TheProtato In an other parallel universe: Albert: ,,Who do you go with? Bernard or me?" Cheryl: ,,Well... Bernard ugly af... so definitely you" Bernard: ,,But i know your birthday!" Cheryl: ,,Who cares m8?"
One of my favourite math jokes operates on a similar principle: Three mathematicians walk into a bar. The bartender asks "Do you all want a beer?" Mathematician A: "I don't know" Mathematician B: "I don't know" Mathematician C: "Yes"
Ok so the answer is the first to arent opposed to it because they would have said no because not all of them were opposed. So the last mathematician knows they want beer and he does too so he says yes.
I'm not sure, but I guess it's like this: Mathematician A Can't say "Yes", because he doesn't know if the others want beer, but if he wouldn't want beer, then it would definitely be "no". So he wants beer but doesn't know what the others want. So now Mathematician B knows that A wants beer but not if C wants beer or not, so the same applies to him. Since he wants beer to he also says "I don't know". Since A and B could've said "no" if they did not want beer, C now knows that A and B want beer, and since he also wants beer he says "yes". I hope it's kinda understandable.
The principle is pretty simple. When asked if ALL three wanted beers, any of them could have said "no", simply because one of them not wanting beer is sufficient information that not ALL of them wanted a beer. Since the first two said "I don't know", it means they wanted the beer, but couldn't assess if the others did. The third one, seeing the two first guys wanted a beer, wanting on himself, said "yes".
I heard a person tell this before but he forgot to limit the dates to a specific range, making it seem like they somehow figured out the Birthday from 365 possible days.
I think the bigger question is, who wants to be friends with a woman like Cheryl? Can you imagine what it'd be like? 'So what time's the party?' 'It's either on the hour or the half hour, between 10am and-' 'OK, forget it. Not going.'
I think solving the actual problem is really messing up priorities; honestly we should be more focused on the totally genius cognition of Albert and Bernard. I mean, they solved such a spontaneous question with such speed and precision, it's amazing Harvord isn't on their case. 😜
The moment he finished drawing the table, I knew exactly what his explanation was going to be, though I didn't know the exact answer. That table cleared everything up so elegantly.
Real world version of this: Albert: “July.” Bernard: “Sixteen.” *high five* They clearly communicate somehow, why couldn’t they be like normal people and just tell each other?
The best thing about this problem: people getting excited about math. The worst thing about the problem: viral sites and people implying that people who solve a fairly straightforward logic prob, similar to those found in any popsci mag quiz page, are geniuses.
DisRes Agreed; I'm no genius, believe me, but I got this after a minimal amount of painful brain activity. The other thing that annoyed was people saying, 'Pfft, this is logic, not maths'.
Buffoon1980 I am among those who said "this is logic, not math." I still believe that assessment. I figured it out with minimal effort once I stopped looking for the math in this "math" problem. I instead focused on the verbage exclusively and almost immediately deduced the correct answer.
whatshendrix Depends what the actual problem about the triangles is. If the problem is trying to stack the triangles into a square like those woodblock puzzle games that kids play, then it is geometry. If the problem is trying to find its height or width or total area, then it's math.
Actually, the pic he uses is from the Brazilian Football Player Bernard, and nobody in Brasil, not even Bernard, pronounces like any of the comments here.
Well it's always that way with math.... Didn't you learn at school that all math problems are made up? Same is this one. Aaaaaand same is with the "media....". It's a math problem pretending to be not a math problem so people would look at it :D
An underappreciated fact of this brilliant logic problem: It's amazing enough that both Albert and Bernard can deduce Cheryl's birthday in this manner. It's even more amazing than an outside observer can also deduce Cheryl's birthday without being told the month OR the date.
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.
Can you explain why it can't be May or June? It's still complicated to me. I understand why it can't be May 19 or June 18, but why do you exclude the whole May and the whole June?
It makes total sense and easy to understand, but for people who still doesn't get it, try this version: A (the one that knows the month): I know B doesn't know because there are AT LEAST 2 options in my month. B (the one that knows the date): If A knows I don't know, then it can't be May or June. Thus, By looking at the remaining months: July and August. There is now only one month to my date. I know the birthday. A (the one that knows the month): Now I know the birthday, since there is only one date for July. (Wonder why A picked July 16 instead of Aug 15 & 17? Well A is the one that knows the month, hence July 16 is the only option A would pick)
I remember in University we had a similar problem presented, but I forgot what it was exactly. I had figured it out though... It was something like... - there are two persons Alice and Bob - we are looking for two numbers a, b - Alice knows the sum of a and b - Bob knows the product of a and b - then there is a conversational snippet presented to us, very similar to the one from the video, where it goes back and forth and then they suddenly know the answer - what are the numbers a and b Don't know how much I remembered or changed or missed in that story, but if this sounds familiar to anyone, please do post the complete (proper) problem.
The puzzle that you're describing sounds very much like a logic puzzle, but the names Alice and Bob make me think of crypto as well. That's probably why Vanko got confused.
Manpreet Kang lol, no the name Alice and Bob I made up, because I couldn't remember the real test's names. It was in german anyways... we did this during maths tutorial after lecture.
Uncle Steez Perhaps I should have been more clear about that. I meant the sum of the ages is the same number as that of A's street address. And sorry to say that's not the right answer.
The thing that pains me the most is the fact that anyone who ever solves this(or sees a solution for any problem,not just this one) goes like : yeah, I knew this, totally easy.. easiest logic math problem ever bla bla" .. It is not that easy, and it's quite amazing to have such a problem at hand. Wonderful video as always.
There's been 93000 views and even more subscribers. What would've been odd if it had been nobody's birthday! There's probably even plenty of cheryls whose birthday it is!
I didn't watch the full video, didn't look at the comments, but let me try to solve it.... If 1st said that he knows that 2nd doesn't know either, that means that we can cross out May and June, which leaves us with 5 dates. The second immideatly solved the problem after that, which means that it isn't 14th, because it had 2 dates left. Because after that the second also realized what is the answer, it means he also had only one option left= July 16 (August had 2 possible dates). Hopefully I was right :3
Oh wow, paused the video around 2:08 and I've managed to solve it. This is actually pretty great; the wording of the problem gives you information where you least expect it. Other than that, it's quite straightforward.
***** It means that the info you have directly leads to the solution. For example, if you have a list of dates like in the video, 18 and 19 don't occur more than once, meaning that you can deduce the month from the day.
