Do this maths. It R Hard.
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use BBCode style, [ spoiler ] [ / spoiler ] it will work in the preview if it's working
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Mine is more long winded...
Spoiler don't work.
Spoiler only works if you have no empty lines. It's stupid:
[spoiler]
thiswont work [/spoiler]
[spoiler]
this will
work [/spoiler]
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Wow, cheryl really was a bitch.... blakeyrat is right, she had better be hot.
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you're forgetting to rule out some dates due to things you wrote in the first step.
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that first step is flawed. You correctly ruled out some dates, but you ruled them out for the wrong reasons, and missed other invalid dates as a result, this made you think that some dates were valid when they weren't, and led to faulty reasoning later on.
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Alright *rolls up sleeves*
Bernard not knowing the day implies it's not the May 19 or June 18. Both A & B could have thought of this.
Since A now knows the month and has discarded June 18, it can't be June 17 either. This is the only detail A knew that B didn't, so it is also the only new information that B got from A: "month not June".
So if B now knows the date, it must be August 17. And if I know that, so does A.
Did I get it right?
*Proceeds to read other comments*
Edit: @powerlord did the same thinking.
Edit2: and so did @CoyneTheDup.This solution assumes that A has a way of knowing B doesn't know the answer before the dialog starts, which is what makes it wrong.
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Yes, I finally figured that out. Of course I didn't discover it until I'd pasted it in from Notepad (where I wrote it originally). If blank lines are needed, must use "br" tags.
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Bernard not knowing the day implies it's not the May 19 or June 18. Both A & B could have thought of this.
It implies a bit more than that. A knows that B can't know, meaning the month must not have any unique dates. This discards both May and June right away.
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In a vacuum it implies what @Zecc said. As you say, it's the fact that A knows from the information he has been given that B cannot know that allows you to exclude the additional dates.
Without excluding all of those dates at once, you build a seemingly valid answer on a flawed foundation that ends up excluding the correct answer.
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It implies a bit more than that. A knows that B can't know, meaning the month must not have any unique dates. This discards both May and June right away.
Huh? B only knows the day."14" could be either Jul or Aug; "15" May/Aug; "16" May/Jun; "17" Jun/Aug.
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that first step is flawed. You correctly ruled out some dates, but you ruled them out for the wrong reasons, and missed other invalid dates as a result, this made you think that some dates were valid when they weren't, and led to faulty reasoning later on.
I'm not sure I'm buying that, if you're thinking of June. Albert wouldn't be able to rule that month out because he doesn't know whether or not Bernard was told the 17th. He only can infer Bernard was told neither the 18th nor 19th.
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A knows that B can't know, based on his knowledge of the month. If the month was May or June, A couldn't say whether B could know the date.
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But if Bernard knew 18 or 19, he'd know the month. So the fact that Albert knows he doesn't know means Albert knows he can't have been told 18 or 19, which means Albert wasn't told May or June (both of which contain a potentially unambiguous date for Bernard to know).
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He doesn't need to infer anything about the month. Albert knows the month. Albert's statement informs Bernard [spoiler]that neither May nor June are the correct month.[/spoiler]
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If the month was May or June, A couldn't say whether B could know the date.
Ok, imagine A was told the month is May.A knows it's either 15, 16 or 19. But he only knows it can't be the 19th because that's the only unique day across all months.
A may hypothesize B was told 15, but — even if this hypothesis is correct and B was in fact told 15 — because B doesn't know the month as far as he is concerned it can still be May 15 or Aug 15 .
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18 is unique too
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Scenario 1: The date is May 18. Albert is told May, Bernard is told 18. Bernard now knows the entire date.
Scenario 2: The date is May 15. Albert is told May, Bernard is told 15. Bernard does NOT know the entire date.How can Albert distinguish between scenario 1 and scenario 2? He cannot, because all he knows is "May".
If he can distinguish, he was not told May. Albert says he knows for sure that Bernard does not know the entire date, meaning it's a scenario 2 situation, meaning he can distinguish.
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...so?
Scenario 1: The date is May 18. Albert is told May, Bernard is told 18. Bernard now knows the entire date.
Scenario 2: The date is May 15. Albert is told May, Bernard is told 15. Bernard does NOT know the entire date.How can Albert distinguish between scenario 1 and scenario 2? He cannot, because all he knows is "May".
If he can distinguish, he was not told May.
once you accept this, do the same for june
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Albert knows the month, but not the day. Since he knows that Bernard cannot know the month, we can conclude that [spoiler]the month does not contain any unique days. That rules out May and June.[/spoiler]
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Bernard knows the day, and since Albert just fed him step one, he now knows the month. That means it is [spoiler]either July or August, but not a day which is shared between the two. That rules out the 14th.[/spoiler]
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This is where I lost the trail for a bit. Albert _still _ knows what month it is, and Bernard just told him [spoiler]that it wasn't the 14th. Since Albert announces that he knows when the date is, it can only be July. If it were August, he still wouldn't know if it was the 15th or 17th.[/spoiler]
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So, [spoiler]July 16th[/spoiler]. And I hope that Albert, Bernard and Cheryl never find themselves in any kind of real trouble which requires effective communication skills.
