Talk:Cheryl's Birthday

Another solution
Is based on iteration and elimination. Goal is to find the date that makes the dialogue or “assertion” true. May 15 not possible because Bernard still has 2 options at this time and can`t tell each is right May 16 not possible same reason May 19 not possible Bernard would have known at first and this is not what he says Etc... The first date making the assumption true is July 16. All previous dates have been eliminated as well as May 16. July 14 is not possible because Albert may think that Bernard has been given 14 as date making July 14 or August 14 still 2 options for Bernard and July or August still 2 for Albert.

Test the dialogue on each date and you will find the answer. The intuitive way is to consider we are May 1st and each following morning，they tell the same dialogue. On Which day the dialogue will come true ?

Comment by IP user
I am missing a part of A's reasoning. All A has done is eliminate May and June and the 14th for B. A says this in his mind: "Alright B, you're smart enough to know that I just eliminated May and June and the 14th for you... let's see what you say".

B says "I know the date".

A now says "Aha, B could not have been told the 15th because if he had been..."

We have no idea what B has been told. If told the 15th, he would have been able to deduce Aug. If told the 17th, same thing. If told the 16th, he would have been able to deduce Jul.

From A's pov why could B not have been told the 15th or 17th?

Because for Albert to say "aha, now I know", means it's not August: if Albert had been told August, learning that Bernard now knows the answer couldn't give Albert the answer: if Albert knows August, he doesn't know whether it's the 15th or the 17th, because although May 15th and June 17th were eliminated Albert doesn't know which of those two eliminations gave Bernard the answer. 174.116.120.187 (talk) 2015-04-15T06:57:24‎

"Solution" 2
Given that the interpretation of solution 2 has to keep making assumptions, and solution 1 is an unambiguous answer, there doesn't seem to be a point to that interpretation or its "solution"

The problem "Cheryl's Birthday" needs rewording
The problem is not well defined. If Albert says "but I know that Bernard doesn't know too", then Bernard cannot say right after it "but I know now", because this means that Albert lies - he knows wrong.

This I think is a correct wording of what Albert and Bernard should say (so that what is written in "Solution" to work):

1.Albert: From (considering) the month I'm given, I can say that before I started talking, Bernard didn't knew which is the exact date.

2.Bernard: After I heard 1.Albert, I can now say that I know the exact date (, using the day that I know).

3.Albert: After I heard 2.Bernard, I can now say that I also know the exact date (, using the month that I know).

Ambiguous perception of first statement
In first statement one has to judge which part is valuable and which is redundant. If you assume that first part is valuable information, like


 * Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.

then you end up with August 17 solution, but if you you assume that second part is valuable and first redundant, like


 * Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.

then you end up with July 16 solution

Comment by User:Albinoowl2015
My apologies to all here. I am new and know I may run foul of the rules of engagement. The Cheryl's Birthday is simple to those who are familiar with this type of puzzle. It only needs logic to solve. My concern is that the solution is not well described. In fact, those solutions offered adopt a wrong approach. So I actually described the proper approach, one with integrity. But I do not know the proper way to share it. It is found at http://whyalbinoowl.blogspot.sg/2015/04/blog-post.html Albinoowl2015 (talk) 10:11, 17 April 2015 (UTC)

Names of days were not in the problem statement
The introduction of day names (Thursday, Saturday) are not helpful in the discussion of the solution that is claimed to be correct. They are not part of the problem statement. They only add extraneous detail and confusion.

In fact, everything in the first paragraph after "One answer to the question is July 16" seems to be extraneous. So I am deleting it. - 71.179.114.4 (talk) 15:49, 19 April 2015 (UTC)

Objection to edit on 14:24, 19 April 2015
The edit summary says, 'rm purported "Alternative Answer" which is just incoherent'.

I disagree that it was incoherent. It seemed clearer than either explanation that remains for either date. - 71.179.114.4 (talk) 16:09, 19 April 2015 (UTC)


 * I think this is supposed to be a recitation of the (wrong) Aug 17 answer in the blog by James Grime. It is not written in English, which is a requirement, because an unadorned list of dates is not a sentence, but ignoring that:

May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17

Albert: I don't know when Cheryl's birthday is, but i know that Benard does not know too. (Albert: "I've no idea when her birthday is, but Benard would have said he does if she told him either 18 or 19.) -Eliminate May 19, June 18 (Albert: I still don't know even after eliminating those two dates)


 * The conclusion (beginning "-Eliminate May 19...") is wrong: A can only know that B does not know if the month is other than May/June; therefore this eliminates all possibilities in those two months. This immediately makes the sentence (beginning "Benard [sic] looks over...") after the following list of dates incoherent. Stop at the first mistake. Imaginatorium (talk) 16:35, 19 April 2015 (UTC)

So-called "Disputed solution"
This is not a "disputed solution", it's simply one of many (approximately 9) wrong solutions. The version given by James Grime (who, astonishingly, claims to be a "mathematician") goes wrong in line 1, as usual: "Albert knows that Bernard doesn’t know. (Maybe Cheryl told him as much)." This is a logic puzzle, and the whole point of logic puzzles is that you are allowed to assume there is no hidden business, such as people being given information without it being stated in the problem. So the argument is wrong. It could be argued that there could be a "Reaction" section, which stuff about the various mistakes people make -- read the Kenneth Chang blog, where he goes with mind-numbing patience through all the wrong answers, pointing out the errors. But is this really noteworthy? I invite comments, but I suggest really this section could just be deleted. Imaginatorium (talk) 17:00, 19 April 2015 (UTC)