I know that, but then how can you be sure that it can't be May? I understand June because there's only one choice left and Albert still doesn't know, however, there are still two choices for May. So how?
June isn't crossed off because there is only one possibility left. May and June are actually crossed off for exactly the same reason. This reason is that they both have a date number that is not present in any of the other months. So, for Albert to say that he knows that Bernard doesn't know, he is essentially saying that he knows that it is either July or August - because July and August both have dates that are repeated in the other months and therefore knows that, with the information that Albert has been given, albert could not possibly know the correct month and date at this stage.
sloonzz1012 Because the 18th and 19th are the only gimmies in the first section (for Bernard), and because Albert somehow knows that Bernard doesn't know. You can eliminate both May and June as potential months. If the birthday WAS in May/June, Bernard COULD possibly know the exact date, but because of the first sentence (Albert saying that he doesn't know and that he also knows Bernard doesn't know) - Cheryl's birthday can be confirmed to not be in May and June
i am from singapore, and we are so focused on the hard and fast rules in mathematics that we fail to appreciate the many other things that maths is about: logic, real- life applications and maybe more. and i think that is what maths is about, its prevalent in every part of our lives.
Can we just appreciate Bernard's smartness He does, what took Simon took 8 minutes to explain, in 5 seconds in his head. That is 96-fold the smartness of Simon Bruh
I don't understand how Bernard's response is enough information for albert to also understand. How is bernanrd to state the last bit of necessary info? edit: I mean, Albert could say he knows the date because it's a 15 or a 17. He doesn't state that bernanrd would also know from his new response.
Yes, so he eliminates the 14th, which leaves two single dates in one month and one date in the other. but, all 3 numbers are different, so there's really no way that albert could have deduced which of those 3 separate dates it was. There was no indication that is was 16 rather than 15 that bernard was thinking but with either of those numbers bernard would know the birthday. Work through the problem as if its august 15th. Albert says "I dont know, but neither do you", eliminates may and june. Then bernard, knowing its the 15th says "Oh, I didnt know before, but now I do", and now albert thinks its july 16th but its actually august 15th. I dont see where august gets eliminated.
@@connerhartman9336 The point is. Had Albert had August he wouldn't have ended up saying, oh! I know then. But he had July. So he could state it as fact. The only scenario where he can end up saying it for a fact after the 14th is eliminated is that he had been told July is the month. Because you are right. It could have been 15, 16, 17. But the only conditions where all their statements are true is July 16th.
Three logicians walk into a bar. "Would you all like a beer?" asks the bartender. The first logician says, "I don't know." The second logician says, "I don't know." The third logician says, "yes."
@@kev117_ the question was, "Would you all like a beer". That means that if the first dude didnt want a beer the answer to the question would have been no. But instead he said that he doesnt know which means that he wants a beer but its possible that one of the other dudes dont. The second guy said he doesnt know so that means that he wants a beer too but he doesnt know if the third guy wants one or not. So the third guy knows that they both want a beer based on their answers and he wants a beer so at that point he can say yes, they all want a beer.
This would be way more funny if the top comment in this comment section wasn't the exact same comment, with way more likes and was made 2 years ago. Basically I'm saying you might've copied the comments
May was removed because it contained a gimme. If Albert had been told a month that contained a gimme, then he would not have been able to say that he knows Bernard doesn't know. Off with May and June. July didn't get taken out. We ruled out May and June, then we ruled out the 14s, and then - since Albert could claim to know - we knew he must have gotten a gimme as well. If he'd been told August, he wouldn't have had a gimme. Therefore, if they can figure it out, we could (finally) rule out August.
my approach was very similar, except I threw out all the gimmes untill there was one date left. So I ended up screwing up at the end and almost solved it but didn't. what a Parker's square
Because Albert realized that if the birthday was May then Bernard may have known the birthday. But since Bernard does not know then it can’t be May or June.
June was eliminated for sure. May? Still had two possibilities for May, so that leaves the 17th as the only day with only one Month possibility, so at that point if he is certain it must be Aug 17, because every other day at that point had multiple possibilities. Right? What am I missing?
I love your accent, could listen to your explanations all week long. I appreciate how you broke it down. this is new to me, and I would be befuddled without your help to understand. love the banter between you and your mate.
There is actually a problem my math teacher gave in my P5 math class called Denise’s birthday, which has Albert, Bernard, and Cheryl knowing the month, day and year respectively about Denise’s birthday.
Can somebody explain why May 15 and 16 were crossed off? I understand May 19 and June 18 are crossed off. And following that June 17 goes away since that is the only one left in the month. But why does that remove the rest of May? May would still have 2 options. 15 and 16 both would still have 2 options as well.
The whole of May and June have to be crossed off because Albert knows that Bernard doesn't know the correct month and date at that stage. Meaning that Albert either knows the answer is july or August. We can deduce that Albert knows it is July or August when he says that Bernard doesn't know. For Bernard to not know at this stage, Albert must know that it is in a month where there are no dates that do not appear in any other months (18th or 19th). If, for example, Albert was told it was may, then he would know that there would be a possibility that Bernard could know the month and date straight away (if Bernard was given 19).
wolphe Because the guy who knew the months knew it wasn't in May. If the birthday was in May there would be no way either of them could know the precise date because the information would be too ambiguous.
Jono Brown I understand that the gimmes go away but it still doesn't clearly explain why the rest of May goes away. From Bernard's POV: May 19 and June 18 go away immediately since they're gimmes. Then he hears Albert saying "I don't know what the day is but I know Bernard doesn't know it either.' With just that, Bernard knows June 17 goes away too and subsequently Aug 17. But that should still leave May 15 and 16, July 14 and 16, and Aug 14 and 15. I guess my question boils down to, How did Bernard know which date it was just from that one statement.
wolphe albert said that he was sure bernard didn't know it. The only way bernard would know it straight away was with days 18 or 19. And the only way for albert to be sure those days are off, is if the month cheryl told him was NOT may nor june. In short, Albert always deals in entire rows, Bernard in entire columns.
Because he says for sure that Bernard doesn't know, if it was in May then there would be a chance Bernard would know for sure, as there is a unique date in May, so the month must have non unique number dates
What initially throws me about this problem is that I assumed that we would know at the same point that Albert knows. When in fact, we can only know AFTER Albert tells us that he knows.
