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Unfortunately, there are a number of rather curious, and culturally specific, assumptions one must make about the problem. The real puzzles are: 1. "Why did A

Unfortunately, there are a number of rather curious, and culturally specific, assumptions one must make about the problem. The real puzzles are: 1. "Why did Albert speak first?" 2. "Why did he speak in such cryptic language?"

anigbrowl 12y ago
These are actually valid questions and you shouldn't be downvoted. The standard interpretation of the problem is highly questionable; Albert's initial remark is not actually dispositive to Bernhard, because if Bernhard had the 19 May date he would know the correct answer immediately without needing Albert to say anything. The suggestion that Albert's first statement necessarily eliminates all dates in May is false, and the answer is indeterminable, as can be readily verified with a Venn diagram. It took me some time to spot the flaw in the problem construction; I initially found the official solution persuasive, but when you think more carefully about it you realize it's actually wholly illogical.
- kleer001 12y ago
  Along the lines of the "Bob uses cigarette butts to make new cigarettes. Bob needs 5 cigarette butts to make one new cig. If Bob starts with 25 butts how many cigs can he make?"
- logicallee 12y ago
  can you make your whole comment more explicit, I don't follow your objection.
  - andrewprock 12y ago
    Let's consider the question: 1. "Why did Albert speak first?" Before we answer this, we need to develop a set of assumptions to operate under. Given the synthetic nature of the problem, we might assume that both Albert and Bernard are of equal ability, and able to make logical inferences based on reasonable assumptions. We'll also assume that both Albert and Bernard are only going to announce the binary state of each others certainty of the answer. Lastly, we'll assume that whoever can deduce the binary state of certainty first, will speak first. These assumptions, while a bit presumptuous, seem on the surface to adhere to the spirit of the puzzle. Given those assumptions, what does it mean when Albert speaks first? It means that he's figured out the binary state of certainty before Bernard. How could that be? If Bernard has the dates 18 or 19, then he knows that he knows, and he also knows that Albert does not know. If Bernard has any other date, he'll know that they both don't know. How does Bernard make this determination? He checks if his date is repeated anywhere. Compare that to the logic that Albert must perform to rule out Bernard's certainty. He must check that all of the dates in his month are in fact repeated. If they both perform these mental operations at the same speed, then Bernard should speak first in the case where he knows a unique date. The only reason why Bernard might not speak first is that he must also reason through whether or not Albert might know the date at this point. If Bernard holds an unrepeated date, the complexity of reasoning through Alberts situation boils down to considering only one month. But if Bernard holds a repeated date, he must consider Albert's situation for two months. So, there exists a time past which Albert must know that Bernard is considering the more difficult situation, and thus he can infer that Bernard does not know. If one assumes precise knowledge of the timing of logical operations, one can make even stronger inferences. To the point of even solving the entire problem without anyone every saying anything, for specific birthdays. I will be the first to admit that this line of reasoning may require certain assumptions which are strained. Thus the question may still remain: 1. "Why did Albert speak first?" Does anyone have a different set of logical assumptions which leads to Albert speaking first? ---- What this exposes really, is the more subtle assumption that the "correct" solution makes: "There is only one way to make inferences in this puzzle." The truth of that statement depends very much on the assumptions one makes about the puzzle. Most problematic is that most assumptions which makes that true, make it impossible for Albert to be the first speaker. It's a kind of logical paradox brought on by the fact that synthetic logic problems do not map very well to real world situations.
    - logicallee 12y ago
      Albert speaks first because he's Albert! They're obviously just going alphabetically. Maybe my other comment was right and they should have been called Alice, Bob, and Carol. The way I read the question, it's as though a moderator said: "Albert, tell me what's on your mind." "Bernard?" "Albert?" I will add that #4 should certainly be in the past tense ("at first I didn't know") because this way Albert and Bernard are in on the fact that they're part of a logical puzzle!! They should not know that they are characters in a puzzle. This is how I read the puzzle: Moderator to Albert: tell the reader what you know. Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too. Moderator to Bernard: And you, Bernard? Bernard: At first in this puzzle I don't know when Cheryl's birthday is (before Albert spoke), but now that you have asked Albert, and I've heard his response, I've figured it out. Moderator to Albert: And any thoughts from you, now that Bernard has figured it out? Albert: Yes. Given the information Bernard has now stated, I would say I also know Cheryl's birthday now.
