The Math Problem That Has Stumped the Entire Internet

[oldjones]

Isn't there a step missing. How does he eliminate the August dates.

There's more than one possible day in August, which would mean Bernie could not know the date, if it was in August. Therefore it must be July.

 

[MissCroft]

Simpler answer
Don't be friend with Cheryl. Because Cheryl is an asshole of a friend..

LMAO She does sound like a bit of an asshole.


I agree it's more of a logic question than a math question, and while I'm usually good with logic questions, this one makes my head hurt.

 

[GPIDEAL]

Yes you can eliminate those months. Albert KNOWS that Bernard doesn't know the date. How can he know that?

He had to have been told a month where EVERY day was duplicated in another month, and the only months like that are July and August. If Albert had been told May or June then it is possible Bernard heard a unique day and knows her birthday, but Albert says that isn't the case. So, he wasn't told May or June, he was told July or August.

That enabled Bernard to figure out it was July or August which was enough information for him to figure out her birthday. Which proves he wasn't told 14, since in that case he wouldn't be able to figure it out.

After that is where I got stuck. I had to read the answer to understand that it can only be July.

I'm re-thinking this again now, and I used a matrix this time.

1. If Albert was told May, Bernard's silence doesn't mean you can exclude May because he could've been told it was either the 15th or 16th, which occur in other months (August and July, respectively). We know Bernard wasn't told the 19th, a unique day, wherein the solution is self-evident. Therefore, Albert knows that Bernard has more choices and has no other way of narrowing down his options. (IOW, he KNOWS that Bernard can't know).

2. If Albert was told June, then Bernard's silence means he wasn't told the 18th, being a unique day, in which case Albert would immediately proclaim the answer. Since Albert admits to still not knowing, it can't be June, which is the only month we can exclude.

3. If Albert was told July, the birthday can be either the 14th or 16th, so he still doesn't know. Bernard is silent because he could've been told the 14th, 15th, 16th and 17th, each occurring in 2 months. His comment can't narrow down the possibilities.

4. If Albert was told August, it can be either the 14th, 15th and 17th. Just like point 3., Bernard's silence or comment doesn't exclude the possibilities.

Why would their presumptuous comments foretell the solution? Am I missing something here?

 

[MissCroft]

I'm re-thinking this again now, and I used a matrix this time.

1. If Albert was told May, Bernard's silence doesn't mean you can exclude May because he could've been told it was either the 15th or 16th, which occur in other months (August and July, respectively). We know Bernard wasn't told the 19th, a unique day, wherein the solution is self-evident. Therefore, Albert knows that Bernard has more choices and has no other way of narrowing down his options.

2. If Albert was told June, then Bernard's silence means he wasn't told the 18th, being a unique day, in which case Albert would immediately proclaim the answer. Since Albert admits to still not knowing, it can't be June, which is the only month we can exclude.

3. If Albert was told July, the birthday can be either the 14th or 16th, so he still doesn't know. Bernard is silent because he could've been told the 14th, 15th, 16th and 17th, each occurring in 2 months. His comment can't narrow down the possibilities.

4. If Albert was told August, it can be either the 14th, 15th and 17th. Just like point 3., Bernard's silence or comment doesn't exclude the possibilities.

Why would their presumptuous comments foretell the solution? Am I missing something here?

Don't you have work to do? Get back to work!

 

[GPIDEAL]

IMO, every step of the thing falls out just fine, logically, without our having to know any (unwritten) rules.

Albert knows the month but not the day

Bernard knows the day but not the month.

If the day is 18, Bernard, who knows the day, can immediately pin down the month as being june. The same if the day is 19 -- Bernard can immediately pin down the month as may.

But Albert, who knows the month, reports that he knows that Bernard does not know the month.

Bernard deduces, from this report, that the month must be july or august, because, if the month were may or june, Albert (who knows the month) could not be certain that Bernard could not pin the month.

So at this point, Albert has deduced that the day is 14, 15, 16, or 17, and Bernard has deduced that the month is july or august.

Next, Bernard reports that he now knows the month.

Now, day 14 is available in both july and august. Therefore, if the day were 14, Bernard would not be able to tell between july and august. But Bernard has reported that he can pin down the month. So Albert knows the day is not 14. That leaves 15, 16, 17 as the possible days.