This is exactly it! People do not realize when they are arguing with each other that one arguee has the 3rd party viewer train of thought (as we watch the exchange unfold), and the other arguee has the 'If I was in Albert's shoes" train of thought. This is the the source of the issue.
before I look ahead, July 16th. if he knows the month and knows the guy knowing the day can't know which it is, it can't be may or June, since those contain unique days. Now that the guy who knows the day knows it's June or August and the day, so it's a unique day to those months, removing 14. Going back to the original guy, if it was August, he wouldn't know if it was 15 or 17, since there's two unique numbers, but because he knows it's July, is has to be July 16th
Why would Albert be saying ”now I know too” as there’s 3 options to pick from Bernards statement. He wouldn’t possibly know the date with the information that Bernard knows as Bernard could be saying that of anyone of those 3 dates. Am I missing something?
It's one of those math problems that are complicated because of the structure/grammar of the question/problem and knowing what is expected of you rather than the actual solution. I always hated worded math problems for this reason.
something similar is used in electronics and computer programming to sort out the result of a program or series of circuits. like if you would have a control panel with circuits that override other circuits, you have to tell the controller to close or open ports when certain other ports are closed or open. doesn't matter how many circuits or inputs you have, once you narrow it down you end up with one determinating signal, and you can write all the other signals as functions of that signal.
My take: at beggining i thought its not from the set but from all days of the year. But if from sets its extremely easy. Albert says they both dont know, its actually big help for Bernad. We have to know Bernard can only know at the BEGGINING if he knows june 18 or may 19. So its either may or june. As second guy answers now i know, its obviously june because Albert said he couldnt know - at first he had two choices june 17 or August 17 but when he said he couldnt know at beggining he knows he talk about june. And when Bernard answers that it becomes obvious to Albert too
I like it because I was able to solve it by thinking it through critically before the explanation, but the video afterward demonstrated an even better way of visualizing the options through a chart that included space for the number of options left in each. I had simply crossed out things in a list that looked exactly like the one he had above the full chart on the paper.
Okay, I'll try to break it down step by step. The answer: July 16 The possible dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, Aug 14, Aug 15, and Aug 17. Albert is aware of the month while Bernard is aware of the date. Albert says: "I don't know when Cheryl's birthday is, but I know that Bernard does not know too." The answer is July 16th. That means Albert is aware that the month of Cheryl's birthday is July. The possible dates for July are the 14th and 16th. Both of those dates are repeated-- there are August 14th and May 16th, so Albert knows that from the dates alone that Bernard cannot know Cheryl's birthday. Bernard says: "At first, I don't know when Cheryl's birthday is, but I know now." How does Bernard know now? When Albert said that he's aware that Bernard does not know the birthday, he showed that he somehow knows Bernard got a date that repeats since if Bernard did get a date that occurs once, Bernard would know the answer. For Albert to be sure Bernard got a date that occurs more than once, Albert must've got a month in which every single date repeats. Months that follow that rule are July and August. Since Bernard knows the date is 16 and there is a July 16 but no August 16, Bernard now knows it's July 16. Albert says: "Then I also know when Cheryl's birthday is!" What Albert could've first done to figure this out is put himself in Bernard's perspective and do the work Bernard did to realize Bernard's options got limited to July and August. Reminder: Albert knows the month is July and the only dates in July and the 14th and 16th. If Bernard got the date "14", there is a July 14th and August 14th so Bernard would not know Cheryl's birthday. However, Bernard *does* know Cheryl's birthday so Bernard must've not gotten the 14th. The only remaining date in July is the 16th so Albert knows it's the 16th. I hope that helped! Feel free to ask questions if it didn't.
thank you for the explanation but im more confused about whether or not Albert and Bernard were given the full list of d ates or did they figure it out with only a month/day.
@@timsim408 did you watch the video? they were obviously given a list of 10 dates. its literally being said at the start of the video. i solved this whole issue not watching the video within 8 minutes of stopping the video at 2:50 on my own all the way. dafuq is wrong with ppl lul
would i be stretching it if i said right here in this RUclips channel us plebe's are actually treated to the literal best of the best? this channel has grown on me and i've only met the narrator of this video just in the last couple of days. i don't' know why i haven't subscribed yet but putting that in now ;)
Started at this problem for about a minute to figure out the answer then skipped to the end. A to B: Obviously eliminates May (unique day in May). B to A: Obviously eliminates everything except July (if ruling out May gave B the answer, then it's on a day shared by only by May and one other month). The only day that satisfies both steps is July 16, no paper/pencil required.
I don't understand why he can cross out May and June after the first exchange, because if the birthday was May 15 or 16 it June 17, they still could have had the same first dialogue exchange. Because Albert would have been told June and Bernard told 17, which they still would not have automatically known at the beginning. All three of those dates are within rows and columns with more than one choice.
It's because Albert knows the month. And Albert says that he knows Bernard doesn't know the birthday either. This is the most confusing part of the puzzle because people interpret it differently. _HOW_ does Albert know that Bernard doesn't know the birthday? The people who wrote the puzzle intended it so that Albert knows this because he is able to _deduce_ this based on the possible birthdays and his knowledge of the month. A lot of people think Albert is able to guess it from Bernard's expression or the fact that Bernard didn't speak up. But this is _not_ what was intended. It was intended that Albert is able to deduce with 100% certainty that Bernard _cannot_ know the birthday. But since Bernard _cannot_ know the birthday, it means that the date cannot be 18 or 19. But remember that this information comes from _Albert_ who knows the _month._ The only way Albert could be certain that Bernard didn't know the birthday is if the _month_ Albert was given didn't have a unique _date._ This means that Albert cannot have May or June. If, for example, Albert had May, then May 19th could have been the birthday (as far as Albert knew), and it would have been possible that Bernard had 19, meaning that Bernard could have known the birthday exactly. So Albert would not have been able to conclude that Bernard didn't know the birthday. The same sort of reasoning shows that Albert could not have June.
It's like the first math problem I actually figured out myself by just pausing the video before he started explaining the answer and thinking. I didn't write anything; the only thing I did is sometimes covered the "excluded" dates with my finger to have a better look at what options I have left. And somehow, without even explaining it properly to myself, I got it. Nobody probably cares (and it's not like I can even prove it), but I'm proud of myself.