      - andrewprock 12y ago
        I believe assuming they are "just going alphabetically" and/or that there is some sort of implicit moderator managing the conversation qualify as non-obvious assumptions.
        Nursie 12y ago
        Assume nothing, simply take what's stated. This happened and then this and then this. If you can't piece everything together then... well you're not suited to logical analysis.
        andrewprock 12y ago
        On the contrary, logical analysis is generally not well suited to the understanding of human behavior.
        Nursie 12y ago
  - deleted 12y ago
    [deleted]
- stephen_g 12y ago
  Your objection doesn't make sense. The fact that Albert can make the statement relies on the fact that he was given a month that rules out Bernard being given a unique date, such as the 19th, otherwise Albert would have to say, "I don't know when the birthday is but perhaps Bernard does" and the problem would be different. Albert knows the month, and his statement, which translates directly to "given the month I know, it is not possible for Albert to independently determine the date" certainly does rule out the two months.
- thuffy 12y ago
  Solved this without even a pencil and paper, just in my head, in under 60 seconds while being distracted by another person in the room asking me what to have for breakfast. There is only one possible answer as the others pointed out; you are definitely wrong that the answer is indeterminable. The whole ruckus surrounding this problem seems to be more a reflection of the sad state of the intelligence in our population, rather than anything to do with Asia.
- Nursie 12y ago
  If we take silence as indicative of lack of knowledge, then nobody needs to speak. Bernard: Silence (he doesn't know the answer) Albert: Silence (he doesn't either) Bernard: I know it! Interestingly it then becomes relevant who was silent first. Basically it's nonsense.
  - sukilot 12y ago
    If you assume Albert and Bernard are identical computers running identical programs, then it isn't nonsense. And that's not just a gimmick , timing analysis is how some side-channel attacks work in crypto.
    - anigbrowl 12y ago
      Thank you.
    - Nursie 12y ago
      Of course it's nonsense. If we can deduce the answer from silence then there's no need for any of the information given in the question, it's not a logic puzzle it's bullshit. I don't assume Albert and Bernard are anything, if you've made assumptions beyond what's stated in the question then you've done it wrong. And yes, I understand timing oracles.
  - deleted 12y ago
    [deleted]
stephen_g 12y ago
Maybe I'm missing something, but we know exactly what Bernard would have said first from statement 2. He says, "At first I didn't know", so all he could have said if he had spoken first would have been "I don't know when the birthday is". Then Albert would have said, "I don't know when the birthday is, and I knew that Bernard couldn't have". So the problem is unchanged regardless of who speaks first. It also doesn't seem that cryptic to me... It doesn't take that much reading between the lines to understand the statement "at first I didn't know, but I know now" to mean "the information that Albert just provided gives me enough information to determine the birthday"...
- andrewprock 12y ago
  IIRC, if Bernard speaks first, then the correct answer is August 17.
  - stephen_g 12y ago
    That doesn't make any sense to me. Can you post exactly the sequence of statements if Bernard speaks first? Simply reordering the questions does not make sense, so I can't see it happening any way other than what I posted, which shows that it wouldn't change anything.
    - andrewprock 12y ago
      It really depends on who says what, but here a version of the problem where Bernard speaks first: Bernard: I don't know when Cheryl's birthday is. Albert: I don't know when Cheryl's birthday is. Bernard: I know when Cheryl's birthday is now. Albert: Then I also know when Cheryl's birthday is.
      - stephen_g 12y ago
        That breaks the whole problem because you've removed the part where Albert says something that gives Bernard the information he needs to work out the date. I don't think it's really a good critique of a logic problem to say, "but if you remove this extremely important part, it doesn't work anymore"! The conversation would need to be: Bernard: I don't know when Cheryl's birthday is Albert: I don't know when Cheryl's birthday is, and I knew that Bernard didn't know. Bernard: Then I know when Cheryl's birthday is now. Albert: Then I also know when Cheryl's birthday is. Then it works. You only have to assume that the parties are logical and tell the truth.