 * I think the fact that it's a common mistake, and the fact that the conventions of a logic puzzle are (obviously) not stated in the question, makes it noteworthy. (For example: it is not stated in the question, and it is assumed by all readers, but it needs to in fact be common knowledge that Cheryl gives Albert the month and Bernard the date -- or at least, both players should know this and that the other knows too, and that no other information is given.) Besides, this being the most popular wrong answer, if we remove it there will be hordes of people coming to the article and trying to edit it back it. We could probably rename the section to "Incorrect solution" though. I already changed the section from being a detailed working-out of its reasoning to a description of precisely how it differs. Shreevatsa (talk) 17:11, 19 April 2015 (UTC)


 * No, the bit about who knows what is not "common knowledge", it is explicitly stated in the problem: "Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively." The last word, "respectively" tells us that Albert knows the month and Bernard the day.
 * I take your point about the problems of removing this section. The problem is that the Aug 17 answer is making (quite strange) modifications to the question, so of course it gets the wrong answer. There is simply no end to the number of ways the problem could be stated differently, and have a different answer. This is why I think more general stuff about wrong answers, for example citing the Kenneth Chang blog, would be more interesting and less likely to provoke confused argument. Imaginatorium (talk) 18:45, 19 April 2015 (UTC)


 * The bit about who knows what need not be common knowledge, but it needs to be at least mutual knowledge of the third-order. Specifically not just the first but all three of the following need to be true:
 * Cheryl tells Albert the month and Bernard the day.
 * Both Albert and Bernard know that Cheryl tells Albert the month and Bernard the day.
 * Both Albert and Bernard know that both Albert and Bernard know that Cheryl tells Albert the month and Bernard the day.
 * The Kenneth Chang blog and general stuff about wrong answers would definitely be worthwhile to include; I agree about that. Shreevatsa (talk) 21:23, 19 April 2015 (UTC)

Presentation of disputed solution is flawed
There is no reason to say this solution relies on an initial statement from Bernard, "I don't know when Chery's birthday is."

Givens:
 * Neither Albert nor Bernard know when Cheryl's birthday is.
 * An array of 10 dates contains the correct answer.
 * Albert knows only correct the month is (multiple days are possible for each month).
 * Bernard was given only correct the day (some days are possible in only one month).

If Cheryl's birthday were either May 19 or June 18, then Albert would know from the outset that Bernard already possess the correct answer with certainty.

For this solution:
 * Cheryl tells Albert the correct month is August.
 * Cheryl tells Bernard the correct day is the 17th.

Since Albert knows the birthday is in August, he is sure that neither day with a unique number can be the correct answer. Those are the only days Bernard could know with certainty.

Without any initial statement from Bernard, Albert knows by inspection of the available dates and from his knowledge of the correct month that Bernard has insufficient information to know Cheryl's birthday.

The initial statement that is claimed to be the starting point for the alternate solution is not necessary. - 71.179.114.4 (talk) 17:16, 19 April 2015 (UTC)


 * It is true that any birthday in July or August is compatible with the statement of Albert. (Indeed, that is the conclusion drawn from it in the correct solution.) The difference is that in the original problem, when Albert deduces that Bernard does not know, he effectively makes a statement that his month is July or August (and hence not May or June). If instead Albert already knew that Bernard did not know, then it is the second part of his statement that is redundant, and the first part only makes a statement that the month is not June. This leads to the August 17 solution. That is how the two problems differ.
 * In the original problem as opposed to this one, both dates July 16 and August 17 are possible from Bernard's statement ("I know now"), and we (the problem-solver) need Albert's last statement ("Then I also know") to narrow it down to July 16. Shreevatsa (talk) 18:19, 19 April 2015 (UTC)


 * Arguments based on English grammar seem weak for a question composed in Korea. I balk at the phrasing "but I know that Bernard doesn't know too." I would have expected the last word to be "either," but I am not going to try to make a point based on this grammar choice made by someone writing in their non-native language.
 * What is wrong with Albert making a deduction from the given information? Why is that disallowed in a logic problem? - 71.179.114.4 (talk) 18:34, 19 April 2015 (UTC)
 * I did not mention anything about grammar. And Albert making deductions is not disallowed; it is necessary! In fact, the difference between the original problem and the modified problem is that in the original problem Albert can only deduce that Bernard doesn't know, while in the modified problem he has to get this information via some other means not specified in the problem. Shreevatsa (talk) 18:43, 19 April 2015 (UTC)

Here are the two versions of the problem, with the redundant bits (those already known at the time the statement is made, or those not strictly needed by us for a solution) crossed out: "Original problem (solution: July 16): Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't know too. Bernard: At first I didn't know when Cheryl's birthday is, but I know now. Albert: Then I also know when Cheryl's birthday is."

versus "Modified problem (solution: August 17): Bernard: I don't know when Cheryl's birthday is. Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't know too. Bernard: At first I didn't know when Cheryl's birthday is, but I know now. Albert: Then I also know when Cheryl's birthday is."

That's the difference. Shreevatsa (talk) 18:43, 19 April 2015 (UTC)


 * Neither of which is the problem as stated:
 * Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't know too.
 * Bernard: At first I didn't know when Cheryl's birthday is, but I know now.
 * Albert: Then I also know when Cheryl's birthday is.
 * I disagree that:
 * Albert's declaration of ignorance is irrelevant after he eliminated May 18 and June 19.
 * Albert needed a cheat sheet to conclude at this time that Bernard was similarly ignorant.
 * If one makes up a different problem, then it would not be unusual for it to have a different solution. -71.179.114.4 (talk) 19:11, 19 April 2015 (UTC)


 * You say "Neither of which is the problem as stated", but the words of the "Original problem" above are identical. So how can it be different? (The only change is marking some bits of text as not strictly necessary.) I really can't understand what you are trying to say: can you follow the correct solution as given by Alex Bellos or Kenneth Chang? Are you saying you think that somehow August 17 is a solution to the original problem? Imaginatorium (talk) 19:25, 19 April 2015 (UTC)


