CHERYL'S BIRTHDAY - an irrefutable solution
SINGAPORE'S SEEMINGLY MIND-BOGGLING MATHEMATICS PROBLEMApparently, there is a big fuss being made about the above maths problem which was originally a question from the Singapore and Asian Schools Math Olympiad (SASMO) contest meant for Secondary 3 and 4 students. People are questioning why such a question is now being set as homework for Primary 5 students.
Well, I'm more interested in the maths problem itself.
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Official 'July 16' Solution
I think there is something problematic about this official solution. Its basic premise is that the key to the solution lies in the answer to the question: "Why does Albert know that Bernard does not know Cheryl's birthday?" It went on to assume that the reason is that Albert must have been told that Cheryl's birthday month is either July or August. That's because this would have prevented the possibility of Bernard being told that her birth day is 18 or 19. If indeed Bernard was told that her birth day is 18 or 19, he would have known straightaway that her birthday is on June 18 or May 19 respectively.
The grave error here is to mistake possibility for certainty. This is only one possibility of how Albert knew that Bernard did not know Cheryl's birthday at the outset. There are several other possibilities: Albert must have known that Cheryl is not so stupid as to render the guessing game pointless by giving the game away right at the beginning in telling Bernard that her birth day is 18 or 19; Albert knew that if Bernard knew her birthday at the beginning he would have blurted out the answer without waiting for Albert to begin the conversation since finding out her birthday was their original intention anyway; Albert might be merely making a statement of mutual ignorance in the hope of getting some clues from Bernard's response; etc, etc.......
So, it is reckless and presumptuous to rule out all the May and June dates just based on one possibility. In a logical analysis, all possibilities must be explored and excluded. What if that one possibility fails to materialize, the whole argument collapses. It could well be that even if Albert was told that her birth month is May or June, he might still say that he knew Bernard did not know her birthday at the outset. So, I think that too much weight is placed on Albert's initial statement that he knew that Bernard did not know. How Albert knew that, is still an open question as Albert did not tell us how he came to that conclusion; and it is against logic to prefer one possibility over all others without any factual confirmation.
Furthermore, for the official solution to work, Bernard must also think the same way as Albert. This does not make sense. From his point of view, he did not know Cheryl's birthday because Cheryl's birth day as told to him was not 18 or 19. To him, he would not need to rule out May and June completely to know that he did not know Cheryl's birthday at the outset. Whether Bernard presumed that Albert's declaration of the former's ignorance was because Albert had been told that her birth is July or August is another open question.
So, this official solution is unlikely, unrealistic, twisted, complicated, tentative and rather inelegant.
Contrast that with this 'August 17' solution:
All three of them knew that Cheryl's birthday is never going to be May 19 or June 18, or else it was pointless to play this game. Albert first declared that he did not know Cheryl's birthday and claimed that he knew Bernard didn't know too.
Bernard did not deny that, but deduced that May 19, June 18 and June 17 can all be ruled out. So, the remaining possibilities were May 15, May 16, July 14, July 16, August 14, August 15 and August 17. If the number told to him was 14, it could be July or August; if 15, then May or August; if 16, then May or July; and if 17, then there is no ambiguity ... BINGO! The answer must be August 17.
Bernard promptly stated that despite his initial ignorance, Albert's corresponding declaration of his mutual ignorance had helped him come to an undeniable conclusion. On hearing that, Albert knew that the answer must be the odd unpaired number 17, that is August 17.
This solution is based on common sense, factual statements and logical deduction. It uses no presumptions and shows no preference for one possibility over another. It does not require Albert nor Bernard to read each others' minds. It is simple and elegant and I'm sure Ockham will approve. Not to mention, Cheryl!
Postscript
Which of these 2 solutions is 'correct'?
As a mathematical problem, the official solution is impeccably correct, but as a philosophical or logical problem, the August 17 solution is more convincing and passes the test of Ockham's Razor better.
Which solution you prefer will depend on whether you think it to be a mathematical problem disguised as a logical puzzle or is it the other way round, a philosophical problem to be analyzed in abstract terms. Do we follow Aristotle's direction to use reason to judge earthly matters or do we direct our gaze heavenwards like Plato?
