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That Viral Math Problem (Cheryl’s Birthday) – Numberphile

December 22, 2019


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, “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.

100 Comments

  • Reply WarpRulez July 16, 2019 at 12:49 pm

    Watching this video again after 4 years, I must say that I find it a bit annoying to watch.

    No offense intended for Mr. Pampena, but that presentation was a bit annoying. A bit too much repetition, a bit too much of saying the same things again and again, and with needless detail, the actual whispering was unnecessary and a bit annoying, and the whole thing just takes too much time to get to the point. I think this could have well been explained, clearly and understandably, in 5 minutes.

  • Reply ziv shayer July 16, 2019 at 5:02 pm

    Happy birthday Cheryl 🙂

    Great Video- watched it today for the 3rd time. (last time about 3 years ago)

  • Reply Tushar Goyal July 16, 2019 at 6:03 pm

    and coincidentally I am watching this video on 16th July

  • Reply agarRoyale 2002 July 16, 2019 at 8:54 pm

    11:06 in column 14 there's an "o" not a "0"

  • Reply Steel Beard July 17, 2019 at 2:51 am

    When I read the problem, I understood it as meaning that Albert knew that Bertrand didn't know, not from logic, but from observation. After Cheryl gives each man a piece of the answer, Albert and Bertrand watch each other and then Albert says that he doesn't know, and Bertrand doesn't either. That eliminates only June 18 and May 19. But then Bertrand, seeing that Albert doesn't know, realizes that June 17 is off the table as well, since if Albert had been told June he'd have immediately known the full date. Since Cheryl told Bertrand "17" then he knows now that August 17 must be correct, since it is the only other date with a 17.

  • Reply Hackman July 21, 2019 at 9:20 am

    It took me like, 2 minutes to solve it and i am still in school. Its not all that hard tbh… Its just the wordings that get most ppl, me included. At first i thought it was a joke but then somebody told me it was actually possible, and once i knew it was possible, it was a cake walk…

  • Reply MacGamer Media July 24, 2019 at 6:47 pm

    8:54 Ok just worked it out, Cheryl’s birthday is July 16.

  • Reply GURJOT JASSAL July 26, 2019 at 11:56 am

    On which sheets they write?

  • Reply Domihork August 1, 2019 at 3:11 pm

    Why does the guy sound like he's talking to an idiot?

  • Reply conner hartman August 5, 2019 at 5:31 pm

    Bernard never indicates that albert would know now, so in albert's head, it could have been either 15, 16 or 17. If it was 15, bernard would have known but it could have also been the 17th. I dont see how albert could have known just from the statement that bernard made.

  • Reply Bilb Ono August 9, 2019 at 4:00 am

    0:23 Cheryl definitely let smash.

  • Reply Hihkuhro August 10, 2019 at 6:24 pm

    Lol i just used a little logic. The wording was bs so i just counted the words. Theoreticly saying that Bernard made a long pause in his sentence the total words up to the comma are 7. And he knows the month so it has to be July. And Alberts total words are 16 so its the 16th. And because they are mathmaticians and as we all know they count every word they both know the answer.

  • Reply gore buster August 12, 2019 at 5:05 am

    (1 + (1/100000000000000))^100000000000000

  • Reply gore buster August 12, 2019 at 5:07 am

    Mr Pampena is a funny man ??

  • Reply Ben Hoogendyk August 12, 2019 at 2:51 pm

    That was super fun

  • Reply 5Gonza5 August 13, 2019 at 1:34 am

    I will be honest I absolutely didn’t understand a thing…

  • Reply Kevin Salim August 13, 2019 at 8:28 am

    But… But… 16th July is my birthday.

  • Reply ༺ڳOpernce.ฟ༻ August 13, 2019 at 10:07 am

    Legit figured this out, first time I heard this,
    this is easy wth.

  • Reply Tamás Koncsos August 13, 2019 at 2:14 pm

    I was wrong.

  • Reply Bbduck Gaming August 14, 2019 at 1:14 pm

    Ive randomly guessed someones birthday before, first try too.

  • Reply Eddie Byrne August 18, 2019 at 7:41 pm

    Sorry dude , staring at you from under that proverbial rock, as I don't use social media much , but looking forward to your explanation .