anigbrowl 12y ago

These are actually valid questions and you shouldn't be downvoted. The standard interpretation of the problem is highly questionable; Albert's initial remark is not actually dispositive to Bernhard, because if Bernhard had the 19 May date he would know the correct answer immediately without needing Albert to say anything. The suggestion that Albert's first statement necessarily eliminates all dates in May is false, and the answer is indeterminable, as can be readily verified with a Venn diagram. It took me some time to spot the flaw in the problem construction; I initially found the official solution persuasive, but when you think more carefully about it you realize it's actually wholly illogical.

kleer001 12y ago
Along the lines of the "Bob uses cigarette butts to make new cigarettes. Bob needs 5 cigarette butts to make one new cig. If Bob starts with 25 butts how many cigs can he make?"
logicallee 12y ago
can you make your whole comment more explicit, I don't follow your objection.
- andrewprock 12y ago
  Let's consider the question: 1. "Why did Albert speak first?" Before we answer this, we need to develop a set of assumptions to operate under. Given the synthetic nature of the problem, we might assume that both Albert and Bernard are of equal ability, and able to make logical inferences based on reasonable assumptions. We'll also assume that both Albert and Bernard are only going to announce the binary state of each others certainty of the answer. Lastly, we'll assume that whoever can deduce the binary state of certainty first, will speak first. These assumptions, while a bit presumptuous, seem on the surface to adhere to the spirit of the puzzle. Given those assumptions, what does it mean when Albert speaks first? It means that he's figured out the binary state of certainty before Bernard. How could that be? If Bernard has the dates 18 or 19, then he knows that he knows, and he also knows that Albert does not know. If Bernard has any other date, he'll know that they both don't know. How does Bernard make this determination? He checks if his date is repeated anywhere. Compare that to the logic that Albert must perform to rule out Bernard's certainty. He must check that all of the dates in his month are in fact repeated. If they both perform these mental operations at the same speed, then Bernard should speak first in the case where he knows a unique date. The only reason why Bernard might not speak first is that he must also reason through whether or not Albert might know the date at this point. If Bernard holds an unrepeated date, the complexity of reasoning through Alberts situation boils down to considering only one month. But if Bernard holds a repeated date, he must consider Albert's situation for two months. So, there exists a time past which Albert must know that Bernard is considering the more difficult situation, and thus he can infer that Bernard does not know. If one assumes precise knowledge of the timing of logical operations, one can make even stronger inferences. To the point of even solving the entire problem without anyone every saying anything, for specific birthdays. I will be the first to admit that this line of reasoning may require certain assumptions which are strained. Thus the question may still remain: 1. "Why did Albert speak first?" Does anyone have a different set of logical assumptions which leads to Albert speaking first? ---- What this exposes really, is the more subtle assumption that the "correct" solution makes: "There is only one way to make inferences in this puzzle." The truth of that statement depends very much on the assumptions one makes about the puzzle. Most problematic is that most assumptions which makes that true, make it impossible for Albert to be the first speaker. It's a kind of logical paradox brought on by the fact that synthetic logic problems do not map very well to real world situations.
  - logicallee 12y ago
    Albert speaks first because he's Albert! They're obviously just going alphabetically. Maybe my other comment was right and they should have been called Alice, Bob, and Carol. The way I read the question, it's as though a moderator said: "Albert, tell me what's on your mind." "Bernard?" "Albert?" I will add that #4 should certainly be in the past tense ("at first I didn't know") because this way Albert and Bernard are in on the fact that they're part of a logical puzzle!! They should not know that they are characters in a puzzle. This is how I read the puzzle: Moderator to Albert: tell the reader what you know. Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too. Moderator to Bernard: And you, Bernard? Bernard: At first in this puzzle I don't know when Cheryl's birthday is (before Albert spoke), but now that you have asked Albert, and I've heard his response, I've figured it out. Moderator to Albert: And any thoughts from you, now that Bernard has figured it out? Albert: Yes. Given the information Bernard has now stated, I would say I also know Cheryl's birthday now.
    - andrewprock 12y ago
      I believe assuming they are "just going alphabetically" and/or that there is some sort of implicit moderator managing the conversation qualify as non-obvious assumptions.
      - Nursie 12y ago
        Assume nothing, simply take what's stated. This happened and then this and then this. If you can't piece everything together then... well you're not suited to logical analysis.
        andrewprock 12y ago
        On the contrary, logical analysis is generally not well suited to the understanding of human behavior.
        Nursie 12y ago
- deleted 12y ago
  [deleted]
stephen_g 12y ago
Your objection doesn't make sense. The fact that Albert can make the statement relies on the fact that he was given a month that rules out Bernard being given a unique date, such as the 19th, otherwise Albert would have to say, "I don't know when the birthday is but perhaps Bernard does" and the problem would be different. Albert knows the month, and his statement, which translates directly to "given the month I know, it is not possible for Albert to independently determine the date" certainly does rule out the two months.
thuffy 12y ago
Solved this without even a pencil and paper, just in my head, in under 60 seconds while being distracted by another person in the room asking me what to have for breakfast. There is only one possible answer as the others pointed out; you are definitely wrong that the answer is indeterminable. The whole ruckus surrounding this problem seems to be more a reflection of the sad state of the intelligence in our population, rather than anything to do with Asia.
Nursie 12y ago
If we take silence as indicative of lack of knowledge, then nobody needs to speak. Bernard: Silence (he doesn't know the answer) Albert: Silence (he doesn't either) Bernard: I know it! Interestingly it then becomes relevant who was silent first. Basically it's nonsense.
- sukilot 12y ago
  If you assume Albert and Bernard are identical computers running identical programs, then it isn't nonsense. And that's not just a gimmick , timing analysis is how some side-channel attacks work in crypto.
  - anigbrowl 12y ago
    Thank you.
  - Nursie 12y ago
    Of course it's nonsense. If we can deduce the answer from silence then there's no need for any of the information given in the question, it's not a logic puzzle it's bullshit. I don't assume Albert and Bernard are anything, if you've made assumptions beyond what's stated in the question then you've done it wrong. And yes, I understand timing oracles.
- deleted 12y ago
  [deleted]

