Remember Albert is basing his declaration on the month he has been told. He is ruling out the months containing the 18th and 19th, not just the 18th and 19th days. He is saying it can only be a month with ambiguity if someone knows the day.
The Math Problem That Has Stumped the Entire Internet
- Thread starter Kilgore Trout
- Start date
How can May be eliminated? Where does Bernard indicate that it can't be May?May is eliminated exactly like June is.
Albert is saying that it is not a month where Bernard knows the full solution, no matter what day she told Bernard. Think of it in reverse - if Albert knew it was May, it could be May 19, leaving the possibility that Bernard was told the day was 19, and so Bernard would know the date from the unique May 19 - the only month with a 19. Since Albert states that Bernard cannot possibly know, then Bernard is revealing that the month is not May. He is ruling out that Bernard could possibly know, so all of May is out.
Ditto for June. The only month with a day of 18 is June. If she had told Bernard that the day was 18, Bernard would know the month. Since Albert is telling them this is impossible for Bernard to know, he is revealing that he knows that it is not June.
Bernard could've been told that the day was the 15th or the 16th but he can't know if that is May or August, or May and July?
June is easier. Since we know she didn't tell Bernard that it was the 18th (otherwise he would have yelled BINGO). As a result, she couldn't have told Albert that is was June because he would've used the process of elimination and deduce the day as the 17th.
Whereas with May, she obviously didn't tell Bernard it was the 19th, BUT she could've told him either the 15th or the 16th. And if she told Albert it was the month of May, he wouldn't know if it was either the 15th or the 16th.
Albert is indicating they are ruled out, not Bernard. Step back and read it through again, and forget about silences and yelling bingo.How can May be eliminated? Where does Bernard indicate that it can't be May?
Bernard could've been told that the day was the 15th or the 16th but he can't know if that is May or August, or May and July?
June is easier. Since we know she didn't tell Bernard that it was the 18th (otherwise he would have yelled BINGO). As a result, she couldn't have told Albert that is was June because he would've used the process of elimination and deduce the day as the 17th.
Whereas with May, she obviously didn't tell Bernard it was the 19th, BUT she could've told him either the 15th or the 16th. And if she told Albert it was the month of May, he wouldn't know if it was either the 15th or the 16th.
Not it doesn't.I will take a crack at explaining. I started with buttercups logic, so want to give credit.
1. Albert knows the month but not the day
2. Bernard knows the day but not the month.
Statement by Albert: "I don't know when your birthday is, but I know Bernard doesn't know, either."
Albert is saying that he can tell that the day does not have only one month associated with it, as he is observing that Bernard cannot identify the date at this point. Note that the 18th and 19th have only one possible month for each (May and June respectively.) This means that May and June are eliminated; if Albert knew the month was May or June, it would leave open the possibility of May 18th or June 19th, which Albert is saying is not possible (ie Bernard can't possibly know.) So Albert is revealing that the month is not May or June.
This leaves these possibilities in both their minds given Albert's statement:
July 14 & July 16
Aug 14, Aug 15, and Aug 17
Statement by Bernard: "I didn't know originally, but now I do."
Bernard is saying that given Albert's statement, Bernard can now uniquely identify the date given the day. He is revealing to Albert that the day is not the 14th, which has two possible months (July and August.)
This means Bernard knows the exact date, and is revealing to Albert that it is one of August 15, or July 16, or August 17.
Statement by Albert: "Well, now I know, too!"
Remember, Albert already knows the month. If Albert knew the month was August, he could not know the full date – there are two possibilities (August 15 or 17.) If he knew the month is July though, he can uniquely identify the date - there is only one possible July date left.
Therefore, the full date is July 16.
The 18th and 19th are red herrings.
It simply means that her birthday is not on those days but that it could still be on another day for either May or June (later, we know that it can't be June).
Pls readNot it doesn't.
The 18th and 19th are red herrings.
It simply means that her birthday is not on those days but that it could still be on another day for either May or June (later, we know that it can't be June).
May and June have unique dates. May 18 and june 19
July and August do not.
Albert knows the month. So if he thinks that Bernard cannot know the birthday (before Bernard speaks) then it cannot be may or June. Albert doesn't know the day so for him to say that it must be a month without a unique date.
Correct. And the reason why Albert knows Bernard cannot have been told either of those days is that Albert knows the month does not contain them.Albert's statement that he's sure Bernard doesn't know, merely means that Bernard was told any day other than the 18th or the 19th, because any other of those days have duplicates in a second month.