**For those who have enjoyed this article, please read my follow-up at the link below:
CHERYL'S BIRTHDAY - The Final Verdict
Read at:
http://singaporedialectic.blogspot.sg/2015/04/cheryls-birthday-it-must-be-sign-of.html?m=1
I think there is something problematic about this official solution. Its basic premise is that the key to the solution lies in the answer to the question: "Why does Albert know that Bernard does not know Cheryl's birthday?" It went on to assume that the reason is that Albert must have been told that Cheryl's birthday month is either July or August. That's because this would have prevented the possibility of Bernard being told that her birth day is 18 or 19. If indeed Bernard was told that her birth day is 18 or 19, he would have known straightaway that her birthday is on June 18 or May 19 respectively.
The grave error here is to mistake possibility for certainty. This is only one possibility of how Albert knew that Bernard did not know Cheryl's birthday at the outset. There are several other possibilities: Albert must have known that Cheryl is not so stupid as to render the guessing game pointless by giving the game away right at the beginning in telling Bernard that her birth day is 18 or 19; Albert knew that if Bernard knew her birthday at the beginning he would have blurted out the answer without waiting for Albert to begin the conversation since finding out her birthday was their original intention anyway; Albert might be merely making a statement of mutual ignorance in the hope of getting some clues from Bernard's response; etc, etc.......
So, it is reckless and presumptuous to rule out all the May and June dates just based on one possibility. In a logical analysis, all possibilities must be explored and excluded. What if that one possibility fails to materialize, the whole argument collapses. It could well be that even if Albert was told that her birth month is May or June, he might still say that he knew Bernard did not know her birthday at the outset. So, I think that too much weight is placed on Albert's initial statement that he knew that Bernard did not know. How Albert knew that, is still an open question as Albert did not tell us how he came to that conclusion; and it is against logic to prefer one possibility over all others without any factual confirmation.
Furthermore, for the official solution to work, Bernard must also think the same way as Albert. This does not make sense. From his point of view, he did not know Cheryl's birthday because Cheryl's birth day as told to him was not 18 or 19. To him, he would not need to rule out May and June completely to know that he did not know Cheryl's birthday at the outset. Whether Bernard presumed that Albert's declaration of the former's ignorance was because Albert had been told that her birth is July or August is another open question.
So, this official solution is unlikely, unrealistic, twisted, complicated, tentative and rather inelegant.
Contrast that with this 'August 17' solution:
All three of them knew that Cheryl's birthday is never going to be May 19 or June 18, or else it was pointless to play this game. Albert first declared that he did not know Cheryl's birthday and claimed that he knew Bernard didn't know too.
Bernard did not deny that, but deduced that May 19, June 18 and June 17 can all be ruled out. So, the remaining possibilities were May 15, May 16, July 14, July 16, August 14, August 15 and August 17. If the number told to him was 14, it could be July or August; if 15, then May or August; if 16, then May or July; and if 17, then there is no ambiguity ... BINGO! The answer must be August 17.
Bernard promptly stated that despite his initial ignorance, Albert's corresponding declaration of his mutual ignorance had helped him come to an undeniable conclusion. On hearing that, Albert knew that the answer must be the odd unpaired number 17, that is August 17.
This solution is based on common sense, factual statements and logical deduction. It uses no presumptions and shows no preference for one possibility over another. It does not require Albert nor Bernard to read each others' minds. It is simple and elegant and I'm sure Ockham will approve. Not to mention, Cheryl!
Postscript
Which of these 2 solutions is 'correct'?
As a mathematical problem, the official solution is impeccably correct, but as a philosophical or logical problem, the August 17 solution is more convincing and passes the test of Ockham's Razor better.
Which solution you prefer will depend on whether you think it to be a mathematical problem disguised as a logical puzzle or is it the other way round, a philosophical problem to be analyzed in abstract terms. Do we follow Aristotle's direction to use reason to judge earthly matters or do we direct our gaze heavenwards like Plato?