 * The crossing out of words implies changes to the text. You claim some bits of text are not strictly necessary. We seem to disagree on what those bits might be. No, I don't follow the solution by Alex Bellos. The elimination of May 16 takes more than a hand wave. I think August 17 is the solution to the original problem. - 71.179.114.4 (talk) 19:43, 19 April 2015 (UTC)


 * I agree that "crossing out" is not the best way to mark this text. Perhaps putting it in square brackets would be clearer. Just to look at the first sentence... Remember that the rules of logic problems are that we are allowed to assume that everything written in the question is true, is known to us and to the participants, and nothing else is known to anyone. Since Albert knows only the month, and each month has more than one possible date, it is already clear to us, and to Bernard, that Albert cannot know the birthday. Therefore, when Albert says "I do not know the birthday", he is saying something we already know to be true, so he is not giving us any new information. Thus this part could be omitted without changing the problem. The second half of the sentence does tell us new information: the only thing Albert knows that we don't is the month, and therefore the extra information he gives us (that Bernard doesn't know the birthday) must be deducible from the month. This is true if the month is July or August, and it is false if the month is May or June. Therefore, we now know, and so does Bernard, that the month must be July or August. And this is the only new information that Bernard has been given.
 * I don't understand your comment about May 16: by the end of the first statement, we know (and Bernard does) that the month is July or August, so the birthday cannot possibly be May 16. Imaginatorium (talk) 07:53, 20 April 2015 (UTC)


 * Yes, crossing out wasn't the best way; wish I had thought of using square brackets. Actually I was originally thinking of putting it in light grey, but hadn't looked up the markup for how to achieve that. Shreevatsa (talk) 16:43, 20 April 2015 (UTC)


 * In my opinion the disputed solution would look more convincing if we interpreted Albert's words "I don't know when Cheryl's birthday is, but I know that Bernard doesn't know too" as follows:
 * Albert: Bernard, maybe you are not aware but the rules of the game are such that you cannot possibly know Cheryl's birthday from what she has told us alone, AND I CAN, but I don't know nonetheless. 95.28.166.64 (talk) 12:19, 20 April 2015 (UTC)

Objection to statement added to Alternate Solution
This statement added to the alternate solution seems incorrect to me (emphasis added):


 * This answer is possible under the interpretation that the latter part of this statement is not something that Albert deduced, but something he knew via some means not mentioned in the problem (such as Cheryl telling him that Bernard does not know). For instance, it would be the solution if the sequence of statements were the following (where the difference from the original problem is an additional statement by Bernard at the beginning)

Why could Albert not deduce that Bernard could not know the date until Albert had his say?


 * 1) Albert knows the month is August.
 * 2) May 19 and June 18 are not possible based on Albert's knowledge of the month.
 * 3) All remaining dates might occur in either of two months.

Bernard had no way to resolve which month was correct for his known day.

Until Albert said he still didn't know the birthday, it was an independent and valid deduction that Bernard did not know the date.

No "additional statement by Bernard at the beginning" is needed for this solution. - 71.179.114.4 (talk) 18:45, 19 April 2015 (UTC)


 * Yes, Albert can deduce (if he was given July or August) that Bernard does not know the birthday. But the question that matters to the rest of the problem is whether Albert only deduced this (and conveyed information by saying he deduced this), or whether he knew this already (and thereby did not convey information by saying he knew that Bernard did not know). See the previous section on this talk page. Shreevatsa (talk) 18:49, 19 April 2015 (UTC)


 * If the answer is August 17, there is no if about whether Albert was given August. The rest of the speculation about "what he knew and when he knew it" seems extraneous. It was a logical deduction that he could reach and declare. Why would we imagine Bernard had to tell him what he could deduce? - 71.179.114.4 (talk) 18:57, 19 April 2015 (UTC)


 * The issue is how Bernard suddenly came to know after Albert's statement. For this issue, it matters what the information conveyed to him by Albert's statement was. If Albert deduced it, the information conveyed to him is that the month is either July or August. If Albert did not deduce it, then this is not the information conveyed to him. Shreevatsa (talk) 19:04, 19 April 2015 (UTC)


 * The information conveyed to him by Albert's statement was: June 17 was off the table. Since Cheryl told Bernard the correct day was the 17th, his previous dilemma was resolved. He now knew that Albert knew the correct day was not June 17. - 71.179.114.4 (talk) 19:22, 19 April 2015 (UTC)


 * Yes, that is the information conveyed to him in the modified problem. In the original problem (where Albert deduces it), the information conveyed to him is that the months May and June are off the table. Shreevatsa (talk) 19:25, 19 April 2015 (UTC)


 * It is unclear why you think Albert can't deduce that Bernard doesn't know the correct day. I presented logic how he might do so. Why don't you think he used it? - 71.179.114.4 (talk) 19:47, 19 April 2015 (UTC)


 * Yes, Albert can logically deduce that Bernard doesn't know the birthday. I have never thought or said otherwise. But that is not the issue — the issue is that the statement "I have logically deduced that Bernard doesn't know the birthday, given only the month" carries some information which Bernard can use, and the "August 17" solution does not take this into account properly. Let me post a new section about the two problems. Shreevatsa (talk) 19:52, 19 April 2015 (UTC)


 * So Statement 0 seems unnecessary in the 'modified problem.' That there seem to be two ways to use information suggests the problem was poorly written. I see substantial effort invested in the next section. It will take me some time to digest the volume of text there. I might be persuaded otherwise upon closer examination, but my first impressions are Statement 0 is not necessary in the 'modified problem' and Statement 1a in the 'original' problem does carry new information: The birthday is not June 17; solving the 'original problem' becomes more difficult than necessary by ignoring this information. - 71.179.114.4 (talk) 20:30, 19 April 2015 (UTC)


 * The main point of difference is that if Albert says he has deduced the fact, then this conveys more information (see the line in bold about Statement 1b below; the solution that arrives at August 17 ignores this information that Bernard gets), and with this additional information (e.g. that month is not May) Bernard can deduce a unique birthday even if he was given 15 or 16, not just 17. The correct solution does not ignore any information (and "not June 17" is subsumed by "not May or June"). Shreevatsa (talk) 20:49, 19 April 2015 (UTC)

The modified problem that leads to August 17
Just for clarity, let's break down and number the problem's statements.


