# Birthday Logic Question **URL:** \ **Category:** Factual Questions\ **Created:** [April 14, 2015, 5:31am UTC](https://boards.straightdope.com/t/birthday-logic-question/717622 "2015-04-14T05:31:35Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![kanicbird](https://avatars.discourse-cdn.com/v4/letter/k/5f8ce5/32.png) [@kanicbird](https://boards.straightdope.com/u/kanicbird)\ **Post date:** [April 14, 2015, 5:21pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/61 "2015-04-14T17:21:22Z")
> [@don\_t\_ask](#): > > To the OP. > > Let’s say you are playing Bernard’s role. Cheryl tells you the number. If it is 18 or 19 do you now know her birthday? > > So how can Albert be sure that you don’t **already** know her birthday? Because Albert knows the month which means it can only be the 14, or the 16th. Both of them are repeated numbers in other months, thus Albert knows that you can not know. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [April 14, 2015, 5:25pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/62 "2015-04-14T17:25:46Z")
> [@CurtC](#): > > Here’s my analysis: Albert knows the month, Bernard knows the day. Albert knows that Bernard doesn’t know, that rules out the 18th and 19th days because those are unique, and if one of those were it, Bernard would have known right away. Bernard might know right away. Albert does not know this. All that Albert knows is the information he was given, the month. The only information Albert can know that guarantees him that Bernard doesn’t know is if the month is July or August. ---
**Author:** ![Your\_Great\_Darsh\_Face](https://avatars.discourse-cdn.com/v4/letter/y/ac8455/32.png) [@Your\_Great\_Darsh\_Face](https://boards.straightdope.com/u/Your_Great_Darsh_Face)\ **Post date:** [April 14, 2015, 5:31pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/63 "2015-04-14T17:31:23Z")
> [@Czarcasm](#): > > I knew that…but are those common names in Singapore? I wouldn’t rule it out. They seem to be common enough in Indian call centres even when the _lingua franca_ is Hindi. If I venture any more comment on the OP’s understanding of this question, I’m going to be risking a touch of the Inigo Montoyas, so best not. It has been explained with gem-like clarity and there’s no possible way I can improve on it. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [April 14, 2015, 5:38pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/64 "2015-04-14T17:38:54Z")
> [@Your\_Great\_Darsh\_Face](#): > > I wouldn’t rule it out. They seem to be common enough in Indian call centres even when the _lingua franca_ is Hindi. FWIW, one of the few Singaporean friends I have is named “Cheryl.” (And Googling shows that Mrs. Singapore Universe 2014 is a Cheryl Ho.) Can’t speak to Albert or Bernard, though. ---
**Author:** ![malaka](https://avatars.discourse-cdn.com/v4/letter/m/ecc23a/32.png) [@malaka](https://boards.straightdope.com/u/malaka)\ **Post date:** [April 14, 2015, 5:41pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/65 "2015-04-14T17:41:46Z")
How in the hell does one concoct such a puzzle? Solving it was tricky enough. Coming up with it must have been more so. ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [April 14, 2015, 5:41pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/66 "2015-04-14T17:41:47Z")
> [@pulykamell](#): > > Bernard might know right away. Albert does not know this. All that Albert knows is the information he was given, the month. The only information Albert can know that guarantees him that Bernard doesn’t know is if the month is July or August. Thanks - I see the source of my error. Back to the bar napkin… ---
**Author:** ![Dickerman](https://avatars.discourse-cdn.com/v4/letter/d/8baadc/32.png) [@Dickerman](https://boards.straightdope.com/u/Dickerman)\ **Post date:** [April 14, 2015, 5:44pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/67 "2015-04-14T17:44:53Z")
> [@Kiber](#): > > Ah - but logic can help us with this as well. Clearly - if Albert and Bernard are putting up with her, Cheryl is crazy hot. Not necessarily. For example, if Albert and Bernard are nerdy teenage logicians, Cheryl could be any old girl and they’d go along with her antics. ---
**Author:** ![DrCube](https://avatars.discourse-cdn.com/v4/letter/d/a3d4f5/32.png) [@DrCube](https://boards.straightdope.com/u/DrCube)\ **Post date:** [April 14, 2015, 5:50pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/68 "2015-04-14T17:50:50Z")
> [@jezzaOZ](#): > > 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. No, this is where you’re wrong. When the person with the month is sure the person with the day can’t know the birthday, that reveals new information, namely that the month is not one with unique days. Because the day person could have been told a unique day, in which case the month person _would not have known_ that the day person didn’t know the birthday. The only way Monthy could know Day-O doesn’t know the birthday is if the month he was told didn’t have unique days in the list. So, assuming as we always do in logic puzzles that the characters aren’t lying, then we know the month is July or August after the first statement, because May and June have unique days. Does that make sense? ---