**For those who have enjoyed this article, please read my follow-up at the link below:
CHERYL'S BIRTHDAY - The Final Verdict
Read at:
http://singaporedialectic.blogspot.sg/2015/04/cheryls-birthday-it-must-be-sign-of.html?m=1
Once you start making assumptions about the players motivations, all hell breaks loose and any answer is possible. You are also not solving the problem as it was posed, but inventing a (possibly more realistic) problem of your own. For example, it may be that A knows that B is a little slow. Therefore, when A speaks, he knows that B does not know the answer *yet*, because he knows B cannot think quickly. Then B speaks and says he now knows the answer (because he finally worked out that 19 implies 19 May). Then A, knowing May, and realizing the penny has dropped for B, knows the answer is May 19.
ReplyDeleteThis is no less absurd than your August 17 answer, and no more wrong.
I agree with you. We should not make unjustified assumptions. However, making the obvious logical assumption that Cheryl had not told Bernard the day 18 or 19 is fully justified, or else, Cheryl would have been a complete fool to give the boys 10 dates to choose from, and then tell Bernard the answer from the get-go.
DeleteWhat I object as unjustified is the assumption that when Albert said that he knew that Bernard also didn't know, it MUST MEAN that Cheryl had told Albert July or August.
Daniel, you are too engrossed with the story context. What if the story is told this way:
DeleteRussia planned to launch rocket on one of the following dates (10 possible dates). After they decided on final date, USA and China spies managed to capture the data. Unfortunately, China only captured the day, while USA only captured the month. Both sides wanted to figure out the actual date to themselves so decided to trick the other side find out:
USA: we know that you captured the day, but you don't know the month yet. let's exchange!
China: but we know the month now!
USA: a ha, we also know the day now.
Do you think the unique dates in May and June still need to be ruled out from start to be "logical"?
We can't be "too engrossed" with the story context. The mathematical problem is expressed as a story. The first necessity of mathematics is precision. We can't pick and choose what to ignore and what to pay attention to. The official solution is the result of a one-track mind which ignores important details and information. When maths is expressed as a story, it actually makes it more difficult. It is not so straight-forward.
DeleteA ha, so the "spy" story will not exclude the unique days, but the same story when phrased differently will give a different result, because we can pick and choose details? I'm not sure what math you are talking about here (fuzzy math?), but from what I learnt I can only come out with the same answer.
DeleteDear Sat That,
DeleteI don't know about your spy story. Let's stick to Cheryl's Birthday, ok?
Smarter, yes. But if the two solutions are correct, then the problem is ill-posed.
ReplyDeleteIndeed, there are many questions with multiple correct answers. You sometimes prefer one answer over another. A true test is not to test for your answer, but how you arrive at it.
DeleteThis comment has been removed by the author.
ReplyDeleteAugust 17 can't be the answer as Bernard could have deduced that himself. It is clear to both Albert and Bernard that 18 or 19 are not possible. So, if Cheryl had told Albert the month as June, he would have known the date as 17 and would not have required any other information. So June 17th is ruled out.
ReplyDeleteThe above information can also be deduced by Bernard (without needing any clue) and if he knew that the Day is 17th, he would not have needed any conversation with Albert to know that Cheryl's birthday is August 17.
Hence, I think that your explanation does not solve the problem correctly, though I agree with you on being confused as to why May is ruled out (that June is definitely ruled out, can be more easily deduced). Perhaps, as pointed out by others, it has more to do with English than logic :)
BLUEGUITAR has pointed the flaw in Daniel's reasoning for "Aug 17". I will just expand it:
DeleteDaniel said: "All three of them knew that Cheryl's birthday is never going to be May 19 or June 18, or else it was pointless to play this game". OK fine, we remove 18 June and 19 May. But then June 17 is left alone for the month of June, so June is out, otherwise Albert would know the date from start so the game is pointless. But if Bernard knows the day is 17, he could conclude the date is Aug 17 from start. So day 17 is out otherwise the game is pointless. Well, what's left?
Ruling out 18 June and 19 May is the cause of this flaw. The problem doesn't say that Cheryl wouldn't tell Bernard these dates. And we should exclude entire month of May and June after hearing what Albert said. And I don't see any wrong with English or logic in the problem.
Dear BLUEGUITAR, yes, you are right. If Bernard had been told 17, he would highly suspect the answer to be August 17, but he needed Albert to confirm that it was not June. Indeed, when Albert said that he didn't know the answer, it provided the confirmation for him to say "now I know". Yes, it is just a simple deduction, but being simple does not make it wrong.