Based on this explanation, Albert is lucky, or a liar. As there was no clue for him to make a distinction between July or August based on anything Bernard or Cheryl said. If Cheryl had whispered 14, 15, or 17 to Bernard then all of his statements would have remained the same. WE can make an assumption that it was July 16 if we take Albert's final statement as truth, but there is no evidence that it is true.Unless I've made a mistake somewhere...
Zac Jelke The fact that bernard knew it after his first statement means that it can't be the fourteenth, and because he knows it's in July, he knows it's the 16th, you have to realise that both of them have their own info, even if we as viewer don't.
Albert is neither lucky nor a liar. You can think of the words as being the rules for solving the problem. You have to take what they say as fact to solve this problem, even though when Bernard says he knows, there is actually no way that he can know the answer given the information he received. Go back and listen to the last couple sentences Simon Pampena says in this video. Simon is describing how the meaning of the words in this problem are giving an ambiguous Problem an unambiguous solution.
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(In a parallel universe)
Albert: "When's your birthday?"
Cheryl: "July 16th"
The End.
TheProtato In an other parallel universe:
Albert: ,,Who do you go with? Bernard or me?"
Cheryl: ,,Well... Bernard ugly af... so definitely you"
Bernard: ,,But i know your birthday!"
Cheryl: ,,Who cares m8?"
In this case - if we have an Infinite amount of Universes - any date we pick can be the correct date.
So - September 5th is my answer.
White Noise Lots of universes. I hope we have lots of students then too. Did you graduate BTW?
It would probably happen on earth. This Earth.
Meanwhile, in a parallel universe where books are sad:
Tom appears.
One of my favourite math jokes operates on a similar principle:
Three mathematicians walk into a bar. The bartender asks "Do you all want a beer?"
Mathematician A: "I don't know"
Mathematician B: "I don't know"
Mathematician C: "Yes"
:)
Ok so the answer is the first to arent opposed to it because they would have said no because not all of them were opposed. So the last mathematician knows they want beer and he does too so he says yes.
gideon reszka why?!
I'm not sure, but I guess it's like this: Mathematician A Can't say "Yes", because he doesn't know if the others want beer, but if he wouldn't want beer, then it would definitely be "no". So he wants beer but doesn't know what the others want. So now Mathematician B knows that A wants beer but not if C wants beer or not, so the same applies to him. Since he wants beer to he also says "I don't know". Since A and B could've said "no" if they did not want beer, C now knows that A and B want beer, and since he also wants beer he says "yes". I hope it's kinda understandable.
The principle is pretty simple. When asked if ALL three wanted beers, any of them could have said "no", simply because one of them not wanting beer is sufficient information that not ALL of them wanted a beer. Since the first two said "I don't know", it means they wanted the beer, but couldn't assess if the others did. The third one, seeing the two first guys wanted a beer, wanting on himself, said "yes".
Happy birthday Cheryl
to the top
Another year older Cheryl!
Kinda late for this year
Aleksandar Katic oof
His name is Cheryl?
I heard a person tell this before but he forgot to limit the dates to a specific range, making it seem like they somehow figured out the Birthday from 365 possible days.
Yeah same
Ultra-high level logic
Well then it would have to be February
It could be February 29th
Except if Albert knows that Bernard doesn't know, then it cannot be any day in February.
Came for the math. Stayed for the seductive whispering.
That little air kiss on 19 is just a sweet bonus.
Pathetic
Didn't we all? lol
Made my day bro
Lol
I think the bigger question is, who wants to be friends with a woman like Cheryl? Can you imagine what it'd be like?
'So what time's the party?'
'It's either on the hour or the half hour, between 10am and-'
'OK, forget it. Not going.'
What do you want to eat?
Pizza Hut McDonald’s
Burger King subway
Afraid of intelligence, are we?
Wouldn't that be interesting? I mean i can imagine some friends pulling out such as jokes. I'd love to be friends with cheril
It's like living in a Layton game.
false.
I think solving the actual problem is really messing up priorities; honestly we should be more focused on the totally genius cognition of Albert and Bernard. I mean, they solved such a spontaneous question with such speed and precision, it's amazing Harvord isn't on their case. 😜
Very true
+Star Cats >Harvord
+Star Cats And strangely, their solutions require both to know of each other's genius ability to solve this problem.
Albert and Bernard don't want to go into debt.
Bernard has horrible grammar. That's why Harvard isn't after him. :')
The moment he finished drawing the table, I knew exactly what his explanation was going to be, though I didn't know the exact answer. That table cleared everything up so elegantly.
Bernard: “Cheryl, when is you’re birthday?”
Cheryl: “I have a boyfriend”
XD
Nice “you’re”.
I laughed way harder at this than I should have. So much truth is oozing out of this one.
When's your boyfriend's birthday?
Your* but funny
"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
Hey,that's not fair.Nobody was right.I just had my birthday! Cheryl
Real world version of this:
Albert: “July.”
Bernard: “Sixteen.”
*high five*
They clearly communicate somehow, why couldn’t they be like normal people and just tell each other?
Because Math.
But what if they both had guns to their heads and if either said their information they would be shot
@@amyythest yeah. Oof
They could be telling lies
Albert: Obviously not July
Bernard:Obviously not 16
The best thing about this problem: people getting excited about math.
The worst thing about the problem: viral sites and people implying that people who solve a fairly straightforward logic prob, similar to those found in any popsci mag quiz page, are geniuses.
DisRes Agreed; I'm no genius, believe me, but I got this after a minimal amount of painful brain activity.
The other thing that annoyed was people saying, 'Pfft, this is logic, not maths'.
Buffoon1980 This is logical deduction and play on words, not real math but it uses the same logical processing as math.
Buffoon1980 I am among those who said "this is logic, not math." I still believe that assessment. I figured it out with minimal effort once I stopped looking for the math in this "math" problem. I instead focused on the verbage exclusively and almost immediately deduced the correct answer.
Garnett F That's the same as saying "a problem about triangles isn't math, it's geometry".
whatshendrix Depends what the actual problem about the triangles is.
If the problem is trying to stack the triangles into a square like those woodblock puzzle games that kids play, then it is geometry.
If the problem is trying to find its height or width or total area, then it's math.
There are two kinds of people: Those who say Ber-nerd and those say Ber-nard.
You forgot people that say Bear-nard
Lobster Johnson I say Bear-nard
Or, Bər *NARD*
Actually, the pic he uses is from the Brazilian Football Player Bernard, and nobody in Brasil, not even Bernard, pronounces like any of the comments here.