 * [Only present in the modified problem] Statement 0 by Bernard: I do not know the birthday. (Or, Statement 0 by Cheryl: Bernard does not know the birthday.)
 * Statement 1a, by Albert: I do not know the birthday.
 * Statement 1b, by Albert: I know that Bernard does not know the birthday.
 * Statement 2a, by Bernard: At first I did not know the birthday.
 * Statement 2b, by Bernard: Now I know the birthday.
 * Statement 3, by Albert: Now I know the birthday.

In the original problem, only the statements 1a to 3 are made. In the modified problem, all statements 0 to 3 are made.

Let me discuss the modified problem first, as it is simpler.


 * In the modified problem:
 * Bernard does not know ⇔ The date given to Bernard is not 18 or 19.


 * So Statement 0 amounts to declaring that the date is not 18 or 19 (i.e. it is 14, 15, 16, or 17).
 * Statement 1a carries information:
 * Even after knowing that the date is not 18 or 19, Albert still does not know the birthday ⇔ The birthday is not June 17.
 * So Statement 1a amounts to declaring that the birthday is not June 17.


 * Statement 1b carries no new information: Statement 0 has already been made, so everyone knows that Bernard does not know the birthday.
 * Statement 2a carries no new information, for the same reason (as it is already covered by Statement 0).
 * Statement 2b is a deduction by Bernard, based on the information he has: the date, and Statement 1a (i.e. that the birthday is not June 17).
 * If Bernard was given 14, he could not have deduced the birthday (as both July 14 and August 14 are possible).
 * If Bernard was given 15, he could not have deduced the birthday (as both May 15 and August 15 are possible).
 * If Bernard was given 16, he could not have deduced the birthday (as both May 16 and July 16 are possible).
 * So Bernard must have been given 17, and he can deduce that the birthday is August 17.
 * So Statement 2b amounts to declaring that the birthday is August 17.
 * We have already solved the problem.


 * Statement 3 carries no new information. (Even we, the problem solvers, have already deduced the date, so obviously Albert (who was given more information than us) has deduced the date too, and he merely says so.)

The original problem is more elaborate. Let me reproduce the statements again, unchanged from the last time:


 * [Only present in the modified problem] Statement 0 by Bernard: I do not know the birthday. (Or: Statement 0 by Cheryl: Bernard does not know the birthday.)
 * Statement 1a, by Albert: I do not know the birthday.
 * Statement 1b, by Albert: I know that Bernard does not know the birthday.
 * Statement 2a, by Bernard: At first I did not know the birthday.
 * Statement 2b, by Bernard: Now I know the birthday.
 * Statement 3, by Albert: Now I know the birthday.


 * In the original problem:


 * Statement 0 does not exist.
 * Statement 1a carries no new information: no matter what month Albert was given, he could not know the birthday.
 * Statement 1b is a deduction by Albert:
 * Bernard does not know ⇔ The date given to Bernard is not 18 or 19.
 * Albert knows that Bernard does not know ⇔ Albert knows that the date given to Bernard is not 18 or 19.
 * If the month given to Albert was May, then Albert could not know this (birthday may be May 19, and Bernard may have got 19).
 * If the month given to Albert was June, then Albert could not know this (birthday may be June 18, Bernard may have got 18).
 * So as Albert has deduced that Bernard did not get 18 or 19, the month given to Albert is not May or June: it is July or August.
 * So Statement 1b amounts to Albert declaring that the month is either July or August.


 * Statement 2a carries no new information: it only confirms what Albert has just said.
 * Statement 2b is a deduction by Bernard, based on the information he has: the date, and Statement 1b (that the month is July or August).
 * If Bernard was originally given 14, he could not have deduced the birthday (as both July 14 and August 14 are possible).
 * If Bernard was originally given 15, he could have deduced the birthday (as only August 15 is possible).
 * If Bernard was originally given 16, he could have deduced the birthday (as only July 16 is possible).
 * If Bernard was originally given 17, he could have deduced the birthday (as only August 17 is possible).
 * So Statement 2b amounts to declaring that the date is either 15, 16, or 17 (and specifically, that the birthday is one of August 15, July 16, and August 17).
 * We have not yet solved the problem.


 * Statement 3 carries information:
 * If Albert was originally given July, he could have deduced the birthday (as of the three birthdays left after Statement 2b, only July 16 is possible).
 * If Albert was originally given August, he could not have deduced the birthday (as both August 15 and August 17 are possible).
 * So Statement 3 amounts to declaring that Albert was given July (and specifically, that the birthday is July 16).
 * We have only now solved the problem.

Hope that helps make it clearer, Shreevatsa (talk) 20:02, 19 April 2015 (UTC)

From NYT blog
From:
 * http://www.nytimes.com/2015/04/15/science/answer-to-the-singapore-math-problem-cheryl-birthday.html


 * Thus, for this statement by Albert to be true means that Cheryl did not say to Albert, “May” or “June.” (Again, for logic puzzles, the possibility that Albert is lying or confused is off the table.)