  • Reply George PritsipidoulasTech August 19, 2019 at 12:06 am

    Why is may 15,16 crossed out?

  • Reply dddiop August 20, 2019 at 10:42 pm

    Simon has Keira Knightley eyes

  • Reply Dy August 21, 2019 at 3:47 am

    Without watching the video from 2:30 onward, i did get to a point where i had only these (3) as options.
    – July 16
    – Aug 15
    – Aug 17.

    when Bernerd says "at first i didnt know but NOW i do" …., that is applicable for any of those (3) options. I couldn't figure out, from that point, how could Albert know Bernard has 16???

    I'm lost in Simon's explanation on the final clue …. , how can albert "just know" it has to be july"??? how can Albert be 100% sure that Bernard wasn't given '15' or '17'?

    Let's assume Albert was given 'July'. Then since Benard said 'Now i know' …, then this WOULD BE the ansewr.

    But let's assume Albert was given 'August' and , yes, he would've had ambiguity between '15' and '17'. from Bernard's perspective, he knows for sure the birthday since he has the date. But from Albert's perspective, i don't see how he can know for sure what Bernard has (btwn 15 and 17) IF HE WAS GIVEN AUGUST….

  • Reply Da mamoot August 23, 2019 at 11:27 am

    i think it's july 16th, went through it myself after they showed the table

  • Reply tesseract ` August 24, 2019 at 2:17 pm

    I am at 2:08, and I say it is the 16th of July

  • Reply carlosvacos 333 August 27, 2019 at 1:39 am

    I dont understand why he erased 15 an 16 may. Pls explain

  • Reply OmikronWeapon August 27, 2019 at 10:03 am

    Afterwards Cheryl goes: "wow, you guys are so smart. that killed a bit of bit of time waiting for my quarterback boyfriend to pick me up and take me out for my birthday"
    Albert & Bernard: FFFFFFFUUUUUUUUUUUU

  • Reply 1919helio1919 August 30, 2019 at 11:52 am

    5:30 I heard him say you fxxking gimme

  • Reply Aryan Thapliyal September 4, 2019 at 2:53 pm

    The best part about this video is that it was published on my birthday that is 17 April!!!!!! Wow!!!!!

  • Reply acxez knightNite September 6, 2019 at 11:54 am

    Why could it not be August 15th or 17th?

  • Reply ezzz9 September 6, 2019 at 9:32 pm

    It's a cute problem but most times it fails.

  • Reply MyOwn Meadow September 7, 2019 at 8:40 am

    By logic, August 17, because if you don’t want to guess, don’t choose option that has one possible answer.

  • Reply MägiCo M September 9, 2019 at 6:50 am

    Thats was the first Numberphile video I fully understood. Yeay

  • Reply Majd Alusta September 9, 2019 at 12:57 pm

    I would have had a foursome with them and knew everybody’s birthday leaving my own unknown!!!

  • Reply Stephen Kenny September 10, 2019 at 12:28 am

    I love the number five videos and the 60 symbols and the rest that you do

  • Reply Lagg field September 11, 2019 at 1:25 am

    I GOT IT
    Finally
    Bagels are savoury donuts

  • Reply inordirection September 15, 2019 at 6:17 am

    "If he's holding on to 15, 16, or 17 in his head–or really, in his heart, because we're dealing with cheryl here" loool

  • Reply Logis. exe September 29, 2019 at 3:29 pm

    He predicted the death of xxx 5:12

  • Reply Wooft October 1, 2019 at 8:29 am

    Answer*cheryl is a d*ck

  • Reply Horrible Channel October 1, 2019 at 9:30 pm

    The problem should’ve said Cheryl tells him it’s on July and it’s also on the 16th

  • Reply Maximilian John October 2, 2019 at 1:04 am

    Isn t there a failure in the question. I think Bernhard should say at last That he know now the Date and Albert does know it now too. Because Bernhard Could have the 15th, 16th or the 17th and the last sentence he Said doesnt give Albert the informations he needed. Sorry for my bad englisch

  • Reply akash mishra October 2, 2019 at 1:50 pm

    So which is the strongest Pokemon?

  • Reply Raymond C.T October 2, 2019 at 2:16 pm

    July 16 2021

    Spiderman 3 Release Predicted On A Math Video??