And those that say Arnold.
2019 and I'm still laughing about : "19 (kiss)" lol
It really got me off guard... Im still laughing.
5:23
Yea 🤣🤣🤣
OMG! I watched the video at least twice and somehow never caught that. It's great xD thanks for pointing that out
I'm still laughing
Did Bernard's grammar bother anyone else?
At first I am not bothered by it, but I am now ;)
Yeah, "not... too". It should've been "doesn't know, either".
He is mathematician idiots!
Great problem, but it seems I have been living under a rock because I hadn't heard about it before.
2 yrs later .. me too !
Well it's always that way with math.... Didn't you learn at school that all math problems are made up? Same is this one. Aaaaaand same is with the "media....". It's a math problem pretending to be not a math problem so people would look at it :D
@@googletropcurieux8670 2 extra years, haven't heard of it
@@Mr-Noro 2 extra weeks, haven't heard of it
An underappreciated fact of this brilliant logic problem: It's amazing enough that both Albert and Bernard can deduce Cheryl's birthday in this manner. It's even more amazing than an outside observer can also deduce Cheryl's birthday without being told the month OR the date.
99 problems, but Cheryl ain't one
The only mathematical thing I need to know is how many Sharpies Numberphile has
At least 2
James is the best
They have TREE(G64) sharpies.
still less complicated than social interaction
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.
That was so simple and it makes total sense thank u
Nina B No problem
Can you explain why it can't be May or June? It's still complicated to me. I understand why it can't be May 19 or June 18, but why do you exclude the whole May and the whole June?
Hold on, never mind. I got it now. I just looked at other people's comment where they already explained that.
It makes total sense and easy to understand, but for people who still doesn't get it, try this version:
A (the one that knows the month): I know B doesn't know because there are AT LEAST 2 options in my month.
B (the one that knows the date): If A knows I don't know, then it can't be May or June. Thus, By looking at the remaining months: July and August. There is now only one month to my date. I know the birthday.
A (the one that knows the month): Now I know the birthday, since there is only one date for July. (Wonder why A picked July 16 instead of Aug 15 & 17? Well A is the one that knows the month, hence July 16 is the only option A would pick)
3 am numberphile. What am I doing wrong in my life?
***** You are not the only one.
Haha same...I love math and logic and riddles too much
***** Uhhh... Same here
***** Actually i would say you do everything right ,good random internet sir.
***** I find late night maths much more fun for some reason.
I love Simon's sense of humour! Every video featuring him is brilliant!
4:00
"so we have one, two, three, FOR May"
This scared me 4 a short duration
>4 minutes
>4 may
>4 a short duration
>4 likes.
4d confirmed.
I liked Xeverous comment, but then I read Muix The Blob reply, realized I gave the 5th like and undid my wrongs. 4d still confirmed, boys!
Xeverous 16 likes...
=4 squared
ChaseTug 18 likes
Math problem: how much do I have to pay for Simon to whisper “19” then kiss me on the cheek before I go to bed every night?
I don't know but I know that you don't know.
I remember in University we had a similar problem presented, but I forgot what it was exactly. I had figured it out though...
It was something like...
- there are two persons Alice and Bob
- we are looking for two numbers a, b
- Alice knows the sum of a and b
- Bob knows the product of a and b
- then there is a conversational snippet presented to us, very similar to the one from the video, where it goes back and forth and then they suddenly know the answer
- what are the numbers a and b
Don't know how much I remembered or changed or missed in that story,
but if this sounds familiar to anyone, please do post the complete (proper) problem.
***** Maybe there are always three persons and I really might misremembered it, I admit that...
The puzzle that you're describing sounds very much like a logic puzzle, but the names Alice and Bob make me think of crypto as well. That's probably why Vanko got confused.
Manpreet Kang lol, no the name Alice and Bob I made up, because I couldn't remember the real test's names. It was in german anyways... we did this during maths tutorial after lecture.
Thomas Bischoff 3 4 and 6?altho idk what the sum of the billing address means
Uncle Steez Perhaps I should have been more clear about that. I meant the sum of the ages is the same number as that of A's street address.
And sorry to say that's not the right answer.
It's nice that you guys include some easy questions to make us feel smart
Bernard and Albert should have just shared the info they had with each other. Save themselves time.
jimbo 2346 unfortunately we live in an egocentric world m8
jimbo 2346 Nah, Bernard and Albert are like super geniuses, it wouldn't have been any quicker for them to just say the answer.
Wow, you're so clever. When's your Harvard graduation?
That's exactly what they did. They shared the info they had without letting cheryl know that they were sharing info.
I always love watching this channel because i feel like they are talking to me lol
The thing that pains me the most is the fact that anyone who ever solves this(or sees a solution for any problem,not just this one) goes like : yeah, I knew this, totally easy.. easiest logic math problem ever bla bla" .. It is not that easy, and it's quite amazing to have such a problem at hand. Wonderful video as always.
It's 1am and I have to get up at 6am tomorrow for work. So I decided to watch this math video :)!
Justice good for you!
Justice So you have 29 hours to go before work?
Gammel Prutte hahahahahha :D
Gammel Prutte Nice!
the first premise of this statement logically contradicts the second premise. And the conclusion is a non sequitor.
This problem is not hard, people just don't understand what the problem wants them to do.
Arson Bjork id rather say most people are just incapable of thinking logically
Júlio César Caye “Think of how stupid the average person is, and realize half of them are stupider than that.”
― George Carlin
Arson Bjork Basically this, and I think the poor grammar in the problem throws a lot of people off.
Rented Mule It doesn't matter which one knows what
Arson Bjork *this one too*
How odd, a video on birthdays uploaded on my own birthday!
CultOfRevan98 Happy birthday!
CultOfRevan98 I hope you're not Cheryl
CultOfRevan98 happy birthday. have a blessed day ;)
Then have a very happy birthday
There's been 93000 views and even more subscribers. What would've been odd if it had been nobody's birthday! There's probably even plenty of cheryls whose birthday it is!
I didn't watch the full video, didn't look at the comments, but let me try to solve it....
If 1st said that he knows that 2nd doesn't know either, that means that we can cross out May and June, which leaves us with 5 dates. The second immideatly solved the problem after that, which means that it isn't 14th, because it had 2 dates left. Because after that the second also realized what is the answer, it means he also had only one option left= July 16 (August had 2 possible dates).
