xkcd.com/blue_eyes.html
Bernard?
https://www.youtube.com/watch?v=Q1EcAoyOIXk
He and Matt Parker should do a calculator unboxing together. I think they'd be great.
i've said it before but here i go again. this is not a MATH(S) problem. it's a logic problem.
Where is the flaw in my logic, I haven't watched the video but read an explanation elsewhere (stupid meetings):
So Albert knows that Bernard doesn't know which means it's not May or June.
Then Bernard says that he didn't know initially either (meaning he could've been told 14, 15, 16 or 17, the non-unique dates) but now he does know.
So Bernard, knowing the month is either July or August, now knows the date of the birthday.
Wouldn't he having been told 15, 16 or 17 means he knows the date of the birthday? Why does it have to be July 16?
If Bernard were told 17, then, knowing it's not May or June he now knows it's August 17. How can Albert be sure whether it's July 16, Aug 15 or Aug 17?
So today was a pretty awesome day, because the very last question in my MGIS exam just happened to be the Cheryl Problem. Thank god I procrastinated studying to watch this video a couple days ago.
I don't want to humblebrag but solving the problem in my head made the rest of the video much less enjoyable