But the possibility that explainer is confused is not off the table.

Why is it that 'Not May 19" is equivalent to "Not May?"

This is important to the claim in the large section recently added; Statement 1b for the 'original problem' (emphasis added):
 * So as Albert has deduced that Bernard did not get 18 or 19, the month given to Albert is not May or June: it is July or August.

Why not May?

If Cheryl's birthday is May 16, why couldn't Albert be telling the truth when saying, "I don't know when Cheryl's birthday is, but I know that Bernard doesn't know too."?

BTW: I didn't see the exhaustive coverage of other possibilities that Imaginatorium said were debunked on the Kenneth Chang blog. - 71.179.114.4 (talk) 21:21, 19 April 2015 (UTC)


 * Suppose Cheryl's birthday was May 16. Then the only information Albert would have is that the month is May. That is, all that Albert knows is that the birthday is one of: May 15, May 16, May 19. He does not know for sure that it is, or is not, any of these three.
 * For all he knows (remember: he only knows that the month is May), the birthday could be May 19 (it could also be May 15 or May 16).
 * He knows that if the birthday was May 19 (and this is still a possibility as far as Albert knows), then Bernard would be given the date 19.
 * He knows that if Bernard was given the date 19, then Bernard could know the birthday.
 * So Albert, knowing only that the month is May, has no way of ruling out the following possibility: that Bernard has been given the date 19, and therefore knows the birthday.
 * So Albert cannot know with certainty that Bernard does not know, because the possibility (that Bernard has been given 19 and knows the birthday) is still open for all that Albert knows.
 * In other words: if Albert deduces that Bernard does not know the birthday, then he has deduced (among other things) that Bernard was not given the date 19, which Albert cannot deduce if he was given the month May Shreevatsa (talk) 21:31, 19 April 2015 (UTC)


 * Let me say it yet another way: Albert is (among other things) saying "I know it is not May 19", when the only information Albert has been given is the month. The only way Albert can be confident of this, is if Albert knows it's not May. Shreevatsa (talk) 21:34, 19 April 2015 (UTC)


 * And yet another way. When Albert says "I know that Bernard does not know", he's effectively saying "I know that the birthday is not May 19 or June 18". Albert has been given only the month, so imagine yourself as Albert:
 * If you've been told only that the month is May, can you confidently state that the birthday is not May 19 or June 18? No, because the birthday may be May 19, and you'd be wrong.
 * If you've been told only that the month is June, can you confidently state that the birthday is not May 19 or June 18? No, because the birthday may be June 18, and you'd be wrong.
 * If you've been told only that the month is July, can you confidently state that the birthday is not May 19 or June 18? Yes, because the birthday is in July, so it can't be May 19 or June 18.
 * If you've been told only that the month is August, can you confidently state that the birthday is not May 19 or June 18? Yes, because the birthday is in August, so it can't be May 19 or June 18.
 * So you can only confidently make that statement when the month you've been told is July or August. In other words, when Albert confidently states that he knows that Bernard does not know, he's revealing the information that the month is July or August. Shreevatsa (talk) 21:51, 19 April 2015 (UTC)


 * I think I am finally with you. I haven't given up the thought that there might be a loophole around this; but the more I think about it, the less likely it seems that there is one:
 * If you've been told only that the month is May, can you confidently state that the birthday is not May 19 or June 18? No, because the birthday may be May 19, and you'd be wrong.
 * So the only way Albert can eliminate the easy dates is to know the month isn't May or June. Bernard knows this is a condition for both eliminations, so he can eliminate the entire months of May and June.
 * I think it is new information when Albert says, after doing everything he knows how to do, he still doesn't know the birthday. It isn't changed information, but it is still new.
 * Consider an alternate universe, where Cheryl is an even worse choice as a new friend for Albert. The following might happen:
 * Cheryl tells Albert the month is May.
 * Cheryl tells Bernard the day is the 19th.
 * Bernard speaks first: I know Cheryl's birthday, and I know that Albert doesn't.
 * Bernard and Cheryl have a laugh at Albert's expense.
 * So there are scenarios (with appropriate conditions) where the first person can deduce the answer and leave the other person in the cold.
 * In both universes, Bernard knew the answer first. It seems that Cheryl might like Bernard more than Albert.
 * Thanks for your patience and help in understanding this problem. - 71.179.114.4 (talk) 11:55, 20 April 2015 (UTC)


 * Yes, that's right. Glad we agree now! The tricky thing about these logic puzzles is that the information content of a statement is not just what is said, but also what it reveals about the speaker and how they were able to say it. Most people do take this into account for the "I know the answer" statements, but not sufficiently for the "I know that the other person doesn't know the answer" statements. Shreevatsa (talk) 16:34, 20 April 2015 (UTC)

August 17th Should Not be Labeled an "Incorrect Solution" (withdrawn)
While I understand that SASMO is currently standing behind its statement that August 17th is not an acceptable alternate answer, that doesn't mean they are correct. They have merely identified an error in reasoning that led SOME people to choose August 17th. But this does not eliminate August 17th as a possible answer. After all, even if someone tries to solve "2x2=" by adding the numbers together, the answer is still "4" even if the process was wrong.

Admittedly, math problems are a bit of a hobby of mine -- a holdover from my Mensa and Michigan Mathematics Prize Competition days -- so I spent a couple days testing every possible answer and trying to disprove them. No matter how I run it, however, I cannot eliminate August 17th as a possible answer that meets 100% of the conditions of the problem. Yes, it's true that SOME people who claim August 17th is the answer are wrong on the math, but not ALL of them.