DeleteDear Sat That, why 18 and 19 could be ruled out immediately is because they are unique numbers. Telling either number to Bernard is to tell him the answer. On the other hand, June is not a unique month. Yes, it can be easily deduced that June 17 is unlikely to be the answer, and Bernard just needed a simple confirmation from Albert to jump out with the answer. As, I told BLUEGUITAR, being simple does not make it wrong.
DeleteFirst you invented assumption that "Cheryl does not give answer simply", now you said simple is not wrong. I don't see why the day can't be 18 or 19, when you think the month can still be June (because it is too obvious for Albert). But if the month can't be June then the August 17 is obvious anyway.
DeleteAgain, it's all due to your assumption that the 2 unique dates are ruled out because they are too simple. This a logic math problem, and you can only deduce from what is given, not inventing new assumption.
Dear Sat That, uniqueness must not be confused with simplicity. Their concepts are different: uniqueness means one of a kind whereas simplicity means lack of complexity.
Delete18 and 19 are unique in the sense that they only appear once in the slate of dates. If Cheryl were to point either number to Bernard when setting the question, she is giving him the answer without any need for deduction whether simple or complex. That would be ridiculous.
June appears in the slate of dates twice, so it is not unique. So, if indeed Cheryl told Albert June, it just means that Cheryl has made it easy for the boys!
We are not arguing about the philosophy terms here. You excluded the dates with a "fuzzy" reason that "they are unique" or "they are too simple". By applying the same reason, I could also argue June 17 is too simple, or become unique after taking out June 18. But in math only true or false fact is accepted. Unless the problem stated in some way that Cheryl will not tell Bernard the straight date, it's still the fact that the straight date is possible.
DeleteNo, uniqueness and simplicity are not fuzzy concepts, they are clear and distinct.
DeleteYes, straight dates are possible. In fact, since there are 10 dates on the slate, all 10 dates are possible. But, straight dates are unlikely, and they are quickly ruled out by Bernard. When he said "at first, I don't know", he is saying that his number is not 18 not 19. When he went on to say "but now I know", it is because when Albert said he didn't know, Bernard knew he could rule out June 17.
Great, straight dates are possible. What is "unlikely"? is it true or false?
DeleteWhen you are still analyzing and haven't come to a conclusion yet, you use the word unlikely. When you arrive at your final answer, you say it is true.
DeleteWhat information is given to us in the problem description must be taken for a fact, we do not doubt it or question any motivations or anything. If Albert says something, it is not his opinion, it is a confirmed fact in this isolated case. "I know Bernard does not know" = fact "Bernard does not know" at the point in time before Bernard heard this. So after replacing two initial statement places you get conclusions "=>"
ReplyDelete1) Bernard does not know
1 => the day is not 18 or 19 (clear for both)
2) Albert does not know
2 => the month is not June (clear for both)
3) after 2 is known, Bernard knows
3 => only possible if the day number is 17, as june is eliminated
August 17.
I think Bernard should have stayed quiet!
But the first utterance is not
Delete"1) Bernard does not know"
but the more complicted
"1) Albert knows that Bernard does not know".
This changes the working out, because it immediately excludes the months of May and June.
No, May and June are only excluded if you allow the speculation that the only reason why Albert knows that Bernard doesn't know is because Albert has been told that the birth month is either July or August. The crucial question is whether given the facts of the conversation, is that the only compelling conclusion? Or is such speculation even allowed in logical analysis?
DeleteIt's not "speculation" when you refrain from assuming information that is not given in the problem. In fact you've got the definition of "speculation" completely backwards -- you've managed to characterize a purely logical deduction from given premises as some kind of a priori assumed premise ("speculation")! No cookie for you!
DeleteIn logic (syllogism) there's only one truth why Albert knows that Bernard doesn't know the date.
Delete1. Bernard doesn't know the birth date, because whichever days that Bernard knows, he can't point to a unique month yet.
=>2. (May) 19th can point to a unique month.
=>3. The month is not May.
Anything else you said is speculation.