"Help! I am faced with a problem but I can only tell you that it starts with the letter F! There is a fire hose, a large bucket full of whole oats, a stepladder, a large block of ice and decorative glass pipe in the hallway, but you can only bring one of them into the room!"
"Don't worry, I will save you! All I need to do is know whether the combined weight of three of the items is equal to, greater than or less than the other two, and if there are any two items which cannot be left alone together!"
"It's too late, Albert. The pack of angry ferrets already got her."
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Hmm... I think I need to put some for thought into this.
Took me some re-reading to interpret what you wrote (not your fault).
I also haven't finished reading the posts people made before I joined the thread.
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Yes, I figured that out while I was away for a moment. The problem is that my story is incorrectly written; it combines third person and first person in a confusing way.
The logic is that of a third-party observer, who sees the list and hears what Albert and Bernard has to say; and from that infers Albert and Bernard's reasoning. But the writing is told from point of view of Albert and Bernard, which is confusing.
How about this:
[spoiler]The observer sees the list and is told that Cheryl told the month to Albert and the day to Bernard. The observer knows neither.
The observer then hears Albert state that neither he nor Bernard know the birthday. This means that the day cannot be the 18th or 19th, because if it were, Albert would know that Bernard knows the date. Upon reflection, the observer also realizes that the month cannot be June; for Albert knows that it is neitehr the 18th or 19th and the only remaining day in June is the 17th, and if Albert had been told June, he would have reasoned the birthday. But Albert can't do that, because he was told some month other than June.
The observer now hears Bernard state that he knows the birthday. Bernard knows the day he was told, but the observer does not know what that is, though he knows it cannot have been the 18th or 19th, from Albert's statement. But since Bernard stated he knows the date, he must have been able to rule out all but one month, which he does not know.
The observer realizes that Bernard can't have been told the 14th, for that could involve July or August; Bernard would not have been able to rule either month out. Same thing for the 15th (May and August) and the 16th (May and July). But the observer already knows the month was not June, for if Albert had been told June, Albert would have known it was June 17th (Albert having known that June 18th is impossible). So if Bernard was told the 17th, the observer realizes that Bernard would have known it was August, June having been ruled out by inference.
So the observer infers that only the 17th would have allowed Bernard to know the month, because of his prior inference that the month could not have been June. So the observer knows the birthday must be August 17.[/spoiler]
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once you accept this, do the same for june
Already, I have accepted.
I was assuming A knew that B didn't know the answer because if he did he would have answered already. A stupid assumption, I know.
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Without checking down, because you asshats probably spoiled it already: [spoiler]July 16.[/spoiler]
[spoiler]Albert has a month. He knows Bernard doesn't know, so it can be neither May (because if Bernard got "15", he'd know) nor June ("18"). Bernard is by now limited to July and August, and he knows which one it is, so it can't be "14" - it can either be Aug 15, Jul 16, or Aug 17. But if it was August, Albert wouldn't be able to figure out the day in the last step - so the only answer left is
JuneJuly - obviously, and we ruled out the 14th.[/spoiler]
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[spoiler]The observer then hears Albert state that neither he nor Bernard know the birthday. This means that the day cannot be the 18th or 19th, because if it were, Albert would know that Bernard knows the date. Upon reflection, the observer also realizes that the month cannot be June; for Albert knows that it is neitehr the 18th or 19th and the only remaining day in June is the 17th, and if Albert had been told June, he would have reasoned the birthday. But Albert can't do that, because he was told some month other than June.[/spoiler]
This is still incomplete.
[spoiler]The observer hears Albert, who knows only the month, state that neither he nor Bernard knows the full date. The only way this statement can be valid is if the month Albert has been told does not contain any unique days. If Albert is told May, he cannot make this statement as Bernard could have been told the 19th. If Albert is told June, he cannot make this statement because Bernard could have been told the 18th. Both of these facts mean that neither May or June can be the month that Albert was told.[/spoiler]
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This post is deleted!
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Guess what, I was right, my explanation is flawless, and you guys are still arguing the thing.
Filed under: bow down to my superiority
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What if Cheryl reveals to Albert one day that isn't the right day? Or if her brother was born on Tuesday?
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Guess what, I was right, my explanation is flawless, and you guys are still arguing the thing.
No, I think you'll find that if you check again emacs is clearly superior to vi.
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What if Cheryl reveals to Albert one day that isn't the right day? Or if her brother was born on Tuesday?
What if Cheryl's parents reveal to her that she was adopted after being found in a dumpster?
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Alright I've seen the light and I'm ready to accept the answer which was first put up by @Yamikuronue and @algorythmics and confirmed by @darkmatter. (hope I didn't get those names wrong)
@DCRoss' post made it really clear for me.
This means that the day cannot be the 18th or 19th, because if it were, Albert would know that Bernard knows the date.
You did the same mistake I did. You assumed Albert was informed whether Bernard knows or not through external means. But this is not a given. It is strongly implied, but not given.
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You assumed Albert knows whether Bernard knows or not.
Albert: [...] I know that Bernard does not know too
Post can't be empty
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Amended.