  • Reply Floordford October 3, 2019 at 6:33 pm

    Your logic is flawed. Go back to the beginning and act as though Cheryl said one of the days that you crossed out.

  • Reply ElPikachu October 4, 2019 at 12:04 am

    Ok i promise i calculated it myself, my estimation is july 16, because albert knows for fact bernard doesnt know when cheryl birthday is, we can remove from the ecuation the months june and may, as those have the days 18 and 19, respectively, wich are unique and would let bernard deduce the date. The dates we are left with are july 16, aug 15 and aug 17. months with day 14 cant be as they are present both in july and aug, wich are completely possible. however albert responds he knows the date too. so, whats the only month that has 1 unique correct day left? july, july 16. Hope it is correct.

  • Reply Dan M October 4, 2019 at 11:04 pm

    Omg i didnt know russell brand was on this channel!!

  • Reply Cherry October 5, 2019 at 4:57 am

    I dont understand why may got thrown out. Just because it had a day that was a gimmie doesnt mean it couldnt have been the 15th or 16th of may.

  • Reply Siddhant Kaushik October 5, 2019 at 5:30 pm

    Why he cuts the whole month of May and june ?
    Nobody knows, everyone pretends !

  • Reply Phi Gaming October 6, 2019 at 10:10 am

    4 years late, but july 16th is my birthday!

  • Reply Drift October 6, 2019 at 7:00 pm

    i gave this a go before he explained it it and got i right! it was messy but it worked

  • Reply Maxwell Eckelbarger October 7, 2019 at 6:30 am

    We pay people to do this all day

  • Reply Rento October 7, 2019 at 10:33 am

    I was actually able to solve this!! Big brains!

  • Reply Midoune Fateh October 8, 2019 at 5:11 am

    2019 and I'm still laughing about : "19 (kiss)" lol

  • Reply Fabian Zimmermann October 9, 2019 at 7:26 am

    Hey cool, my birthday is also July 16.

  • Reply Noah Cliff October 9, 2019 at 12:07 pm

    Great video. Thank you so much.

  • Reply Paras Gautam October 12, 2019 at 12:13 pm

    great professor

  • Reply d0 October 12, 2019 at 9:05 pm

    this is a logic problem, not math.

  • Reply Nothing October 15, 2019 at 8:14 am

    I didn't understand it only because the word gimme what is that

  • Reply Chris Robinson October 15, 2019 at 10:04 pm

    July 16

  • Reply Lazy Genius October 16, 2019 at 8:23 am

    How did this become a math problem?

  • Reply Phinehas Priest October 18, 2019 at 8:54 am

    FUC%ING YOUTUBE APP PAUSE!!!

    Idiots at YouTube decided the pause should darken the image and cover it with writing so you can't see the image.

    So, let's pause to see the problem… NOPE AS$HOLES AT YOUTUBE MADE THAT IMPOSSIBLE!!!

  • Reply אריאל פוקסמן October 21, 2019 at 5:36 pm

    I still did not understand why he took july and may out

  • Reply Cathelijne Visser October 23, 2019 at 8:06 am

    what if albert is blufing?

  • Reply Blonde Kat October 24, 2019 at 9:35 pm

    I am unreasonably proud of myself for solving a four year old logic problem.

  • Reply KURB前 October 26, 2019 at 8:13 pm

    How tf did I get this in 30 sec.

  • Reply Woojin Son October 28, 2019 at 7:48 pm

    gimme

  • Reply Garrett October 30, 2019 at 5:59 am

    I only got it right because i guessed my own birthday

  • Reply page394 October 30, 2019 at 8:27 pm

    You are totally wrong, the right answer is august 17.

  • Reply ᏢᏆᏃᏃᎪ ᏩᎾᎠ October 30, 2019 at 11:27 pm

    Albert: what's your birthday
    Cheryl: whisper whisper whisper

  • Reply Ezra Garber October 31, 2019 at 4:57 am

    This is so fun, it reminds me of sudoku. Also, my birthday is July 16 as well!

  • Reply Anupam Mathur October 31, 2019 at 5:11 pm

    Man…Thats my birthday

  • Reply Anthony Turner November 1, 2019 at 3:18 pm

    At about the 7 minute mark, can someone explain how he was able to also get rid of the dates in May?

