No one is asking the obvious question: Why wouldn’t Albert and Bernard at this point immediately choose to not remain friends with Cheryl? Seriously. Cheryl is being ridiculous. If she’s going to be this difficult having just begun the friendship, she’s only going to get worse as time goes one.
Albert and Bernard should have just turned and walked away.
The framework for the word puzzle is that Albert knows that Bernard knows month, and Bernard knows that Albert knows the day, and they both know all the available month/date combination. If you are challenging those assumptions then there’s no point in bothering with the logic puzzle.
Ah - but logic can help us with this as well. Clearly - if Albert and Bernard are putting up with her, Cheryl is crazy hot.
She knows where to find the best weed.
Because Albert and Bernard realize she knows they like logic puzzles and is making a cool puzzle for them. People who don’t like logic puzzles wouldn’t have been able to figure it out.
Normally I would recast a sentence like that, but I think it fits with how you have to parse logic tables.
This is apparently the OP’s hang-up. You have to accept this fact to be able to solve the puzzle.
Then solve this problem - logically - and prove each assumption at each stage. If you can’t, perhaps don’t comment?
The logic follows correctly
In order for Albert to know that Bernard does not know is for the date to be a repeating date, it can not be a unique date or Bernard would know.
So we know by Albert’s statement that any month with a unique date is out., this leaves May June as candidates.
From that statement Bernard now can deduce that it must be either July or August and he knows the date.
From Bernard’s statement he says he now knows both. This means his number is not repeated in July or August. Which rules out July 14 and Aug 14th. So the day, now known must be a non repeating date of the remaining dates: July 16, August 15, August 17
Now Albert’s statement is he now knows, the only way that can be is if he was given the birth-month of July, as if he were told August as her birth month he still would not know.
It’s been done, above. You’re fighting the setup of the logic puzzle and there’s really no point. If you don’t accept what I wrote above then the puzzle makes no sense. What are you looking to get from this thread?
jezzaOZ, I’m not quite sure where your objection is, so let’s take this step by step. First, the premises, because the way the problem is stated, we might be making different assumptions:
Both A and B know the list of different dates and they know that they both know this.
A knows the correct month, and B knows the correct day number, and they each know which fact the other person knows.
Do you agree with this setup for the logic puzzle?
There’s also an implicit assumption that A and B each know that the other will make correct and logical deductions about the information available.
Let’s disregard the three statements for the time being, and hypothetically suppose that the month given to A was “August.” Looking at the list of dates, he would notice that the dates within August are the 14th, the 15th, and the 17th, and that for each of those numbers, there’s a possible date that falls within another month. From this, he can conclude that if B doesn’t have any further information that A doesn’t know he knows, then B doesn’t know the birthday yet.
Would you agree that this is a logical conclusion to my hypothetical at this point? If not, can you point out where my logic seems insufficient to you or where I’m depending on knowledge that should be unavailable?
I am not surprised at this response from the Dope. Not at all.
I am surprised it took 20 replies to show up, however. The fact it was posted at 1:30 AM EDT notwithstanding.
I’m pointing out that the logic deductions in the standard ‘proof’ do not follow. If you can make a well argued solution, well and good, but you haven’t done one so far.
I fully understand the initial conditions and state of knowledge of the parties. What I don’t accept is the logical leaps involved to get one of many proffered solutions. I state the problem is insoluble and ask that you come up with a well reasoned argument to prove otherwise.
This is where you’re going wrong. When Albert says what he says, this gives Bernard the information that it’s not one of the unique day numbers.
Huh? It’s pretty clearly explained in the second post, under the spoiler. But let me try.
First, though, you have to work through this puzzle two different ways. The first, easier way, is after seeing the answer, work through everyone’s thought process. The second is figuring out the single answer that would lead to that sequence of events, and is a bit trickier, but can be done by process of elimination if necessary.
Albert is told “July”. He therefore knows that Bernard was told “14” or “16”. Both dates appear in multiple months, so he now knows that Bernard can’t have a unique solution given only the day, and he says so. If he’d been told “May”, he could not have made this assertion, because Bernard might have been told “19”, which is sufficient for Bernard to know the full date.