Hopefully I was right :3
+Hunor Tóth You're right!
thanks :D
"In his head or really in his heart because we're dealing with Cheryl here" haha this guy is great! 😂
Oh wow, paused the video around 2:08 and I've managed to solve it. This is actually pretty great; the wording of the problem gives you information where you least expect it. Other than that, it's quite straightforward.
Gamesaucer Same here. I did it with a table just like the video, except I didn't have cells for option counts.
Gamesaucer Me too! There's no way I could have explained it coherently, though. I kept losing the train of logic.
***** It means that the info you have directly leads to the solution. For example, if you have a list of dates like in the video, 18 and 19 don't occur more than once, meaning that you can deduce the month from the day.
***** It means A Give Away. but it's also what lil kids say when they want something so.. Gimme that ICE CREAM NOW! Gimme comes from Give me.
Gamesaucer me too ! At first I tried to guess it but then I realized I needed a table to understand it better
No link to singing banana's video :o
gosh, I get the impression that linking to everyone's videos and articles about this would be quite a task...
Numberphile Not everyone's videos:P Professor Grimes is a numberphile regular, so that one could be considered a "gimme" ;)
McJaews James Grime doesn't teach
John Hilbert I didn't know this:)
What would be the proper title then?
McJaews You can call him Dr Grime or something
Question: At 6:34, why is the month May a 'gimme'? There are still two choices left, right? 15 and 16? Or am I missing something here?
sloonzz1012 19th is a gimme for Bernard, not May for Albert!
I know that, but then how can you be sure that it can't be May? I understand June because there's only one choice left and Albert still doesn't know, however, there are still two choices for May. So how?
sloonzz1012 if he was told may, then he wouldn't have said I know he doesn't know, because if the other guy was told 19, he would know.
June isn't crossed off because there is only one possibility left. May and June are actually crossed off for exactly the same reason. This reason is that they both have a date number that is not present in any of the other months. So, for Albert to say that he knows that Bernard doesn't know, he is essentially saying that he knows that it is either July or August - because July and August both have dates that are repeated in the other months and therefore knows that, with the information that Albert has been given, albert could not possibly know the correct month and date at this stage.
sloonzz1012 Because the 18th and 19th are the only gimmies in the first section (for Bernard), and because Albert somehow knows that Bernard doesn't know. You can eliminate both May and June as potential months. If the birthday WAS in May/June, Bernard COULD possibly know the exact date, but because of the first sentence (Albert saying that he doesn't know and that he also knows Bernard doesn't know) - Cheryl's birthday can be confirmed to not be in May and June
very fascinating stuff. Could you do more puzzle videos? I love listening to someone deduce their logic.
i am from singapore, and we are so focused on the hard and fast rules in mathematics that we fail to appreciate the many other things that maths is about: logic, real- life applications and maybe more. and i think that is what maths is about, its prevalent in every part of our lives.
Can we just appreciate Bernard's smartness
He does, what took Simon took 8 minutes to explain, in 5 seconds in his head. That is 96-fold the smartness of Simon
Bruh
I guessed July 16 for no reason and got it right
Cole Christie haha
me too but i guessed that if you have to deduce something it got to be in the middle cause if it was on the side t would be easier to guess
I don't understand how Bernard's response is enough information for albert to also understand. How is bernanrd to state the last bit of necessary info?
edit: I mean, Albert could say he knows the date because it's a 15 or a 17. He doesn't state that bernanrd would also know from his new response.
BigSalo But he knows the month.
A1: eliminates May/June
B1: eliminates the 14th,
A2: he knows it’s July and only 16th is left
Yes, so he eliminates the 14th, which leaves two single dates in one month and one date in the other. but, all 3 numbers are different, so there's really no way that albert could have deduced which of those 3 separate dates it was. There was no indication that is was 16 rather than 15 that bernard was thinking but with either of those numbers bernard would know the birthday. Work through the problem as if its august 15th. Albert says "I dont know, but neither do you", eliminates may and june. Then bernard, knowing its the 15th says "Oh, I didnt know before, but now I do", and now albert thinks its july 16th but its actually august 15th. I dont see where august gets eliminated.
@@connerhartman9336 The point is. Had Albert had August he wouldn't have ended up saying, oh! I know then. But he had July. So he could state it as fact. The only scenario where he can end up saying it for a fact after the 14th is eliminated is that he had been told July is the month.
Because you are right. It could have been 15, 16, 17. But the only conditions where all their statements are true is July 16th.
oh, this is satisfying to solve by yourself. that moment when it clicks and you know the answer is priceless
I was hoping to find someone else who solved it themselves! This was a fun one.
Explained so well. This channel is superb.
Three logicians walk into a bar. "Would you all like a beer?" asks the bartender. The first logician says, "I don't know." The second logician says, "I don't know." The third logician says, "yes."
Thats dope
@@loofa1707 can you explain to me what it means
@@kev117_ the question was, "Would you all like a beer". That means that if the first dude didnt want a beer the answer to the question would have been no. But instead he said that he doesnt know which means that he wants a beer but its possible that one of the other dudes dont. The second guy said he doesnt know so that means that he wants a beer too but he doesnt know if the third guy wants one or not. So the third guy knows that they both want a beer based on their answers and he wants a beer so at that point he can say yes, they all want a beer.
@@loofa1707 oh lol thanks a lot bro
This would be way more funny if the top comment in this comment section wasn't the exact same comment, with way more likes and was made 2 years ago.
Basically I'm saying you might've copied the comments
I still did not understand why he took july and may out
May was removed because it contained a gimme. If Albert had been told a month that contained a gimme, then he would not have been able to say that he knows Bernard doesn't know. Off with May and June.
July didn't get taken out. We ruled out May and June, then we ruled out the 14s, and then - since Albert could claim to know - we knew he must have gotten a gimme as well. If he'd been told August, he wouldn't have had a gimme. Therefore, if they can figure it out, we could (finally) rule out August.
my approach was very similar, except I threw out all the gimmes untill there was one date left. So I ended up screwing up at the end and almost solved it but didn't.
what a Parker's square
Finding this again after a few years and being able to solve it feels amazing
Although the video is over ten minutes long, the hands on the clock donot move. The time is 7:16.
At 6:51 I don't get why they removed may though
@Zeineb THANK YOU. I have been wondering the same thing. Makes sense vertically but not horizontally, if that makes any sense. Same for June. Strange.
