# Do this maths. It R Hard.

• This is a question that is allegedly going viral (apparently helped by me). can you identify the correct answer?

As programmers we should be able to figure this one out reasonably well, so I am interested to see how this community fairs as compared to the average

I'll post the source later, but you can cheat if you want by using google image search. That's no fun though!

• [spoiler]June 17[/spoiler]

• A million more:

http://puzzling.stackexchange.com/questions/1968/3-impossibly-intelligent-mathematicians?lq=1

• incorrect

[spoiler]Albert KNOWS that Bernard doesn't know[/spoiler]

• [spoiler] August 17. Albert knows Bernard can't know, because it could be June 17 or August 17, or August 14 or july 14, or August 15 or May 15, so knowing only the number won't tell him. Bernard knowing it's a 17 knows it had to be August 17, because if it was June that Albert knew, it could have been 18 that Bernard knew, so he can't have known that Bernard knew. [/spoiler]

• that was my first answer, but I don't think it's correct anymore.

[spoiler]Albert knows Bernard doesn't know, so the month must be one of the 2 which have no unique values, i.e. it cannot be May or June[/spoiler]

• That is my answer as well

• [spoiler]July 16[/spoiler]

• This I believe to be correct also.

edit clarify:
this is the answer that I believe to be the single correct answer

• This kind of problems have only one solution. Prove me wrong.

• Figured it out.
[spoiler]whylfvkgrra, rot13d[/spoiler]

• [spoiler]
If Bernard knows the number is 17, he knows that the month is either June or August.
Albert knows the month, and as he states he knows Bernard can't know, so that means the month cannot be June, so Bernard knows it is August and he tells Albert he now knows.
How does Albert then know the day?
[/spoiler]

@wft your answer is the same as mine, and I'm 99% sure it's right.

• How I did it?
Excel.

[spoiler]

[/spoiler]

• I'm guessing the numbers are the steps at which each result is eliminated?

• Yep!
This was fun.

• this was where I fell down and I think possibly @Yamikuronue and @Vault_Dweller did too since we came up with the same answer, we all thought on our first stab that we had got the correct answer but we hadn't fully eliminated all the possibilities.

• (insert Sherlock Holmes quote here)

Filed under: however, improbable, blah blah blah

• This is the same reasoning I ended up using. I do find it interesting that we came up with a different answer than aliceif / wft though.

I do hope everyone is catching that Albert knows the month and Bernard knows the day... because if you get that backwards, the entire answer changes.

• I am sorry, maybe it's a language barrier but I am having trouble imagining how this is going down. Can somebody verify / correct me here?

So, first Albert and Bernard meet Cheryl.
Then Cheryl hands the a list of 10 possible birthday dates (obviously so she can expect 10 times the presents)
Then they get drunk and Cheryl forgets the whole 10 dates thing.
-- Here is where the conversation takes place:
She starts telling Albert the month and the day
Now she tells Bernard the month and the day.
Albert is also drunk and can't reason that she just told him her birthday.
Bernard is being more sober and tells Albert the date.
Albert now also knows the date
-- Here is where the conversation ends.
Since Cheryl can see things more clearly now (at least one day after that fateful drinking night) she just poses this question to us, no doubt once again trying to bait for more gifts.
Since you guys clearly have more time than I do, you just do some random mathematics and claim to know her birthday to save your money.
Luckily I am not stupid and am not gonna gift her anything.

Lesson Learned: I am a jerk who apparently can't read.

• Cheryl gives a list of 10 possible dates to both of them.

She then tells Albert the month and Bernard the day.

Then, the two start talking.

Filed under: [Why didn't they just use Alice and Bob (and Charlie)?](#tag)

• Cheryl States 10 possible dates that her birthday could be.

Cheryl tells Albert in secret the MONTH of her birthday, i.e. we know Albert knows she was born in a specific value in the set May, June, July or August.

Then Cheryl tells Bernard in secret the DAY of her birthday.

Albert uses the set of dates and the information he has to make a statement about Cheryl's birthday.

Bernard uses this statement with the data he was given to find the value.

Albert, knowing that his statement was sufficient to provide Bernard with a definitive answer, knows the answer also.

Using all of this information, find Cheryl's birthday

• [spoiler]1. Well, we know right off the bat that it can't be May 19 or June 18 because if they were then Bernard, knowing the day, would have known the date instantly.