Dear Jeff Young,
DeleteAccording to dictionary.reference.com, "speculation" (noun) means: "1.
the contemplation or consideration of some subject, 2. a single instance or process of consideration." Speculation does not mean "some kind of a priori premise" (your words).
So, saying that Cheryl MUST have told Albert July or August just because Albert said that he knew that Bernard also didn't know is a logical inference, but not an exclusive one. It is just one of several possible and equally plausible inferences, so it is speculation.
By the way, Jeff, thanks for the cookie that you did not give.
DeleteDaniel, let's just use math here. This is not a socio-psycho problem. In math, deduction to July and August is EXCLUSIVE.
DeleteDo not assume that 18 or 19 are ruled out (it's not stated anywhere, so both days are still possible).
If the month is May or June, this statement is wrong: "B doesn't know the date", because B possibly got the final date.
But that statement is correct, so the month is not June or May.
Sat That convinced me.
DeleteDear Sat That,
DeleteI'm using maths all along. Perhaps, you are not familiar with maths expressed as a story. Not just numerical quantities, but all the details and information in the story including its grammar, logic and inferences are like variables in an equation. You can't ignore some variables because you prefer others or because these others lead to the answer you want.
The correct answer is the one that does not contradict any part of the story and is consistent with any of the inferences.
Your correct answer contradicts with the case that Bernard deduced the month is not May or June (the above math statement I said is correct, or do you want to prove it wrong?). So when Bernard said he found the date, how did Albert found it is 17, when 15 is also unique ( it's possible that Bernard decided entire May is out, not just May 19)?
DeleteJust to add: among these 2 "facts":
Delete"The problem context affirms that Cheryl will never tell the boys a straight date"
and
"The problem doesn't rule out the possibility that Chery tells the boy(s) a straight date"
Which one is correct? I'm not sure how you apply grammar, information, logic, whatever to come out with your "variable"
Dear Sat That,
DeleteYour first part:
Bernard did not deduce that the months of May and June are out. It is we, the audience (not me, though), who deduced it. Bernard already knows what months to and what months to discard because he already got that one number in his head!
Only Albert knows for sure May and June are out because he got the correct month in his head. He cannot presume that Bernard can read his (Albert's) mind. Bernard did not tell Albert that he has ruled out May, though he should have ruled out June. So, when he takes the point of view of Bernard, he knows that Bernard faces a choice between a pair of 14s, a pair of 15s, a pair of 16s and a single 17. Given those choices, if Bernard says he got the answer, then Albert will know that it's August 17.
Sorry mate, it's still possible that Bernard rules out May. And he should, the math is correct. Because Albert knows only the month, his statement naturally rule some months out, not some days. Your thinking just create contradicting possibilities (with some assumptions). Even if Bernard only ruled out June, Albert cannot assume that and cannot be sure the date is 17 and not 15.
DeleteLook like your Aug 17 is accidental, seemingly correct, but bases on some assumptions (you want them to think like real life, not just apply simple logic formula?). I guess ideally those who wrote this problem must change the numbers so that such "alternate answer" is not possible, and therefore the only way to find the answer is to work out the deductions with basic boolean math etc. But well it's late, and I guess you also stubbornly does not care to explore any changes I suggest (like the "spy" story above :) )
DeleteI think the issue arises out of the assumption made by Daniel that both A and B need to talk to find the solution and they both are aware of this situation. Even under this circumstance, both A and B will start with a depleted set of dates, which will not have May 19, June 18, June 17 and August 17. So I am not sure how Daniel is able to arrive at August 17 as the solution.
DeleteIn any case let's start by assuming that C told A the month as August and B the Day as 17.
- With this scenario, A can make the first statement (hence validated), which gives a clue to B that the months are not May or June.
- Based on this information, B can make the second statement (hence validated).
- This second statement though, still leaves A with two choices 15th August or 17th August.
- There's no way that he could have made the third statement based on the leftover choices he has.
So August 17 will not provide the solution that satisfy the three statements made in the problem.
BLUEGUITAR, of course when we do the math. we generalize and rule out invalid sets. But this Daniel applies "logical thinking" and decided that because the date is 17, Bernard is waiting for Albert to say to rule out June only? That opens to all possibilities (did Bernard rule out June, May, or both????). Anyway at least now he accepted straight dates are possible, which mean he has to accept that ruling out entire month of May and June also possible. And what the hell all these possibilities create? I guess he's not doing math but some kind of life reasoning.