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I think @aliceif nailed it too, with a spreadsheet to boot.
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If Albert is told May, he cannot make this statement as Bernard could have been told the 19th.
You're correct. This was a logic error on my part: p and q does not imply not p and not q. Albert knows that if Bernard was told the 18th or 19th, he would know the date. But the only way Albert could know for sure that Bernard was told neither of these dates is if he was told July or August.
Edit: But that leaves us with a conundrum. Obviously, Bernard was told one of the 15th, 16th or 17th, that's why he can say he now knows the date. But how does Albert know which is which? Oh, duh, he was told the month. But the third party observer actually cannot know, correct?
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But the third party observer actually cannot know, correct?
That was where I had a problem. But you CAN know as the 3rd party observer because of Albert's last statement. Albert tells you he knows. So now you also know because it has to be just 1 date for Albert to know.
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Okay, I have it now. Whew.
[spoiler]Albert ruled out May and June, but he wasn't able to rule out July or August because he doesn't know if it is the 14th, 15th, 16th or 17th. Bernard had not known the month until Albert ruled out May and June, but now he does. But if he had been told the 14th, he would still be lost, since he would not know if it was July or August. But he says he now knows the date, so his date was either July 16, August 15, or August 17. But he says he knows the date, which tells Albert that the date is not the 14th, since he knows Bernard would not have been able to rule out either month, if it were the 14th. But Albert had been told the one month, either July or August. If he had been told August, he would be lost, because he wouldn't know if it was the 15th or 17th. So the amazing, superhuman, extraordinary, astute observer (i.e., not me) knows that, if Albert was able to identify the date, then the month must be July and the day 16.[/spoiler]
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You know this problem is just 2-SAT right? Hint: there are algorithms to check for satisfiability.
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Without reading the thread:
[spoiler]
- Albert knows the month, Bernard knows the day.
- Albert knows Bernard does not know. So the month is one for which all days also occur in another month. This disqualifies May (19th) and June (18th)
- Bernard now knows. This disqualifies the 14th (because it appears in both those months)
- Albert now knows. This disqualifies August, as there are still 2 potential days for august.
Hence Cheryl's birthday is July 16th.
[/spoiler]
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Hint: there are algorithms to check for satisfiability
Post to the internet and wait for a consensus?
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Better:
- recognize that it's 2-sat.
- visit http://en.wikipedia.org/wiki/2-satisfiability#Algorithms
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Why didn't they just use Alice and Bob (and Charlie)?
Because they weren't talking in code.
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Albert knows the month
If Albert says neither can know, then it can't be 18th or 19th, because if it was, then he would know Bernard knows.If it were in May or June, he wouldn't be able to say Bernard doesn't know, because Bernard could have heard 18 or 19 and would then know.
So it must be July 14th, July 16th, August 14, 15 17.
Now, Bernard knows this information and his choices are limited to these.
We can eliminate 14th because they now have 2 months, because Bernard would still not know.
But there isn't enough information for us to decide, it could be 15th, 16th, or 17th, because each of these now has one month.
The problem people are having at this point, is knowing because Bernard knows. But we don't have to know right now. We just have to know that Benard knows.
So at this point It does not matter whether it is August 15th, July 16th, or August 17th. Just that it is one of them.
So, pass the ball back to Albert.
Albert now claims he knows.
Ok, so, if he knows Bernard knows, he now knows it is one of those three dates, but he also knows the month.
If he heard it was August, he wouldn't know.
If he heard it was July, he would now know it is July 16th.
But, in reality, none of these jokers would be able to figure out whether the other knew, because they'd have a high probability of making the same mistakes we have made.
Attached image of
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Actually it can be done with simple rules.
- As row-owner knows, eliminate rows with more than 1 option.
- As column-owner knows, eliminate columns with more than 1 option.
- If row-owner still doesn't know, eliminate rows with 1 option.
- If column-owner still doesn't know, eliminate columns with 1 option.
- If column-owner knows that row-owner doesn't know, eliminate columns and rows where rows have only one option.
- If row-owner knows that column-owner doesn't know, eliminate columns and rows where columns have only one option.
- If column-owner knows that the row-owner knows, eliminate rows with more than 1 option.
- If the row-owner knows that the column-owner knows, eliminate columns with more than 1 option.
following the rules.
- Albert doesn't know, eliminate month with only 1 option.
There are none. - Albert knows that Benard doesn't know, eliminate 18th, 19th, May and June, because 18th, and 19th have only one option.
- Benard now knows, eliminate days with more than one option.
- Albert now knows, eliminate months with more than one option.
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Better:
- recognize that it's 2-sat.
- visit http://en.wikipedia.org/wiki/2-satisfiability#Algorithms
- Implement algorithm
- Get answer
- ???
- Profit
- Realize algorithm implementation has a bug
- Hide results showing algorithm's bug until you can find a job somewhere else
(thanks for re-numbering these for me in my first attempt to post, dickhorse.
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.6. Profit
Actually, don't profit, because I just lost 2 hours of work time.
Nerd sniped.
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psh, I posit that you were going to lose that time either way... it's just that now it was all spent in this topic rather than any of the other topics.