Because Albert realized that if the birthday was May then Bernard may have known the birthday. But since Bernard does not know then it can’t be May or June.
Yeah same
June was eliminated for sure. May? Still had two possibilities for May, so that leaves the 17th as the only day with only one Month possibility, so at that point if he is certain it must be Aug 17, because every other day at that point had multiple possibilities. Right? What am I missing?
When he said “if your living under a rock” I instantly thought about Patrick from spongebob.
Albert: what's your birthday
Cheryl: whisper whisper whisper
I love your accent, could listen to your explanations all week long. I appreciate how you broke it down. this is new to me, and I would be befuddled without your help to understand. love the banter between you and your mate.
This is explained really clearly! I love this guy.
This is easy. I stopped right after the problem was explained. It is May 19th
Might wanma check that...
@@lexhumphrey9665 You are a whole 4 years too late.
Kane wants to know your location
Fun Fact: It has been a usual trait for tough math questions from Singapore to include 3 persons with names starting with A, B and C.
I like the ending: *Pencil Drop, then leans back like a G*
There is actually a problem my math teacher gave in my P5 math class called Denise’s birthday, which has Albert, Bernard, and Cheryl knowing the month, day and year respectively about Denise’s birthday.
Wonderful. Now that summer's approaching I will finally have some time to try and do this kind of stuff, I love it.
Why did Cheryl not tell them directly? WHY
"18" or "19 :*"
Love the role play :)
Can somebody explain why May 15 and 16 were crossed off?
I understand May 19 and June 18 are crossed off. And following that June 17 goes away since that is the only one left in the month. But why does that remove the rest of May? May would still have 2 options. 15 and 16 both would still have 2 options as well.
The whole of May and June have to be crossed off because Albert knows that Bernard doesn't know the correct month and date at that stage. Meaning that Albert either knows the answer is july or August. We can deduce that Albert knows it is July or August when he says that Bernard doesn't know. For Bernard to not know at this stage, Albert must know that it is in a month where there are no dates that do not appear in any other months (18th or 19th). If, for example, Albert was told it was may, then he would know that there would be a possibility that Bernard could know the month and date straight away (if Bernard was given 19).
wolphe Because the guy who knew the months knew it wasn't in May. If the birthday was in May there would be no way either of them could know the precise date because the information would be too ambiguous.
Jono Brown I understand that the gimmes go away but it still doesn't clearly explain why the rest of May goes away.
From Bernard's POV:
May 19 and June 18 go away immediately since they're gimmes.
Then he hears Albert saying "I don't know what the day is but I know Bernard doesn't know it either.' With just that, Bernard knows June 17 goes away too and subsequently Aug 17.
But that should still leave May 15 and 16, July 14 and 16, and Aug 14 and 15.
I guess my question boils down to, How did Bernard know which date it was just from that one statement.
wolphe albert said that he was sure bernard didn't know it. The only way bernard would know it straight away was with days 18 or 19. And the only way for albert to be sure those days are off, is if the month cheryl told him was NOT may nor june.
In short, Albert always deals in entire rows, Bernard in entire columns.
Because he says for sure that Bernard doesn't know, if it was in May then there would be a chance Bernard would know for sure, as there is a unique date in May, so the month must have non unique number dates
What initially throws me about this problem is that I assumed that we would know at the same point that Albert knows. When in fact, we can only know AFTER Albert tells us that he knows.
This is exactly it! People do not realize when they are arguing with each other that one arguee has the 3rd party viewer train of thought (as we watch the exchange unfold), and the other arguee has the 'If I was in Albert's shoes" train of thought. This is the the source of the issue.
before I look ahead, July 16th. if he knows the month and knows the guy knowing the day can't know which it is, it can't be may or June, since those contain unique days. Now that the guy who knows the day knows it's June or August and the day, so it's a unique day to those months, removing 14. Going back to the original guy, if it was August, he wouldn't know if it was 15 or 17, since there's two unique numbers, but because he knows it's July, is has to be July 16th
Exactly my train of thought, no need for tables and whatnot.
In this video,
Albert is Albert Einstein
Cheryl is Cheryl (Cole)
Who's Bernard?
Cribbins
This is precisely why symbolic logic needs to be applied more.
U lost me at 0:00
Why would Albert be saying ”now I know too” as there’s 3 options to pick from Bernards statement. He wouldn’t possibly know the date with the information that Bernard knows as Bernard could be saying that of anyone of those 3 dates. Am I missing something?
think the same as you, bernard might be a psychic
It's one of those math problems that are complicated because of the structure/grammar of the question/problem and knowing what is expected of you rather than the actual solution. I always hated worded math problems for this reason.
I love how he sits back and sighs at the end like some great load just flew off his shoulders.
And then they shared Cheryl.
I don't get it! :'( But it sounds pretty cool!
Thank you I love your enthusiasm and the way you teach.
It's July 16th in 36 minutes. Happy early birthday, Cheryl!
@5:24 that was so weird 😰
Plot twist: it was 19th June
Congrats on 1,234,567 subscribers :D
something similar is used in electronics and computer programming to sort out the result of a program or series of circuits.
like if you would have a control panel with circuits that override other circuits, you have to tell the controller to close or open ports when certain other ports are closed or open.
doesn't matter how many circuits or inputs you have, once you narrow it down you end up with one determinating signal, and you can write all the other signals as functions of that signal.
Have not heard of the problem. Nice presentation and explanation!
“My month sounds like ju-lie”
“I know the answer”
“I do not know the answer. Why didn’t you tell me the day?”
Singingbanana got to it first :P
Idk about you guys but that's my birthday so me and Cheryl boutta go gang out together.
Edit: where my July 16 bois at
Here
Here
My take: at beggining i thought its not from the set but from all days of the year.
But if from sets its extremely easy. Albert says they both dont know, its actually big help for Bernad. We have to know Bernard can only know at the BEGGINING if he knows june 18 or may 19. So its either may or june. As second guy answers now i know, its obviously june because Albert said he couldnt know - at first he had two choices june 17 or August 17 but when he said he couldnt know at beggining he knows he talk about june. And when Bernard answers that it becomes obvious to Albert too
I like it because I was able to solve it by thinking it through critically before the explanation, but the video afterward demonstrated an even better way of visualizing the options through a chart that included space for the number of options left in each.