But Bernard now knows the month. If the day is 15, Bernard cannot pin the month, because 15 appears on Cheryl’s list in both july and august. The same is true of 17, which also appears in both july and august. Only if the day is 16, can Bernard pin the month, i.e july, because 16 appears only in july.

So Albert can deduce, from the fact that Bernard says he knows the month, that the day must be 16.

In other words, Cheryl’s birthday is july 16th.

Every step follows in logical sequence as the new facts are laid out.

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.

 

[GPIDEAL]

Don't you have work to do? Get back to work!

I'm having my chocolate and tea break darling. (Wish I can break away to be with you girl).

 

[fuji]

I'm re-thinking this again now, and I used a matrix this time.

1. If Albert was told May, Bernard's silence doesn't mean you can exclude May because he could've been told it was either the 15th or 16th

You haven't understood the "trick". Bernard's silence isn't relevant, Albert knows Bernard doesn't know her birthday based only on information known to Albert. If Bernard said he knew, Albert would know someone is lying.

Albert knows the month, and based on that SPECIFIC month, he can see that no matter what date Bernard heard, Bernard doesn't know the date. That is because the month Albert has been told does not include any days like 18 or 19 that are definitive.

Put it another way:

Bernard CAN'T have been told 18 or 19 because at Albert can see that July doesn't contain 19, July only contains days that would all leave Bernard unsure. If Albert had been told May, then he couldn't be sure whether Bernard knows or not, because one of the days in May is a gimme.

 

[MissCroft]

You haven't understood the "trick". Bernard's silence isn't relevant, Albert knows Bernard doesn't know her birthday based only on information known to Albert. If Bernard said he knew, Albert would know someone is lying.

Albert knows the month, and based on that SPECIFIC month, he can see that no matter what date Bernard heard, Bernard doesn't know the date. That is because the month Albert has been told does not include any days like 18 or 19 that are definitive.

Put it another way:

Bernard CAN'T have been told 18 or 19 because at Albert can see that July doesn't contain 19, July only contains days that would all leave Bernard unsure. If Albert had been told May, then he couldn't be sure whether Bernard knows or not, because one of the days in May is a gimme.

My head really hurts.

 

[GPIDEAL]

You haven't understood the "trick". Bernard's silence isn't relevant, Albert knows Bernard doesn't know her birthday based only on information known to Albert. If Bernard said he knew, Albert would know someone is lying.

Albert knows the month, and based on that SPECIFIC month, he can see that no matter what date Bernard heard, Bernard doesn't know the date. That is because the month Albert has been told does not include any days like 18 or 19 that are definitive.

Put it another way:

Bernard CAN'T have been told 18 or 19 because at Albert can see that July doesn't contain 19, July only contains days that would all leave Bernard unsure. If Albert had been told May, then he couldn't be sure whether Bernard knows or not, because one of the days in May is a gimme.

Silence from both guys is relevant to US in ascertaining that June can be excluded for either the 17th or the 18th.

That is, we can exclude June, and only June, based on the reactions of Albert and Bernard (Bernard would've immediately figured out June if he was told 18 - and if Albert was told June but without any reaction from Bernard, he would've immediately deduced it to be the 17th, which he failed to do and even admitted he still didn't know after Bernard was given a date).

We still can't exclude May, which has two days remaining that occur in other months. If there was only one other day to choose from in May, then we can exclude it like June, based on their reactions.

How do you know that Albert wasn't told May? There are two dates there, the 15th and the 16th (which occur in August and July, respectively, and that's why Bernard can't know the month). Albert can't know which of those two days are Cheryl's birthday.

Bernard could've been told the 14th, 15th, 16th and 17th.

(I haven't looked at the 'solution').

 

[IM469]

My head really hurts.

Mine too. Too many assumptions - it assumes that given a unique day Bernard is smart enough to recognize the month ... he could be an idiot ..

I think we need a teacher to explain it...

 

[fuji]

How do you know that Albert wasn't told May?

Because if he were told May he couldn't be sure that Bernard doesn't know her birthday.