DeleteHi, BLUEGUITAR,
DeleteThanks for your comments. Yes, you are right! There are 2 Cheryl's Birthday Problems here.
One is a straight-forward secondary school maths problem whereby each sentence of the dialogue helps you to eliminate the invalid dates till you arrive at the answer. That follows a certain structure and if you are careful, you can solve the problem quite easily. Obviously, in that case, there is no argument, all should agree that July 16 is the answer. Of course, the narrative and the elimination process will not make sense to anybody. Seen in this light, nobody would be quite interested in it.
Yet, there is another Cheryl's Birthday Problem that had captured the public's imagination and even worldwide attention. We, Singaporeans, were caught off-guard, but we soon realized that people are disputing the answer because they are seeing it as a real-life philosophical or logical puzzle. It was with the intention of participating in this surprising social phenomenon and to get people thinking about philosophical issues that this article was written. This, singaporedialectic blog is a philosophy blog after all. I hope everyone had fun.
Dear Sat That,
DeleteThanks for the discussion today. My reply to BLUEGUITAR above was meant for you too. Thanks for your great patience and interest.
As in all internet phenomena, an event like this can turn viral suddenly and die down just as quickly. I had great fun and I hope you had too!
The discussion is great and teaches us well to formulate our statements to make them as clear as possible to others (quite a task!). My two cents would be:
Delete- the two solutions branch out at this point:
1) Cheryl CAN give Bernard number 18 or 19
2) Cheryl CAN NOT give Bernard 18 or 19.
OK, now if 1 is true:
It kills the whole point of the problem! She already gives the answer away. This "challenge" would not have even happened. She might as well give Bernard her telephone number and favorite wine name right away (this is a family blog after all, so I am watching my language). Don't you think?
2 is true.
now. why does A say that B does not know? Because A knows, the month is August, therefore Bernard, knowing any number except 18 or 19 cannot possibly know. Additionally, by saying "i dunno" A says "it is not June". You know the rest.
Yes, its not "the" pure logic to assume that human behavior is logical. But ask anyone, they will assume that Cheryl wanted to measure the two gentlemen by giving them the challenge.
Hi Daniel, no problem at all. I was having fun as well, at least had a chance to touch maths gain (even if it's quite a simple math). It's interesting to see how this problem becomes viral, even though it's not a novelty (it appeared many years ago mathforum.org/library/drmath/view/68613.html). Perhaps it's the way they tell the "story" that arouses people interest.
DeleteHi Andrejus. Yes I think this boils down to how you understand the statement "Albert knows that Bernard doesn't know the answer"
Delete- In strict Math terms: you only have the fact as told in the problem (Albert knows the month) which deduces to "Albert knows that because he knows the month doesn't have exclusive dates".
- Using common understanding: Albert knows that because the 2 obvious dates shouldn't be counted. Or Albert knows that because Bernard didn't say he knows the answer.
It's interesting nevertheless, and yes it's a case for problem creators to consider how to make sure their statement is not misunderstood.
Hi Andrejus and Sat That,
DeleteWell said!
In solving a real life Cheryl' Birthday Problem, Secondary school maths will be grossly inadequate. We must realize that every line of the dialogue between Albert and Bernard has its own ambiguity. Different ways of judging and interpreting these ambiguities will lead to different answers.
We must also be careful when we try to get into the minds of both men. We should not see things from the audience's perspective, but to face their choices from their point of view.
My conclusion is that this problem is like quantum physics. It's answer is not constant. It changes as your point of view changes and it mutates as you try to perceive it.
I first came to the solution of 17 August. I then thought there were two solutions. Now I'm convinced the one solution is 16 July.
ReplyDeleteThe problem is confusing the fact with us not knowing the month and day, with the situation Albert and Bernard are in and the statements they make.
Exploring both solutions ...
Albert DOES know the month. He doesn't exclude 18 June and 19 May because he knows Bernard doesn't know; he can exclude them because he knows it's July or August; Cheryl has told him!