I had simply crossed out things in a list that looked exactly like the one he had above the full chart on the paper.
I dont get this at all even after watching this 5 times. I get how he got the solution but not how Albert or bernard got the information.
Okay, I'll try to break it down step by step.
The answer: July 16
The possible dates:
May 15, May 16, May 19, June 17, June 18, July 14, July 16, Aug 14, Aug 15, and Aug 17.
Albert is aware of the month while Bernard is aware of the date.
Albert says: "I don't know when Cheryl's birthday is, but I know that Bernard does not know too."
The answer is July 16th. That means Albert is aware that the month of Cheryl's birthday is July. The possible dates for July are the 14th and 16th. Both of those dates are repeated-- there are August 14th and May 16th, so Albert knows that from the dates alone that Bernard cannot know Cheryl's birthday.
Bernard says: "At first, I don't know when Cheryl's birthday is, but I know now."
How does Bernard know now? When Albert said that he's aware that Bernard does not know the birthday, he showed that he somehow knows Bernard got a date that repeats since if Bernard did get a date that occurs once, Bernard would know the answer. For Albert to be sure Bernard got a date that occurs more than once, Albert must've got a month in which every single date repeats. Months that follow that rule are July and August. Since Bernard knows the date is 16 and there is a July 16 but no August 16, Bernard now knows it's July 16.
Albert says: "Then I also know when Cheryl's birthday is!"
What Albert could've first done to figure this out is put himself in Bernard's perspective and do the work Bernard did to realize Bernard's options got limited to July and August. Reminder: Albert knows the month is July and the only dates in July and the 14th and 16th. If Bernard got the date "14", there is a July 14th and August 14th so Bernard would not know Cheryl's birthday. However, Bernard *does* know Cheryl's birthday so Bernard must've not gotten the 14th. The only remaining date in July is the 16th so Albert knows it's the 16th.
I hope that helped! Feel free to ask questions if it didn't.
thank you for the explanation but im more confused about whether or not Albert and Bernard were given the full list of d
ates or did they figure it out with only a month/day.
@@timsim408 They were given the full list
@@timsim408 did you watch the video? they were obviously given a list of 10 dates. its literally being said at the start of the video. i solved this whole issue not watching the video within 8 minutes of stopping the video at 2:50 on my own all the way.
dafuq is wrong with ppl lul
Not enough #NCSS comments.
#NCSS2015 #NCSS2014 #NCSSreturnerreasons
inb4 illumitati video
Plot twist: She lied.
Lmao
would i be stretching it if i said right here in this RUclips channel us plebe's are actually treated to the literal best of the best? this channel has grown on me and i've only met the narrator of this video just in the last couple of days. i don't' know why i haven't subscribed yet but putting that in now ;)
Started at this problem for about a minute to figure out the answer then skipped to the end.
A to B: Obviously eliminates May (unique day in May).
B to A: Obviously eliminates everything except July (if ruling out May gave B the answer, then it's on a day shared by only by May and one other month).
The only day that satisfies both steps is July 16, no paper/pencil required.
Illuminati Confirmed!!! #NCSS2K15 #NSCC #NCSS2015
Like if you saw this awesome guy at #NCSS2K15!
February first? Genuine guess from the beginning
Oh never mind, I didn’t know those dates listed were the actual only choices
I don't understand why he can cross out May and June after the first exchange, because if the birthday was May 15 or 16 it June 17, they still could have had the same first dialogue exchange. Because Albert would have been told June and Bernard told 17, which they still would not have automatically known at the beginning. All three of those dates are within rows and columns with more than one choice.
It's because Albert knows the month. And Albert says that he knows Bernard doesn't know the birthday either.
This is the most confusing part of the puzzle because people interpret it differently. _HOW_ does Albert know that Bernard doesn't know the birthday? The people who wrote the puzzle intended it so that Albert knows this because he is able to _deduce_ this based on the possible birthdays and his knowledge of the month. A lot of people think Albert is able to guess it from Bernard's expression or the fact that Bernard didn't speak up. But this is _not_ what was intended. It was intended that Albert is able to deduce with 100% certainty that Bernard _cannot_ know the birthday. But since Bernard _cannot_ know the birthday, it means that the date cannot be 18 or 19.
But remember that this information comes from _Albert_ who knows the _month._ The only way Albert could be certain that Bernard didn't know the birthday is if the _month_ Albert was given didn't have a unique _date._ This means that Albert cannot have May or June.
If, for example, Albert had May, then May 19th could have been the birthday (as far as Albert knew), and it would have been possible that Bernard had 19, meaning that Bernard could have known the birthday exactly. So Albert would not have been able to conclude that Bernard didn't know the birthday. The same sort of reasoning shows that Albert could not have June.
It's like the first math problem I actually figured out myself by just pausing the video before he started explaining the answer and thinking. I didn't write anything; the only thing I did is sometimes covered the "excluded" dates with my finger to have a better look at what options I have left. And somehow, without even explaining it properly to myself, I got it. Nobody probably cares (and it's not like I can even prove it), but I'm proud of myself.
Is it just me, or was this solution immediately obvious?
Based on this explanation, Albert is lucky, or a liar. As there was no clue for him to make a distinction between July or August based on anything Bernard or Cheryl said. If Cheryl had whispered 14, 15, or 17 to Bernard then all of his statements would have remained the same. WE can make an assumption that it was July 16 if we take Albert's final statement as truth, but there is no evidence that it is true.Unless I've made a mistake somewhere...
Zac Jelke The fact that bernard knew it after his first statement means that it can't be the fourteenth, and because he knows it's in July, he knows it's the 16th, you have to realise that both of them have their own info, even if we as viewer don't.
Zac Jelke Well,he made a distinction between July and August because he knew the month already
Albert is neither lucky nor a liar. You can think of the words as being the rules for solving the problem. You have to take what they say as fact to solve this problem, even though when Bernard says he knows, there is actually no way that he can know the answer given the information he received. Go back and listen to the last couple sentences Simon Pampena says in this video. Simon is describing how the meaning of the words in this problem are giving an ambiguous Problem an unambiguous solution.
No, he simply knew the month because Cheryl told him at the start. lol
If we assume either of them is a liar the problem becomes unsolvable
You are so handsome. ,, those locks beautiful.. ..
I am unreasonably proud of myself for solving a four year old logic problem.
Great work, it was an awesome explanation, truly enjoyed these 11 33(iykyk) minutes