If he was told May, Bernard could have been told any of 15, 16, or 19. In that case there is a chance Bernard knows her birthday, it could be May 19. But Albert said he is sure Bernard doesn't know so it can't be May.

Specifically, for the month Albert was told every listed day had a duplicate in another month. This is how he is sure Bernard doesn't know.

Only if Albert were told June or July can he be SURE that Bernard doesn't know. In June and July any of the days have another month possible. So Albert must have been told June or July.

You are getting hung up on silence, the problem can be solved without considering silence. It can be solved by considering only the information explicitly carried by their statements.

 

[benstt]

But Bernard now knows the month. If the day is 15, Bernard cannot pin the month, because 15 appears on Cheryl’s list in both july and august. The same is true of 17, which also appears in both july and august. Only if the day is 16, can Bernard pin the month, i.e july, because 16 appears only in july.

Buttercup, you are really close, bute note that the 15th is in both May and August, and the 17th appears in both June and August. (You put them both in July.) May and June are eliminated by this point.

 

[red]

Oh- is it july 16th? (pretending I didn't read the answer already)

 

[benstt]

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.

 

[Kilgore Trout]

This whole riddle hinges early on on whether it is justified to toss out all 5 dates in May and June because if you can do that the problem is easy to solve.

This thing from vox.com gives the best explanation on why it is okay to toss out everything from May and June even though it feels wrong.

Basically the only way Albert can know for one million per cent certain that Bernard doesn't know the date is because Albert was given either July or August as the month by Cheryl.

Once Bernard figures out that this is what Albert is saying to him in opening remarks the solution is easy.

http://www.vox.com/2015/4/15/8420577/cheryls-birthday-singapore-math

 

[GPIDEAL]

Buttercup, you are really close, bute note that the 15th is in both May and August, and the 17th appears in both June and August. (You put them both in July.) May and June are eliminated by this point.

16 appears in May too, not just July.

I can see how June is eliminated because we know it's not June 18th (a unique day that gives away the month), otherwise Bernard would say so, but since he didn't, then Albert would have said so, had he been told it was June, because it can only be the 17th.

But if Bernard is told the 15th, he doesn't know whether it's May or August.

If Albert is told May, he doesn't know if it's the 15th or the 16th. So how can one eliminate May in this scenario?

 

[benstt]

16 appears in May too, not just July.

I can see how June is eliminated because we know it's not June 18th (a unique day that gives away the month), otherwise Bernard would say so, but since he didn't, then Albert would have said so, had he been told it was June, because it can only be the 17th.

But if Bernard is told the 15th, he doesn't know whether it's May or August.

If Albert is told May, he doesn't know if it's the 15th or the 16th. So how can one eliminate May in this scenario?

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.

 

[GPIDEAL]

Because if he were told May he couldn't be sure that Bernard doesn't know her birthday.

If he was told May, Bernard could have been told any of 15, 16, or 19. In that case there is a chance Bernard knows her birthday, it could be May 19. But Albert said he is sure Bernard doesn't know so it can't be May.

Specifically, for the month Albert was told every listed day had a duplicate in another month. This is how he is sure Bernard doesn't know.

Only if Albert were told June or July can he be SURE that Bernard doesn't know. In June and July any of the days have another month possible. So Albert must have been told June or July.

You are getting hung up on silence, the problem can be solved without considering silence. It can be solved by considering only the information explicitly carried by their statements.

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.

Other than June as previously resolved, your explanation doesn't reduce the possibilities.

 

[maurice93]

Without even checking, I'm going July 16.

When Albert says "I don't know when your birthday is, but I know Bernard doesn't know, either."
- Bernard would know if the Number was 18 or 19
- The month can't be May or June (where 18 and 19 exist)
- The month must be July or August
When Bernard says "I didn't know originally, but now I do."
- He knows it's in July or August based on the above
- If the number were 14 he wouldn't know, so it must be 15, 16 or 17
- That leaves July 16, August 15 and August 17
- At this point Bernard knows (16 = July 16)
When Albert says "Well, now I know, too!"
- If he had August as a month he wouldn't know, so he must have July. He knows it isn't the 14th (or Bernard wouldn't know) so it must be the 16th

Cool story bro

 

[red]

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.

Other than June as previously resolved, your explanation doesn't reduce the possibilities.

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.