stephen_g 12y ago

Maybe I'm missing something, but we know exactly what Bernard would have said first from statement 2. He says, "At first I didn't know", so all he could have said if he had spoken first would have been "I don't know when the birthday is". Then Albert would have said, "I don't know when the birthday is, and I knew that Bernard couldn't have". So the problem is unchanged regardless of who speaks first. It also doesn't seem that cryptic to me... It doesn't take that much reading between the lines to understand the statement "at first I didn't know, but I know now" to mean "the information that Albert just provided gives me enough information to determine the birthday"...

andrewprock 12y ago
IIRC, if Bernard speaks first, then the correct answer is August 17.
- stephen_g 12y ago
  That doesn't make any sense to me. Can you post exactly the sequence of statements if Bernard speaks first? Simply reordering the questions does not make sense, so I can't see it happening any way other than what I posted, which shows that it wouldn't change anything.
  - andrewprock 12y ago
    It really depends on who says what, but here a version of the problem where Bernard speaks first: Bernard: I don't know when Cheryl's birthday is. Albert: I don't know when Cheryl's birthday is. Bernard: I know when Cheryl's birthday is now. Albert: Then I also know when Cheryl's birthday is.
    - stephen_g 12y ago
      That breaks the whole problem because you've removed the part where Albert says something that gives Bernard the information he needs to work out the date. I don't think it's really a good critique of a logic problem to say, "but if you remove this extremely important part, it doesn't work anymore"! The conversation would need to be: Bernard: I don't know when Cheryl's birthday is Albert: I don't know when Cheryl's birthday is, and I knew that Bernard didn't know. Bernard: Then I know when Cheryl's birthday is now. Albert: Then I also know when Cheryl's birthday is. Then it works. You only have to assume that the parties are logical and tell the truth.