Specifically Albert was told July, and he can see from the list that none of the unique days are in July. Therefore, knowing it is July, Albert is confident Bernard doesn't know her birthday even before anyone asks.
(This would also be true if Albert had been told August, it takes more analysis to rule out August though).
The fact that May has two other candidate days is not relevant - Bernard can eliminate May and June together, simply upon hearing Albert's first report.You can only exclude June by their responses because neither party proclaims to know after Bernard is given the date of the day; May has two other days found in other months.
To elaborate on why/how May and June can be excluded, as the month:
Before Bernard says a word, Albert makes his first report, that Albert knows that Bernard cannot pin the month.
Bernard (having the deductive reasoning capabilities of a good Terbite) deduces how/why Albert was able to make this report.
Bernard deduces that, if Albert knew the month was May, Albert would not dare to make his first report, because, for all Albert knows, Cheryl might have whispered "19" to Bernard -- in which case Bernard would then be able to pin the month to May.
Equally, Bernard deduces that, if Albert knew that the month was June, again Albert would not dare to make his report, because, for all Albert knew, Cheryl might have whispered "18" to Bernard -- in which case Bernard would be able to pin the month to June.
Now, because Bernard hears Albert say that Bernard does not know the month, Bernard knows that the month cannot be May or June -- because if it were May or June, Albert could not be certain that Bernard did not know the month. Therefore, Bernard knows that the month must be either July or August.
So now, at this point, Albert (to whom Cheryl whispered July) knows he has to decide between 14 and 16. Similarly, Bernard (to whom Cheryl whispered 16) knows that 16 appears in both May and July. But Bernard has just eliminated May -- so July it is. So, now, Bernard is able to report that he didn't know the birthday at first, but now he does.
So Bernard now knows, simply from having heard Albert's first report, that the month is not May nor June (i.e that the month must be July or August.) May and June are equal in this regard -- both can be excluded for the same reason.
Just a comment on the assumptions that need to be made:
1) - that the facts as stated in the problem are true;
2) - that no-one has reported any relevant facts, other than as stated;
3) - that Albert and Bernard are telling the truth in their reports.
These assumptions are clearly acceptable, for the purposes of the game.
If people don't find those assumptions acceptable, they probably also wouldn't find it acceptable to assume there is oxygen in the atmosphere, and that gravity acts downwards.
Before Bernard speaks. Before anyone asks. Aye ya ya. Ok. When Bernard gets the hint, he knows, and then Albert.
I agree with Kilgore that the solution here is the best => http://www.vox.com/2015/4/15/8420577/cheryls-birthday-singapore-math
I agree with Kilgore that the solution here is the best => http://www.vox.com/2015/4/15/8420577/cheryls-birthday-singapore-math
The fact that May has two other candidate days is not relevant - Bernard can eliminate May and June together, simply upon hearing Albert's first report.
To elaborate on why/how May and June can be excluded, as the month:
Before Bernard says a word, Albert makes his first report, that Albert knows that Bernard cannot pin the month.
Bernard (having the deductive reasoning capabilities of a good Terbite) deduces how/why Albert was able to make this report.
Bernard deduces that, if Albert knew the month was May, Albert would not dare to make his first report, because, for all Albert knows, Cheryl might have whispered "19" to Bernard -- in which case Bernard would then be able to pin the month to May.
Equally, Bernard deduces that, if Albert knew that the month was June, again Albert would not dare to make his report, because, for all Albert knew, Cheryl might have whispered "18" to Bernard -- in which case Bernard would be able to pin the month to June.
Now, because Bernard hears Albert say that Bernard does not know the month, Bernard knows that the month cannot be May or June -- because if it were May or June, Albert could not be certain that Bernard did not know the month. Therefore, Bernard knows that the month must be either July or August.
So now, at this point, Albert (to whom Cheryl whispered July) knows he has to decide between 14 and 16. Similarly, Bernard (to whom Cheryl whispered 16) knows that 16 appears in both May and July. But Bernard has just eliminated May -- so July it is. So, now, Bernard is able to report that he didn't know the birthday at first, but now he does.
So Bernard now knows, simply from having heard Albert's first report, that the month is not May nor June (i.e that the month must be July or August.) May and June are equal in this regard -- both can be excluded for the same reason.
Just a comment on the assumptions that need to be made:
1) - that the facts as stated in the problem are true;
2) - that no-one has reported any relevant facts, other than as stated;
3) - that Albert and Bernard are telling the truth in their reports.
These assumptions are clearly acceptable, for the purposes of the game.
If people don't find those assumptions acceptable, they probably also wouldn't find it acceptable to assume there is oxygen in the atmosphere, and that gravity acts downwards.