Bernard is told “16”. He therefore knows that Albert was told “May” or “July”. When he hears Albert’s bit of information, he learns that Albert was told a month where every date appeared in multiple months, so it couldn’t have been May. Only July remains.
The second approach (figuring out that July 16 is the unique solution that would work in the process above) is left to the reader as an exercise.
I certainly agree with your initial conditions. What I don’t agree with is that you can discard months with unique dates. You have to remember that the first statement is made on purely public knowledge. A can only know that B has a number of dates and B has no information about what A knows. When A makes their pronoucement all B can learn is that A thinks he has no idea - not that A thinks that only months with multiple dates should be considered. B still has multiple months with single dates he can choose from.
As far as B is concerned he has months with multiple dates, and an aggregate ‘month’ (made up from single date months) that also has multiple dates.
His dataset has not been reduced by the A statement and so any statement he makes is still based on the public conditions.
The logic proof works sorry you can’t see it.
I don’t think this is true, at least not if you accept the conditions that A and B are both working logically to solve the problem and stating true conclusions.
To start with, B knows that A might have been given any of four months. Each of those is a possible hypothesis that would lead to different conclusions.
Hypothesis: A was given “June”
Thus, it’s possible that the birthday is June 18th
But if B was given “18”, then he would know the birthday by simple process of elimination, and A would not have been able to truthfully make his first pronouncement.
Thus, this hypothesis is eliminated by the first pronouncement.
It seems to me like you might not be familiar with this sort of logic, of supposing hypotheses and evaluating their consequences. If so, I can understand why you’re having some trouble. Does this help you understand where I’m coming from at all?
Yeah, I’m confused to as to where the hang-up is.
Let’s see if recasting it in terms of playing cards, with two additional suits (square and circle) helps to visualize this easier, as dates can be a bit hard to visualize.
Cheryl deals out the following cards on the table:
A♦ A♣ A•
K♠ K■
Q♥ Q♣
J♥ J♦ J♠
Cheryl tells Albert and Bernard that she is thinking of one of the cards on the table. She tells Albert the rank and Bernard the suit.
So, let’s follow the conversation:
Albert: I don’t know what Cheryl’s card is, but I know that Bernard does not know too.
The only way Albert can say this truthfully at this stage is if the card is not an Ace or a King. There are two possible cards where Bernard knows both the rank and suit of Cheryl’s card if Bernard is only told the suit: the Ace of Circles and the King of Squares. So, if Albert knows for certain that Bernard cannot know the card, Cheryl could not have told Albert the rank is Ace or King, so that eliminates all those possibilities.
So now, we’re down to only queens and jacks.
Bernard: At first I didn’t know Cheryl’s card, but now I know.
If he’s been told a heart, then he can’t say this. He’s still deciding between queen and jack of hearts. He doesn’t know.
If he’s been told a club, he could say this, as Alberts first statement eliminated Aces and Kings, and the Queen of Clubs is the only club left.
If he’s been told a diamond, he could say this, too, as Aces and Kings are eliminated, and the Jack of Diamonds is the only diamond left.
If he’s been told spade, he could say this, too, as Aces and Kings are eliminated, and the Jack of Spades is the only spade left.
So, now we’re down to three cards: Queen of Clubs, Jack of Diamonds, Jack of Spades.
A: Then I know Cheryl’s card, too.
If Albert was told a jack, then he still has to decide between Jack of Diamonds and Jack of Spades. He doesn’t have enough information. The only way he could say this with certainty is if he’s holding the Queen of Clubs.
Therefore, only the Queen of Clubs can satisfy these three statements truthfully and logically.
Moreover, Albert knows that Bernard has been told the suit, and (obviously) that he, Albert, has been told the rank. Albert knows that Bernard also knows that Albert has been told the rank, but not the suit.
Also, Bernard knows that Albert has been told the rank but not the suit, and he knows that Albert is aware that he, Bernard, knows the suit but not the rank.
I feel it is these facts which are confusing the OP.
Well explained, but I have to ask why didn’t you stick with four suits and six ranks? Such as ace, king, queen, jack, ten, and nine… 
:smack: Because I like to complicate things. :smack:
(It’s just the way I immediately visualized it for some reason.)