[anigbrowl]

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.

[stephen_g]

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]

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.

[kleer001]

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?"

[Nursie]

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]

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.

[Nursie]

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.

[anigbrowl]

Thank you.

[logicallee]

can you make your whole comment more explicit, I don't follow your objection.

[andrewprock]

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.

[stephen_g]

> Lastly, we'll assume that whoever can deduce the binary state of certainty first, will speak first.

The speed at which they come to their conclusions, and who speaks first is meaningless. I think perhaps if you are taking them into account then you are trying to come up with a completely different problem, or intentionally being disingenuous.

Given the context (that this is a question on a high school test), it is safe to assume that Albert and Bernard are only drawing logical conclusions from the information Cheryl provides and what each other say.

Given that the problem works with no problems under these assumptions, and that there is enough information to re-word it with Bernard speaking first that does not change the answer, it seems pointless to try and look for timing attacks or other outlandish ways to change the answer...

[andrewprock]

"The speed at which they come to their conclusions, and who speaks first is meaningless."

That's your own assumption. And that's a perfectly fine assumption to make, but not a universally chosen one.

[logicallee]

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]

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]

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.

[anigbrowl]

The vociferous objections on this sub-thread are rather amusing. It seems several people missed the bit where I said I was OK with the official solution at first, but kept being bothered about the problem construction. I doubt Andrew has any problem articulating the default 'correct' solution either. I was thinking about the problem construction anyway because I was annoyed that the problem as stated in Singapore includes several glaring errors of English grammar which were an annoying distraction, eg' I know that Bernhard does not know too' rather than '...does not know either.' English is an official language in Singapore so I was surprised that such obvious errors would be allowed to creep into a logic problem; it's akin to muddying up a mathematical equation with '-(-x)'.

That started me thinking outside the confines of the problem and about the implicit assumptions that were in the problem statement itself. The 'inability to piece everything together' is entirely imaginary on your part.

[andrewprock]

On the contrary, logical analysis is generally not well suited to the understanding of human behavior.

[Nursie]

>> Let's consider the question: 1. "Why did Albert speak first?"

If you're even thinking about this then you have failed the question, it's a puzzle that asks you to derive a correct answer from the data provided, not from your conjectures about human behaviour.