  • Reply Jonny P November 1, 2019 at 3:48 pm

    Idk I did this in like 40 seconds

  • Reply Ádám Nemes November 3, 2019 at 1:14 am

    i'v got aug 17 teen lol

  • Reply Denis Polyakov November 4, 2019 at 8:22 am

    The clock on the fireplace shows 7-16 🙂

  • Reply Yeah, that is TOTALLY right. : November 4, 2019 at 7:48 pm

    I did it in my head before he had a chance to explain it. 😀
    EDIT: Help, I'm too exited to stop smiling and it hurts.

  • Reply Renato Pires November 8, 2019 at 4:18 am

    easy

  • Reply The Night November 10, 2019 at 11:23 am

    A: I know B doesn't know because there are 2 options in my month.

    B: If A knows I don't know, then it can't be May or June. There is now only one month to my date. I know the birthday.

    A: Now I know the birthday, since there is only one date for July.

  • Reply legendary skumem November 13, 2019 at 11:27 pm

    At the end is it wrong because bernard knew because he was told the date so only he knows what date it was but the 3 options for albert cant be taken apart because he has the option of 3 dates he impossibly could know

  • Reply Steffen Fenchel November 15, 2019 at 5:06 pm

    but why cant it be any date in August except for the 14th? he could exclude may and june now it isn't the 14th because in that case a wouldn't know for sure but is it was August 15 then B would know because he could exclude may and june and there is only one 15 left. but why does A know? He cant assume it is July because B has 3 gimmies!!!!

  • Reply Eric P November 19, 2019 at 12:09 am

    @5:24 that was so weird ?

  • Reply Chukwunonso Okoro November 20, 2019 at 7:58 am

    game theory!

  • Reply Noa Haroz November 23, 2019 at 2:03 am

    The answer is my birthday?

  • Reply Paphos Life November 28, 2019 at 8:35 pm

    Sorry, but if Albert can have the 15th, 16th or 17th, how can Bernard know he has the 16th?

  • Reply Jason Zheng November 30, 2019 at 10:42 am

    Reminds me a bit of sudoku

  • Reply SeveN November 30, 2019 at 2:29 pm

    But they never told eachother date or month it doesn’t make sense

  • Reply MacGamer Media December 1, 2019 at 11:08 am

    3:30 July 16th.

  • Reply Benpeterscode December 8, 2019 at 6:19 pm

    Only with the knowledge that Albert by some magic knows the date by the end of the problem does the logic hold up. How would Albert know it was in July and not August? Just because there is only 1 option in July doesn't logically prove it must be in July right? If you follow the same logic but assume the date was August 17th then Albert would have been wrong. So we have to assume that Albert, by some magic, knows that it's in July and only then can we assume that it must be the only month with 1 option left. I don't like that lol

  • Reply Muhilan Selvaa December 13, 2019 at 6:30 pm

    This was such as delightful little problem!

  • Reply Pyeonghoi (Derek) Lee December 16, 2019 at 11:59 am

    WOW

  • Reply American Enigma _ December 16, 2019 at 8:37 pm

    I’d say FCK Cheryl and Move on ….

  • Reply Timothy Y. December 19, 2019 at 3:41 am

    Nice, I figured out the solution to this one

  • Reply SHASWATA DUTTA December 20, 2019 at 3:57 pm

    A fantastic logic question; and I really don't know why I made a silly mistake while solving it; but yeah, I did it all by myself.

  • Reply C N December 20, 2019 at 6:32 pm

    Very basic game theory problem…

  • Reply J Bizzle December 21, 2019 at 12:26 am

    Mate once you put it in a matrix I saw the answer… Maybe that's the aspergers talking

  • Reply WoulfShadowGaming December 21, 2019 at 4:56 pm

    Is it just me, or was this solution immediately obvious?

  • Reply Christine Wennerberg December 21, 2019 at 11:55 pm

    My birthday's June 18th lol

  • Reply Josh Timmins December 22, 2019 at 1:29 am

    My birthday!! 🙂

  • Reply Gabriel Reyes December 22, 2019 at 4:39 am

    Or just stalk cheryl on facebook and find it

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