Sometimes, I over-analyze or over-complicate things. Sometimes, the solution to a problem is the simplest.
It is Albert's initial comment that he's virtually certain that Bernard doesn't know the answer, that we are to infer that he was told a month other than May or June, because these latter months contain dead giveaway dates.
P.S. The funny thing is that my initial solution was July 16th, but lost sight of the forest for the trees.
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Ok my brain hurts - But I vote for Aug 17
Assumption 1 - If Cheryl had whispered 18 or 19 there would be no discussion we know it is either May 18th or June 19th as Bernard could have figured that out. (and he later admits he couldn't figure it out at first)
When Bernard does not figure that out -
Assumption 2 if Albert had been told June he would have been able to deduce it was June 17th, but he didn't so we can eliminate June as his month.
Next - Albert: "I don't know when your birthday is, but I know Bernard doesn't know, either."
Currently this leave us with 7 Dates
May 15 16
July 14 16
Aug 14 15 17
If albert was told may july or august he could not determine the correct date. Using the same logic Bernard knows that June is eliminate as well
If he had 14 15 or 16 he still would not be able to determine the date, but he claims he can, so he must have been told 17.
Once he claims he knows it - Albert eliminates the other dates as well.
The assumption that Bernard does not proclaim the answer before Cheryl asks Albert if he knows.
Assumption 1 - If Cheryl had whispered 18 or 19 there would be no discussion we know it is either May 18th or June 19th as Bernard could have figured that out. (and he later admits he couldn't figure it out at first)
When Bernard does not figure that out -
Assumption 2 if Albert had been told June he would have been able to deduce it was June 17th, but he didn't so we can eliminate June as his month.
Next - Albert: "I don't know when your birthday is, but I know Bernard doesn't know, either."
Currently this leave us with 7 Dates
May 15 16
July 14 16
Aug 14 15 17
If albert was told may july or august he could not determine the correct date. Using the same logic Bernard knows that June is eliminate as well
If he had 14 15 or 16 he still would not be able to determine the date, but he claims he can, so he must have been told 17.
Once he claims he knows it - Albert eliminates the other dates as well.
The assumption that Bernard does not proclaim the answer before Cheryl asks Albert if he knows.
The month of May and June were eliminated because of the 18th and 19th. Bernard could have figured that out. Also Albert pronounced that he was sure that Bernard didn't know either which eliminated May and June. How was he sure that Bernard didn't have the 18th or 19th? Which eliminated those two months. Bernard then says I know too.Ok my brain hurts - But I vote for Aug 17
Assumption 1 - If Cheryl had whispered 18 or 19 there would be no discussion we know it is either May 18th or June 19th as Bernard could have figured that out. (and he later admits he couldn't figure it out at first)
When Bernard does not figure that out -
Assumption 2 if Albert had been told June he would have been able to deduce it was June 17th, but he didn't so we can eliminate June as his month.
Next - Albert: "I don't know when your birthday is, but I know Bernard doesn't know, either."
Currently this leave us with 7 Dates
May 15 16
July 14 16
Aug 14 15 17
If albert was told may july or august he could not determine the correct date. Using the same logic Bernard knows that June is eliminate as well
If he had 14 15 or 16 he still would not be able to determine the date, but he claims he can, so he must have been told 17.
Once he claims he knows it - Albert eliminates the other dates as well.
The assumption that Bernard does not proclaim the answer before Cheryl asks Albert if he knows.
Which leaves the following
July 14 16
Aug 14 15 17
Keep in mind Albert has no dates only the month, but states he knows the answer now.
Which eliminates the 14th. What's the only month left with one date. July 16th
The month of May and June were eliminated because of the 18th and 19th. Bernard could have figured that out. Also Albert pronounced that he was sure that Bernard didn't know either which eliminated May and June. How was he sure that Bernard didn't have the 18th or 19th? Which eliminated those two months. Bernard then says I know too.
Which leaves the following
July 14 16
Aug 14 15 17
Keep in mind Albert has no dates only the month, but states he knows the answer now.
Which eliminates the 14th. What's the only month left with one date. July 16th
The 14th is eliminated because Bernard knows the month after May and June are implicitly eliminated with Albert's earlier-stated certainty. If Bernard was told the 14th, he wouldn't yet know because it could be July or August.
Ok my brain hurts - But I vote for Aug 17
Assumption 1 - If Cheryl had whispered 18 or 19 there would be no discussion we know it is either May 18th or June 19th as Bernard could have figured that out. (and he later admits he couldn't figure it out at first)
When Bernard does not figure that out -
Assumption 2 if Albert had been told June he would have been able to deduce it was June 17th, but he didn't so we can eliminate June as his month.