**Author:** ![Great\_Antibob](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Great\_Antibob](https://boards.straightdope.com/u/Great_Antibob)\ **Post date:** [April 14, 2015, 5:51pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/69 "2015-04-14T17:51:19Z")
Well, I suppose there’s the chance these two are chaotic evil, and they’re just screwing with people. But the reasonable thing to do is suppose they won’t lie, reason logically, and are willing to play along with the silly game. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [April 14, 2015, 5:56pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/70 "2015-04-14T17:56:35Z")
> [@chrisk](#): > > But in the puzzle, it’s given that Albert believes he has deduced the correct date and proclaims it at the end. Are you leaving open the possibility that he made a mistake? 😉 Albert can’t base his solution on the premise that the problem must be solvable. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [April 14, 2015, 5:58pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/71 "2015-04-14T17:58:05Z")
> [@Omar\_Little](#): > > Yes A does. He has the month, with which he is able to deduce the day, since B says they know both the day and month, now. You’d be correct if Bernard had said they both now have sufficient information. But, as noted, he didn’t say that. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [April 14, 2015, 6:07pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/72 "2015-04-14T18:07:12Z")
> [@Little\_Nemo](#): > > You’d be correct if Bernard had said they both now have sufficient information. But, as noted, he didn’t say that. That’s correct. Bernard actually does have enough information to say that Albert knows the date once Bernard declares he knows, but he doesn’t give that information away. It’s not necessary, and each step is only giving one bit of information away. Once Albert knows that Bernard knows the date, the only way Albert could know the date is if he was given July as the month. If the month were August, Albert is still stuck with choosing between two dates, and all Albert could say at that point is “I still don’t know.” In that case, we know the date is either August 15 or August 17 with no way to further narrow it down. ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [April 14, 2015, 6:15pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/73 "2015-04-14T18:15:42Z")
> [@Little\_Nemo](#): > > Albert can’t base his solution on the premise that the problem must be solvable. No–where did he do that? **We** are basing our solution on the premise that the problem was solvable. Albert had sufficient information to determine if the premise was solvable or not, and we are given that he solved it. At this stage of the puzzle, Albert knows the month, (we’ve already established that it must be July or August,) and he knows that Bernard knows the exact birthdate. So he can rule out the 14th. If Cheryl had told Albert August, then he’d say “Dammit, I still don’t have enough information,” or something to that effect. But that’s not what he said, thus we can deduce what information Albert had available to solve the puzzle with. I love these logical meta-puzzles, where the characters have information that we don’t, but based on the conclusions they come to we can deduce that information. 😃 ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [April 14, 2015, 6:17pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/74 "2015-04-14T18:17:15Z")
Now, if for the second statement, Bernard says “I still don’t know the date,” then Albert will have enough information to deduce the date, but there are two possibilities for us, as the puzzle solvers, that satisfy these conditions and statements: July 14 and August 14, depending on what month he was given. There is not a solution (that I see immediately) where Albert could say something in the spirit of the logic game that will allow Bernard to narrow it down farther using statement what either person must know or not know. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [April 14, 2015, 6:27pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/75 "2015-04-14T18:27:00Z")
> [@chrisk](#): > > No–where did he do that? **We** are basing our solution on the premise that the problem was solvable. Albert had sufficient information to determine if the premise was solvable or not, and we are given that he solved it. > > At this stage of the puzzle, Albert knows the month, (we’ve already established that it must be July or August,) and he knows that Bernard knows the exact birthdate. So he can rule out the 14th. > > If Cheryl had told Albert August, then he’d say “Dammit, I still don’t have enough information,” or something to that effect. But that’s not what he said, thus we can deduce what information Albert had available to solve the puzzle with. > I love these logical meta-puzzles, where the characters have information that we don’t, but based on the conclusions they come to we can deduce that information. 😃 Exactly. The question is for us. What date satisfies each logical statement such that the conversation can take place, be truthful and logical, and satisfy the condition that after the three statements, both Albert and Bernard know the birthdate. There is only one: July 16. The question is not what questions can Albert and Bernard ask to deduce the date or whether they can assume the premise is solvable. It’s a puzzle for us, the readers, not them, the actors. Nobody in the story has to assume it’s solvable for it to work as a logic puzzle and for the statements to unfold as given. ---