I have done my best to explain why August 17th meets all the criteria of the puzzle in a video I just posted for this discussion:

https://www.youtube.com/watch?v=JTiVzRmEd0Q&feature=youtu.be

I'll be sending this to SASMO and seeing if I can get a comment from them as well. But I really disagree with the phrase "Incorrect Solution" when the matter is clearly still being disputed among mathematicians all over the world, and agreement with SASMO is clearly not universal. If you find any logical flaw in my video, however, please let me know so I can take it down. :)

JK (talk) 19:27, 22 April 2015 (UTC)


 * I'm sorry, but listening to a video is time-consuming anyway, and I am not going to attempt to listen with that horrible jingle noise in the background. If the text is more or less the same as your original addition to the article page, the error is in the last clause "...since Bernard could not have figured out the full date if he had been given the 14th or 15th as its date." Of course if Bernard had been given the 15th, as soon as he knows the month is July or August he can work out the full date, as per the original solution. Starting by assuming the answer you are trying to prove is not usually a good strategy for solving problems like this, because it is extremely easy to miss something.
 * FWIW, I don't think the title ("Incorrect...") is very good; the section should describe the reactions, including this and any other popular wrong answers. Imaginatorium (talk) 04:42, 23 April 2015 (UTC)


 * Well, of course we agree that August 17th must be an equally correct answer only as long as it fits 100% of the conditions of the problem.


 * SASMO claims: "The fact that Albert knows that Bernard does not know means that Cheryl has told Albert that her birth month is either July or August." This is correct. Of the four months Albert could have been told, two of the months (May and June) would not have allowed Albert to make that statement, because if Bernard had been told the 18th or 19th, Bernard WOULD know the full answer. If it was July or August, Bernard could NOT know the answer.


 * But later, the SASMO explanation commits a logical fallacy with this line: "Since Bernard did not say [at first] that he does not know when Cheryl's birthday is, then how did Albert know that Bernard does not know?" Simple. If Albert was told the month of August, he knows that Bernard was either given “14th," “15th,” or “17th,” and none of those numbers on their own would allow Bernard to know the answer at this point. SASMO is forgetting that Albert was told it was August, which disallows the possibility that Bernard was given any date other than the 14th, 15th, or 17th. Those are the only three numbers Bernard could have been given.


 * Let me repeat this. If Albert was told it was August, then (1) he does not know when Cheryl's birthday is (since there are three possibilities), and (2) he knows for a fact that Bernard does not know (since there are two options each for the 14th, 15th, and 17th). It has absolutely nothing to do with May 19th or June 18th at this point in the puzzle. There is no possibility of those dates being correct anyway, because in this example Albert knows the birthday is in August.


 * Anyway, Bernard was given the 17th, so he can eliminate May and July, but didn't know if the birthday was in June or August. Since Albert has said he knows Bernard does not know the answer, Bernard now has new information. As we saw above, if Albert had been given the month of June, Albert could NOT have made the statement that he knows that Bernard does not know. Because if Albert HAD been given the month of June, it is possible that Bernard COULD know the birthday if he had been told the 18th. Therefore, June is eliminated, and Bernard knows the answer is August 17th. Bernard says he knows the date, and is correct.


 * Now Albert has new information. If Bernard had been told the 14th, he would not have been able to eliminate July. If Bernard had been told been told the 15th, Albert would not have been able to make the statement that Bernard couldn’t know. The fact that Bernard says he now knows the answer tells Albert that Bernard must have been able to figure out the month. The only day Bernard could have done that with was the 17th. Therefore Albert knows the answer is the 17th, and is correct.


 * To recap. Albert knows the month is August, which means Albert knows Bernard could have only been told the 14th, 15th, or 17th as his numbers.  Albert therefore knows that Bernard could not know the full date, because none of those numbers are unique.  Bernard was given the 17th, which means he knows it must be June or August.  Only when Albert says that he KNOWS Bernard does not know the answer can Bernard rule out June.  Because, as SASMO admits, the only way Albert could “know” Bernard does not know the answer is if the date is July or August.  That rules out May and June.  But since July doesn’t have a 17th, August 17th is the only answer.  Bernard’s statement that he now knows the answer is what allows Albert to rule out the 14th and 15th, because Bernard could not have definitively ruled out May and July without Albert’s information.


 * Because August 17th is a date that appears to perfectly fit the condition of the problem, it cannot be excluded from a potential correct answer.


 * I've sent this solution to a variety of college mathematics professors so far trying to determine a flaw in the reasoning above; so far I've received 2 agreements that July 16th and August 17th must be equally correct, 1 skeptical/non-committal comment, and 1 disagreement but without explanation. If I can get a disagreement of the logic above that makes sense, believe me, I'm more than happy to take down the video.  :)  As I said, it's entirely possible the above scenario doesn't work -- but that's the point of testing the hypothesis, even if it means, as you say, starting by "assuming the answer".  JK (talk) 17:29, 24 April 2015 (UTC)


 * I would be interested in seeing evidence that there is someone who is actually maths professor who thinks the above argument is valid. (And it is horrendously waffly: you never ever say "Let me repeat this" in a mathematical argument.) But anyway, I showed you the flaw above. You sort of repeat the error in this line:


 * If Bernard had been told been told the 15th, Albert would not have been able to make the statement that Bernard couldn’t know.