Next - Albert: "I don't know when your birthday is, but I know Bernard doesn't know, either."
Currently this leave us with 7 Dates
May 15 16
July 14 16
Aug 14 15 17
If albert was told may july or august he could not determine the correct date. Using the same logic Bernard knows that June is eliminate as well
If he had 14 15 or 16 he still would not be able to determine the date, but he claims he can, so he must have been told 17.
Once he claims he knows it - Albert eliminates the other dates as well.
The assumption that Bernard does not proclaim the answer before Cheryl asks Albert if he knows.
We don't know if Bernard means the 16th or the 17th UNTIL AFTER Albert says he knows.
Albert can only know what day because it has to be a month remaining that has no possible choices, and that is July 16th, for if Bernard was told the 14th, August would still be in play and Bernard wouldn't have said "I now know".
The NY Times explanation is very clear and, of course, correct.
This was a fun problem to solve but not especially tough if you examine the clues one at a time and work out the result.
I usually find that the sort of "math" puzzle that goes viral is usually lame but this one was fun. It's more fun though to see people argue about it when the logic is airtight.
This was a fun problem to solve but not especially tough if you examine the clues one at a time and work out the result.
I usually find that the sort of "math" puzzle that goes viral is usually lame but this one was fun. It's more fun though to see people argue about it when the logic is airtight.
let me give it a shot
Albert knows Bernard does not know because Bernard knows it is not May or June and only May and June have a singular day that is not repeated in another month
(19 and 18) so we can eliminate May and June
we have the problem one third solved
When Bernard says I know now that eliminates the 14th as both july and august has the 14th ( if Bernard said I do not know now the answer would be the 14th but only Albert would know the month)
problem two thirds solved as 3 days left July 16 and August 15 and 17
when albert says I know now it has to be july because it has only one day left in it whereas august has two and if it was in august albert would not know which of the two days it was
Great fucking puzzle
Albert knows Bernard does not know because Bernard knows it is not May or June and only May and June have a singular day that is not repeated in another month
(19 and 18) so we can eliminate May and June
we have the problem one third solved
When Bernard says I know now that eliminates the 14th as both july and august has the 14th ( if Bernard said I do not know now the answer would be the 14th but only Albert would know the month)
problem two thirds solved as 3 days left July 16 and August 15 and 17
when albert says I know now it has to be july because it has only one day left in it whereas august has two and if it was in august albert would not know which of the two days it was
Great fucking puzzle
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This was a fun problem to solve but not especially tough if you examine the clues one at a time and work out the result.
a lot of people would not figure it out and some never understand the answer
if you figured it out give yourself credit
Bernard knew it was the 16 which also showed up in May. Once may was eliminated by Albert's comment, he had the exact date so it couldn't have been the 14th.let me give it a shot
If Cheryl told Bernard 18 or 19 he would know the month for only May has 19 and only june has 18
Bernard said he did not know originally so it cannot be may or june
we have the problem one third solved
When Bernard says I know now that eliminates the 14th as both july and august has 14th ( if Bernard said I do not know now the answer would be the 14th but only Albert would know the month)
problem two thirds solved as 3 days left
when albert says I know now it has to be july because it has only one day left in it whereas august has two and if it was in august albert would not know which of the two days it was
Great fucking puzzle
yesBernard knew it was the 16 which also showed up in May. Once may was eliminated by Albert's comment, he had the exact date so it couldn't have been the 14th.
that is the reasoning
I figured it out, but my head is still spinning
The question was meant for the better high school students competing in the Math Olympiad
from http://www.vox.com/2015/4/15/8420577/cheryls-birthday-singapore-math
Eliminating the dates that are in both July and August knocks out the 14th. That leaves three possible birthdays out of the original 10: July 16, August 15, or August 17.
But now Albert knows, too. That means Cheryl must not have told him she was born in August, because he'd still be confused; two of the possible dates are in August. The only remaining possibility is July 16.
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let me give it a shot
If Cheryl told Bernard 18 or 19 he would know the month for only May has 19 and only june has 18
Bernard said he did not know originally so it cannot be may or june
we have the problem one third solved
When Bernard says I know now that eliminates the 14th as both july and august has 14th ( if Bernard said I do not know now the answer would be the 14th but only Albert would know the month)
problem two thirds solved as 3 days left
when albert says I know now it has to be july because it has only one day left in it whereas august has two and if it was in august albert would not know which of the two days it was
Great fucking puzzle
That's exactly right.