**Author:** ![panamajack](https://avatars.discourse-cdn.com/v4/letter/p/47e85d/32.png) [@panamajack](https://boards.straightdope.com/u/panamajack)\ **Post date:** [April 14, 2015, 8:23pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/76 "2015-04-14T20:23:20Z")
> [@CurtC](#): > > Here’s my analysis: Albert knows the month, Bernard knows the day. Albert knows that Bernard doesn’t know, that rules out the 18th and 19th days because those are unique, and if one of those were it, Bernard would have known right away. > > Bernard knows that Albert has ruled out the 18th and 19th, and we know that with his month information, Bernard now knows the exact date. The only way this can happen is if the month is June, and the only option left for June is the 17th. > > June 17. This is an interesting result, as it’s correct if the roles are reversed (I missed the ‘respectively’ in the statement and came to that conclusion). The problem doesn’t make it explicit that Cheryl’s passing of information is common knowledge, and I’m trying to see if that makes a difference (I don’t think it does). ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [April 14, 2015, 8:50pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/77 "2015-04-14T20:50:12Z")
Nm ---
**Author:** ![Learjeff](https://avatars.discourse-cdn.com/v4/letter/l/94ad74/32.png) [@Learjeff](https://boards.straightdope.com/u/Learjeff)\ **Post date:** [April 14, 2015, 9:02pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/78 "2015-04-14T21:02:07Z")
> [@jezzaOZ](#): > > You have to remember that the first statement is made on purely public knowledge. This repeats what I called your first mistake above. A knows what he’s been told, which is not “public knowledge”, and he uses this to make his assertion about B. > [@](#): > > A can only know that B has a number of dates and B has no information about what A knows. Again, wrong. A knows the list of possibilities, which very much limits what B might have been told. A also knows what he’s been told, which further limits the possibilities, enough for him to make his claim, which is objectively true, assuming that B has no mystical abilities. > [@](#): > > His dataset has not been reduced by the A statement and so any statement he makes is still based on the public conditions. Did you read my reply? Which statement in my reply is illogical? It leads to the inescapable conclusion, and is logically simple, valid, and sound. If I’ve made a mistake, please point it out. > [@Kimble](#): > > What this thread needs is another participant! > > Not “thinks” – "knows."A knows that B doesn’t know. Good point! B might _think_ he knows, but if he does, he’d be mistaken about that. A does not need to know that B is clever. However, B has to assume that A was correct. > [@DrCube](#): > > No, this is where you’re wrong. When the person with the month is sure the person with the day can’t know the birthday, that reveals new information, namely that the month is not one with unique days. Because the day person could have been told a unique day, in which case the month person _would not have known_ that the day person didn’t know the birthday. The only way Monthy could know Day-O doesn’t know the birthday is if the month he was told didn’t have unique days in the list. So, assuming as we always do in logic puzzles that the characters aren’t lying, then we know the month is July or August after the first statement, because May and June have unique days. Does that make sense? Bingo. A is revealing information, and it happens to be enough for B to find the unique solution. ---
**Author:** ![jezzaOZ](https://avatars.discourse-cdn.com/v4/letter/j/a9a28c/32.png) [@jezzaOZ](https://boards.straightdope.com/u/jezzaOZ)\ **Post date:** [April 14, 2015, 10:59pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/79 "2015-04-14T22:59:04Z")
New argument. Say Albert said \* I don’t know when Cheryl’s birthday is, but I know that Bernard **DOES** know.\* i.e. the opposite of what is posited in the puzzle. Since he can’t possibly say that based on the known facts, then he has no choice but to say _I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too._ i.e. he will always say that, so it passes no information to Bernard. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 14, 2015, 11:16pm UTC](https://boards.straightdope.com/t/birthday-logic-question/717622/80 "2015-04-14T23:16:48Z")
It is not correct to say that he doesn’t have a choice. He has a third option: He could say “I don’t know when C’s birthday is, but I also don’t know if B knows”. [Previous page](https://boards.straightdope.com/t/birthday-logic-question/717622.md?page=3) [Next page](https://boards.straightdope.com/t/birthday-logic-question/717622.md?page=5)