 * If Albert has August, and Bernard has 15, then Albert at the beginning only knows that he has August, but can deduce from this that Bernard does not know the full date. So the above line is not a valid inference. Stop at the first mistake. Imaginatorium (talk) 18:43, 24 April 2015 (UTC)


 * Ahhh yes I misunderstood how you were explaining it the first time. When Bernard says "I didn't know at first, but now I do", this gives Albert new information. Imagine if the answer was August 15th.  Albert would still be able to say that (1) he doesn't know the answer and (2) Bernard doesn't either.  If Bernard was given the 15th, the choices are either May or August.  But Albert's statement ruled out the possibility of May, so now Bernard knows it's the 15th and says so. Albert, upon hearing this..... well, is in the same position he would have been if it had been the 17th.  Albert cannot rule out the 15th or the 17th. (Incidentally, my final count from my emails was 3 professors who agreed both dates are valid, 1 skeptical, and 3 disagreements, including one who identified, as you did, that the logic flaw is in the 15th/17th problem.) JK (talk) 19:42, 30 April 2015 (UTC)

Matrix solution
There is a way of solving this problem by arranging the months and dates in a matrix, counting the number of elements in each row (column), and eliminating rows (columns) based on whether the number of elements in that row (column) is 'one' or 'not one'; where 'one' corresponds to 'definite date' and 'not one' corresponds to 'indefinite date'. This way, there is less language and more computation. Someone will eventually post it, but I haven't seen it on the web yet. Both Albert and Bernard can immediately, completely assemble the same matrix, and completely solve it. Actually I wonder if it is necessary that Bernard knows BEFORE Albert. I don't think so. Neither party requires that the other 'do something' for the answer to become clear to both. Try it. 71.139.161.36 (talk) 07:55, 2 May 2015 (UTC)
 * The problem is about deriving the date from the comments made by Albert and Bernard, so I think you have misunderstood. Can you explain how you know of the existence of this matrix solution? Imaginatorium (talk) 16:05, 2 May 2015 (UTC)

I am considering what you wrote, and I think you are correct. As far as the matrix:

I invented the solution. I thought surly this type of problem could be abstracted to some non-language representation, and solved with an algorithm.

The matrix shows the step-by-step (not really 'time') evolution of the possible dates. The matrix has the months on the y-axis, the days on the x-axis, and starts with all 10 dates, each represented by a dot at the appropriate (day,month) intersection.

If there is only a single dot on a particular column, then the associated y-axis value (month) is certain. If there is only a single dot on a particular row, then the associated x-axis value (date) is certain.

If, at a certain step, Bernard DOESN'T know (cannot know) Cheryl's birthday then at that step, he must NOT have been told a day which exists as a single dot in a column. If, at a certain step, Bernard DOES know Cheryl's birthday then at that step, he MUST have been told a day which exists as a single dot in a column. If, at a certain step, Albert DOESN'T know (cannot know) Cheryl's birthday then at that step, he must NOT have been told a month which exists as a single dot in a row. If, at a certain step, Albert DOES know Cheryl's birthday then at that step, he MUST have been told a month which exists as a single dot in a row.

On step one, the certainty of the month 'June' associated with day '18' is revealed by the fact that there is only ONE dot in the '18' column; same with day '19'. We remove the two dots June 18 and May 19; there are eight dots (dates) remaining.

For it to have been IMPOSSIBLE for Bernard to know the date, Cheryl must definitely not have told him '18' or '19'. For Cheryl to have definitely not have said '18' or '19', she could only have told Albert 'August' or 'July'. This necessitates the removal of the remaining three dots associated with 'June' and 'May'. There are five dots left on the matrix.

At this step, even though we don't know which day Bernard was told, Bernard tells us that at this juncture he is CERTAIN of the Cheryl's birthday. So again, counting the number of dots in each column (because we are considering Bernard's perspective, not Albert's) we see that there are TWO possible months for the day '14', which indicates UNcertainty; so we remove those two dots in the '14' column. We don't know if Bernard was told '15', '16', 'or '17', but we know that since he is certain, there must be only one month associated with whatever day Bernard was told. Only days '15', '16', and '17' meet the 'certainty' criterion of having only one month associated with them. There are three dots remaining.

At the last step, there are only August 15, July 16, and August 17 remaining on the matrix. At this point, Albert says HE TOO is certain of Cheryl's bithday. In order for Albert to be certain, there must be only ONE dot associated with the month Cheryl told him. So counting the number of dots associated with each of the remaining months Albert could have been told, we see TWO dots in the 'August' row (August 15 and August 17), (indicating 'uncertainty' of the date); and only ONE dot in the 'July' row, (July 16), indicating his certainty. So Cheryl's birthday is indicated by the remaining dot - July 16. 71.139.161.36 (talk) 19:59, 2 May 2015 (UTC)


 * Yes, that's certainly a fine solution, and it's not very different from the in-words solution. Because there are two people and the projections (the partial information given to them at the beginning) naturally splits as two dimensions, it is possible to write it as a matrix. (A while ago I wrote a program to solve a few restricted problems of this type.) But of course it's essentially the same kind of puzzle even if it cannot be neatly put as a matrix, consider the one where five logicians walk into a coffee shop:

"Q: Do all of you want coffee? A: I don't know B: I don't know C: I don't know D: I don't know E: No"

This is a simple one where the answer (that A, B, C, D want coffee and E doesn't) is easy to determine, but you can imagine harder puzzles of this type. Shreevatsa (talk) 00:05, 3 May 2015 (UTC)

Thank you for looking my solution over. I wanted to make a framework that would allow arbitrarily large problems of this kind to be solvable by an algo or heuristic. 71.139.161.36 (talk) 06:45, 3 May 2015 (UTC)