1. Clue #1 tells us that Albert knows that Bernard doesn't know. Since Albert, knowing the month, still doesn't know the date. we know it can't be June 17 (the only unique June day left).
2. Clue #2: Since Bernard now knows that Alfred doesn't know, he can also eliminate June 17. Since he now knows what date it is, it has to be the only day that is still associated with just one month. That would be August 17.
3. Clue #3. This isn't hard, it's just the same thing Bernard did in #2, but Albert is doing it since he knows Bernard now knows the whole date.
[/spoiler]

• [spoiler]Can you explain which part of your logic doesn't hold true for August 15?
I think you are also going wrong with point 1. which isn't actually something you know when the first statement is made
[/spoiler]

• [spoiler]Since Bernard can't have known, May & June are out because if the day was 18 or 19, Bernard could have known.
So July or August, and can't be the 14th or Bernard couldn't know even if he knew it was July or August, so left with July 16, Aug 15, or Aug 17.... Not sure off the top of my head how to get farther than that because at this point if Bernard knows whether it's 15, 16, or 17 then he'd know which date it is, but it could be any of those 3 as far as I can tell, so I'm not sure how Albert can know her birthday at the end, unless I guess it's July 16.[/spoiler]

also, blank line in a spoiler breaks the spoiler... wtf.

• [spoiler]Can you explain which part of your logic doesn't hold true for August 15? I think you are also going wrong with point 1. which isn't actually something you know when the first statement is made[/spoiler]

[spoiler]That's the problem I have with the way other people are solving this: While you can throw out June due to June 18th being a gimme (i.e. one of them would have instantly known the date), you can't get rid of May that way due to May 15 and May 16 both being in the potentially valid pool.[/spoiler]

Also, Discourse, why are you stripping out spoiler tags from posts I quote?

• [spoiler]
But you can, because Albert knows Bernard cannot know the full value of cheryl's birthday, we know that the month he has been told has no unique values, otherwise his statement would be false. This allows us and Bernard to fully eliminate the months of May and June.
[/spoiler]

• [spoiler]but it could be any of those 3 as far as I can tell, so I'm not sure how Albert can know her birthday at the end, unless I guess it's July 16.[/spoiler]

[spoiler]I feel like there's a leap in logic to guess that it has to be the month left with only 1 possible date in it. Because Bernard knows whether it's 15, 16, or 17 and any of those 3 will tell him which it is, at which point there's no possible way that Albert can know which. But since they say that he does, then it has to be July 16; when technically Albert is logically incorrect and just guessing. In order for him to be right, July 16 has to be right, but that's dumb.[/spoiler] Unless I'm missing something.

• [spoiler]
Looking at the last step broken down:
Albert knows the month.
If Albert knows the month is August, he can eliminate the 14th Since Bernard is able to identify the month successfully. If Bernard were told 14 Bernard would not know the answer. However Albert cannot tell beyond that whether the day is 15 or 17.
If however Albert is told July, he can still eliminate the 14th since Bernard was able to identify the month successfully. Since there is only 1 value left, he too can identify the full date. The additional fact we are given that Albert can solve it tells the reader that the date must be July 16.
[/spoiler]

• I think whoever wrote that problem up needs to be sent back to remedial English class, but I'm in major Off My Lawn mode this morning after a cashier handed me my change in the worst way: the bills, then the coins on top of that, with the receipt covering the coins. I almost said something.

• its a question for 14 year olds in singapore if that makes you feel better

• [spoiler]The additional fact we are given that Albert can solve it tells the reader that the date must be July 16.[/spoiler]

See above - that "fact" is a logically impossible leap that means you have to solve the problem to the one date for it to be correct, but it's circular logic... the outcome has to be what it is in order for him to "know" except he can't have known that it was that unless the outcome is what it is. (goddamn that sentence is hard to follow....)

• its a question for 14 year olds in singapore if that makes you feel better

I'll give furriners[1] a pass, but it would still be nice to try to get it right[2].

[1]I had a feeling it might not have been written for native speakers because it had the equivalent of a slight code smell.

[2]I'd like to think if I ever had reason to learn and/or use a foreign language I'd make a concerted attempt to be as right in my usage as possible.

• That's not a flaw, that's just how logic works. You know all the statements are true, there is only one answer where that is possible, thus the answer is valid. In the circumstance that the answer is the answer, Albert has enough information to identify it. The fact that he cannot do so for the other possible answers at one point in the problem only means that those answers cannot be valid. He knows it's a month, based on bernard's answer he is able to identify that month. I think the problem you are having is disconnecting Albert's knowledge from your own. You know less than he does right up until the end.

• [spoiler]

1. Albert knows the month. Albert does not know the date. Therefore, it is not any month with only one date on the list. This eliminates nothing.
2. Albert knows that Bernard does not know. Whatever month it is does not contain any date that only exists in one month. The date 18 and the date 19 only appear once, therefore, it cannot be May or June that Albert knows.
3. Bernard knows the date. Bernard does not know the month. Therefore, we can eliminate any date taht only appears once, such as 18 and 19. Which is redundant with 2.
4. Bernard, knowing that Albert has eliminated May and June, knows the exact date. This means that his number must be one that exists in one or both of May and June, as well as one other month. Since it can't be 18 or 19, that means he was told one of 15 [May and August], 16 [May and July], or 17 [June and August]. So he knows the month, which is one of [July or August]
5. Albert now knows the date, knowing that Bernard did this. Since he knows the month...
it's either August 17, August 15, or July 16. We cannot know.
[/spoiler]

Now I'm confused again.