Bernard knows it's the 16 or 17. Albert has said that he knows Bernard doesn't know, i.e. Bernard couldn't possibly have a unique answer, i.e. Albert has excluded the whole of May and the whole of June. We can exclude the whole of these months, (rather than limiting it to just 18 June 19 May) because Albert can exclude the whole of these months, because he know which single month it is. It's then obvious which Month it is to Bernard.
Albert can exclude 14 since Bernard now knows.
The last line is then CRUCIAL.
If the solution is 17 August, Albert still only has August as the bit of information he has, therefore to him it could still be 15 or 17, and he wouldn't be able to say"Then I also know"
so 17 August is NOT a solution, the answer is 16 July.
and forget all the talk about silence, that's a different question. if silence was involved it would be:
Silence
Albert: thinking: (Bernard is quiet, he doesn't know the answer, it can't be 18 or 19.)
Bernard: thinking: (Albert must have worked out it can't be 18 or 19, and he's still quiet. It can't be June.)
Bernard: I know the answer, it's 17 August.
silence
Cheryl: you fool, I told you 16. Come on Albert, come show me a good time.
To inject more realism -
DeleteSilence
Albert: thinking: (Bernard is quiet, has he even started thinking? Should I or should I not initiate elicitation first?)
Bernard: thinking: (Albert is quiet, has he even started thinking? Should I or should I not initiate elicitation first?)
And the rest is history.
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DeleteRe: The last line is then CRUCIAL. If the solution is 17 August, Albert still only has August as the bit of information he has, therefore to him it could still be 15 or 17, and he wouldn't be able to say "Then I also know"
Delete> Albert knows because assuming the alternative premise, there's no other way Bernard could know if it wasn't a 17th. Obviously the point in this case isn't how Albert might know but how one may reject either premise based on inferring dialogue sequence from a summary report to 3rd party which doesn't explicitly state which came after which (as a 2-party 1st persons dialogue would inherently depict). Hence, all the dialogue reconstruction diverges by said ambiguity, i.e. presentation of the question is fundamentally flawed to begin with.
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ReplyDeleteInitially, I also thought the solution is 17 Aug but now I'm firmly convinced that it is 16 Jul.
ReplyDeleteThere are 2 problems with 17 Aug approach.
1) The first is ASSUMPTION. We cannot assume that it cannot be 18 or 19 due to Bernard's silence/slowness or whatever, and that Cheryl could not have given these 2 dates otherwise it would be pointless etc. The rule here is one cannot make use of any statement until it becomes fact.
2) The second is the interpretation of the part on "... I know that Bernard does not know too.". If Albert had not assumed anything, how can Albert be 100% sure? He can only be sure if the month given to him does not contain any unique date(s).
It is possible to arrive at the correct answer (July 16) with faulty reasoning. The difficulty is to solve it with INTEGRITY. Such a solution is given at http://whyalbinoowl.blogspot.sg/2015/04/blog-post.html
ReplyDeleteHi Albino Owl,
DeleteI appreciate your very neat grid charts and your systematic problem-solving approach. It will stand you in good stead in the Singapore school system. I gather you must be a student or a very young person.
Unfortunately, you did not bring anything new to the table. In the adult world, things are not as they appear. As I'd told BLUEGUITAR, Sat That and Andrejus (please see above), Cheryl's Birthday as a secondary school maths problem and Cheryl's Birthday as a surprising internet sensation are 2 separate animals. A lot of people innocently thought that it's the maths that caused the viral fever. Some have made videos explaining the workings of the problem. Even maths professors got into the act!
The 'August 17' people are also maths-literate, but they choose to see things differently, partly as a rebellion against the idea of an Official Correct Answer and partly as an intellectual exercise to see how far left-field they can run. This tongue-in-cheek article is part of this movement. The point is not just to be right, but to explore the boundaries of rightness.
I hope my ideas don't sound dangerous to you. If you are game, I have a second (and final) article on Cheryl's Birthday coming up soon. Watch out for it. All the best wishes to you!
For those who have enjoyed this article, please read my follow-up at the link below:
ReplyDeleteCHERYL'S BIRTHDAY - The Final Verdict
Read at:
http://singaporedialectic.blogspot.sg/2015/04/cheryls-birthday-it-must-be-sign-of.html?m=1