Sequel
Correct my math if I'm wrong but there seems to be a minor mistake. The text says: There are only two possible sets of ages, (using different number sets, the important factor), that give the same sum: 9, 4, 4 and 8, 6, 3. As far as I was able to compute, there is one more possibility: 2, 8, 9 and 3, 4, 12. Their product is 144 while their sum is 19. Of course both of these sets get eliminated after Cheryl says her brothers are twins, but they appear to invalidate the aforementioned statement. — Preceding unsigned comment added by 212.112.100.223 (talk) 10:57, 24 May 2015 (UTC)
 * Verily, I didn't solve the problem in its entirety (that's what I get for thinking I've seen the problem before!). Fixing. Banedon (talk) 01:44, 25 May 2015 (UTC)
 * I removed the sets 16, 3, 3 and 36, 2, 2. The point is Bernard and Albert know the bus number. So if they know the product of the ages is 144 and the bus number is (say) 40, then they can also deduce the ages as 36, 2, 2. Since they weren't able to do this, there must be at least two sets of numbers that produce the same sum. That leads back to the main solution. Note 9, 4, 4 and 8, 6, 3 both sum to 17, and 2, 8, 9 and 3, 4, 12 both sum to 19. Banedon (talk) 01:16, 8 June 2015 (UTC)
 * 2,36,2 and 36,2,2 are possible ages and both sum to 40 (bus 40), which means that a bus number of 40 is ambiguous and cannot be discounted. This means that 36 as an age cannot be discounted. This leaves 36,2,2, and 144,1,1 and 9,4,4 as 3 possibilities, leaving both 36,2,2 and 9,4,4 as possibilities after removing 144,1,1 for age reasons. 162.157.242.139 (talk) 18:52, 6 November 2023 (UTC)
 * I'm wrong. The puzzle clearly says that she has younger brothers. 36,2,2 is thus removed because there is no other combo with bus number/sum of 40 that fulfills this requirement of the brothers being younger. 162.157.242.139 (talk) 19:01, 6 November 2023 (UTC)

Is this "sequel" genuine? Is there clear evidence that it was in any sense issued by the same organisation that produced the original "Cheryl's birthday"? As far as I can see the original was in the SG maths olympiad; the "sequel" was from some university. Unless there is a very clear link, I propose the "sequel" should be removed. After all, anyone (me, for example) could produce another logic problem involving A, B, and C, and claim it is a "sequel". Imaginatorium (talk) 18:20, 8 June 2015 (UTC)

Logical problem with every solution
As I see it, there is a huge logical problem with the way that the puzzle is worded that makes all solutions invalid. It is simply this: at no point are we told that Cheryl tells anyone, out loud, that she is going to whisper the month to Albert and the day to Bernard. We know it, but they don't. For all Albert knows, Cheryl was whispering the name of her cat to Bernard, and for all Bernard knows, she was whispering the name of her favorite movie to Albert. Therefore, once Albert said, "I don't know, but I know that Bernard doesn't either", logically, the only response Bernard could have made was, "I also don't know". — Preceding unsigned comment added by Roachmeister (talk • contribs) 06:30, 30 July 2017 (UTC)

Use of "sic"
The current version uses "sic" in places where the original text has grammatical errors. I cannot understand why it is necessary to propagate grammatical errors. The Wikipedia Manual of Style under Quotations writes "However, trivial spelling and typographic errors should simply be corrected without comment (for example, correct basicly to basically and harasssment to harassment), unless the slip is contextually important." Is this mistake contextually important? I think not.

Further, this use of "sic" appears to be drawing attention to the original author's grammar errors. While I doubt that it is intended, there is a risk that the reader may think the author is being ridiculed. It is better to avoid embarrassing the original author, fix the error and remove sic. Comfortably Paranoid (talk) 01:49, 2 September 2019 (UTC)


 * WP quotes the original question, because otherwise people will argue that the answer might be different. The original is written in Singaporean English with rough edges, so we "sic" the (standard English English) grammatical errors, to stop editors changing them. If you publish something which goes viral, you deserve embarrassment for any grammatical errors. Imaginatorium (talk) 02:56, 2 September 2019 (UTC)


 * Fixing the grammar error does not change the meaning of the question! The article is about an interesting logic problem, not about Singaporean English. I argue that it is actually not necessary to treat this as a quotation, just remove the quotes " " and state the problem in proper English.


 * Just to be clear, the best way forward is to remove sic and correct the error — that will also stop editors from changing them. Individuals have no control if their content goes viral, it is unfair to embarrass them. Comfortably Paranoid (talk) 04:13, 2 September 2019 (UTC)

MOS:SIC
From the relevant guideline:. Please explain how a simple and obviously insignificant typo is relevant to the mathematical content. Paradoctor (talk) 05:11, 11 February 2023 (UTC)

P.S.: Just noticed the previous section. That's not what Wikipedia is for. It's not our job punish people for their mistakes. Paradoctor (talk) 05:28, 11 February 2023 (UTC)


 * The guideline you quote says "spelling and typographic errors" which these are not; they are not typos, they are discrepancies between SingE and standard English. We are not here to ridicule, but claims of ridicule do not justify changing the quote. Imaginatorium (talk) 06:01, 11 February 2023 (UTC)


 * Of course not. And it is not the reason for my edit.
 * Then please cite an RS that supports this claim. Paradoctor (talk) 06:21, 11 February 2023 (UTC)

Ok, it's been two weeks since I WP:CHALLENGED your claim that this is not a grammatical error (which your edit claims!), but correct SingE, and that the quote is actually in that English variety, which is rather unlikely, given the formal context it comes from.

Can't have it both ways. It's either an error not relevant to the problem's content, which gets corrected, or it is grammatically correct SingE, which requires reliable evidence. Unless you provide the latter, or provide a third option, this is an insgnificant error, and I'll fix it accordingly.

FYI: Should you revert again without proper discussion/argument here, you'll be in violation of WP:EW, and I'll act accordingly. You've been here longer than I, so I hope I don't have to remind you of WP:CONSENSUS? Paradoctor (talk) 03:06, 28 February 2023 (UTC)