• That's not a flaw, that's just how logic works.

Nevermind now, I get it now... it was just worded in a way that didn't sit well with me.
I have re-read it and it's clear how it works.

• Unless the image is cropped or I'm missing something (likely) there's not enough info to answer.

Also Cheryl's a bitch. I hope she's hot.

• [spoiler]5. Albert now knows the date, knowing that Bernard did this. Since he knows the month...it's either August 17, August 15, or July 16. We cannot know.
Now I'm confused again.[/spoiler]

[spoiler]
If Albert was told that it was August, then he wouldn't know whether it's the 15th or 17th. But Albert declares in the final statement that he now knows her birthday, so the month he was told had to be July, the month with only 1 valid date left for Albert to know. So July 16.[/spoiler]

• Bernard knows the DATE, not the month. As soon as he knows a month, he knows for sure the whole thing.

• Albert/Bernard mix up

• Sorry - but it's irrelevant, I can just swap the names then, the logic still holds...

• I swapped the names to fit my sentences, but the logical part is still correct.

• Why can't Albert and Bernard just fucking TELL each other what they know? Jesus these people are all dicks.

That is my answer. Fuck them all.

• [spoiler]Assuming Albert knows the month is August, if Bernard knows the full birthday, then it cannot be 14. Albert cannot differentiate 15 and 17.
Assuming Albert knows the month is July, Bernard's finding an answer still allows him to eliminate 14. There is only one day left and that's July 16.
We the reader cannot tell between these 3 values unless we know whether Albert can reach a result. If he cannot find a single value, we know the month is August, but we cannot identify the date. If he CAN find a value, we know that the month is July and the date is 16.
The final statement in the conversation confirms he is able to identify a result, and allows us to reach the final value.
[/spoiler]

• Correct!

• it's really difficult to word this in ways that aren't confusing. I'm hoping that the above is the best way to explain the last step!

• The last step requires looking at the problem from Albert's point-of-view. If you look at it from a 3rd party point of view, it doesn't make sense that he jumps to that conclusion, which is why I thought it was circular logic.

Once you think from Albert's perspective, it all works out.

• Mine is more long winded...

[spoiler]Cheryl told Albert the month and Bernard the day. Albert's statement informs Bernard that neither of them know the date.

This means that May 19 and June 18 are ruled out. Because if it was either of these dates and she had told Bernard that day of month, he would know the month as well. Therefore she must have told Bernard the day was the 14th, 15th, 16th, or 17th.

Now it gets complicated, because this gives Bernard additional information. Bernard now knows that the date must be Jul 14/Aug14, May 15/Aug 15, May 16/Jul 16, June 17/Aug17. Bernard knows that Albert must have reasoned the same information, but Albert still doesn't know the date.

Therefore, Bernard realizes that the month Albert was told must be May, July, or August. If Albert had been told June, he would know it was June 17, because Albert was able to rule out the 18th; so if Albert had been told June, that would leave only the 17th and Albert would already know the answer.

Now Bernard was told the day, which is the 14th, 15th, 16th or 17th. With the combinations that are left, this information must tell him the month.

If he was told the 14th, that would leave him a joice of July or August, and no way to tell which. If he was told the 15th, May and August, same thing. If he was told the 16th, May and July, same thing. But if he was told the 17th, then he knows it must be August, because June was already ruled out...Albert would have been able to figure out June 17th himself.

So Cheryl's birth date must be August 17.By similar reasoning, when Bernard announces he knows the date, then Albert can work out the same answer.[/spoiler]

(I didn't know you had to use breaks for a multi-paragraph spoiler.)

• Albert and Bernard are locked into separate sealed, soundproof Death Chambers.

On the screen in front of each of them are a list of 10 dates.
May 15, May 16, May 19
June 17, June 18,
July 14, July 16
August 14, August 15, August 17.

On a table beneath each screen is a Sealed envelope. Inside the envelope is a message stating that each of them will know either the day or the month, and must answer 3 questions correctly to survive. Each one will see the other's answers, except for the 3rd question. If the one person answers all 3 questions correctly, a countdown timer will appear in the corner of the screen of the remaining person, and after 2 minutes the room will fill with gas unless they too answer correctly. Any incorrect answer will gas both of them.

Albert's envelope contains the month. Bernard's the day.
They are asked "Do you currently know the full date?"
Albert: No, Bernard: No
Then they are asked "Can the other person know the full date?"