NFT: When is Cheryl's Birthday?

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In comment 12234850 yatqb said:

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Incorrect.

but I found this out very, very easy.

In comment 12234907 dep026 said:

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but I found this out very, very easy.

So what's the answer, hotshot?

July 16

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I could get through high school in Singapore

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Correct May & June are eliminated due to having days that are not associated with other months. July & August have 14s that leave July with one date and August with two dates. Therefore the one date in July is Cheryls birthday. July 16.

Just saw the answer. The flaw is Albert. Just because Bernard figured it out, leaving 7/16, 8/15 or 8/17, doesn't mean Albert would know which one....

In comment 12235049 WideRight said:

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Just saw the answer. The flaw is Albert. Just because Bernard figured it out, leaving 7/16, 8/15 or 8/17, doesn't mean Albert would know which one....

Albert knew that Bernard figured it out. Bernard knew the month. If it was August, Bernard could not have know if it was 8/15 or 8/17. Therefore because Bernard knew, it had to be July where there was only one option. Albert could figure that out.

15, 16 or 17 would have allowed Bernard to figure it out

???

July is correct, but now I say 16th

1) "I know Bernard doesn't know" --> the month that Albert was told has no dates that are unique to strictly that month. July and August fit that description. May and June each have one day found in no other month.

2) "I didn't know before, but now I do" --> it must be a day that is not common between July and August. Only the 16th fits that description.

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Because Bernard doesn't know the date, when he tells Albert he doesn't know that tips Albert of that it can't be June 17

(if Bernard were told it was June, he'd know it was June 17th, because it couldn't be 18 or else Albert would know it-there's only one 18 date, June 18).

But if Albert were told 17, he can't be sure if it is June or August. But once he knows that Bernard also doesn't know, then he knows it can't be June (because, as above, if it were June, then the date would have to be June 17th and Bernard would know the birthdate).

So once Albert says know I know (because he now knows it's August), Bernard also knows its the 17th, it's the only date in that month that would have tipped Albert off of what month it is.

Sorry that sounds like total gobbledy gook.

Albert knows the month, Bernard knows the day.

There are sites that provide the way(s) to arrive at that date

I was assuming that both guys new that each didn't know the date prior to their little conversation. If that's the case then August 17th.

But if Albert didn't know one way or the other if Bernard know, then he couldn't rule out Bernard being told "18" or "19" so if for argument's sake, if Albert were told "May" he couldn't truthfully say "I don't know, but I know that Bernard also doesn't know"

trick question

In comment 12234836 Jints in Carolina said:

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LOL

Albert told the month. He is looking for the day.
Bernard told the day. He is looking for the month.

1. Albert claims: Bernard doesn't know.
Eliminate May and June
The only way Albert can make the claim that he knows that Bernard doesn't know is if Albert were told a month in which every possible date in that month appeared in another month as well. That eliminates May and June.

For example, if Albert were told "May," then he couldn't possibly say definitively that Bernard didn't know the birthday, because if it were May, then Bernard would have been told "15th," "16th" or "19th" and if Bernard would have been told the "19th," then Bernard would know the birthday.

So Albert could not have been told May. The same goes for June.

2. Bernard claims: I didn't know, but now I know.
Upon hearing Albert's comment that Bernard couldn't possibly know just from hearing the date, Bernard can now use the same logic as Albert to eliminate May and June because Albert provided the clue that it can't be a month that has a unique date (May and June).

"But now I know"
Eliminate July 14 and August 14. Bernard is still only told the day, so if he were told "14," then he stil would not know the birthday because there is nothing to distinguish between July and April.

This leaves 3 dates: July 16, August 15, August 17. So whichever number Bernard was told, he now knows the birthday.

3. Albert claims: "Then I also know when Cheryl's birthday is"

Keep in mind this whole time that Albert was told a specific month. In step 1, we eliminated May and June, so we know that Albert was told July or August.

When Bernard knew the birthday, that indicated to Albert that it could not have been the 14th, so Albert no knows that Bernard had three choices: July 16, August 15, August 17.

If Albert were told August, he STILL would not know when Cheryl's birthday is, becuase there is nothing to distinguish the 15th from the 17th.

So, the only way for Albert's comment to be true, is if he were told July, because he knows that only the 16 remains as a possible date.

Hence, the birthday is July 16.
=---------

In the end it's about remembering what each knew and what each had to find out.

If Bernard was told August 15 th or 17th, his statement would still be true, and Albert wouldn't know.

So there really isn't anyway Albert actually knew, but since he says he does, and he doesn't lie, I guess it makes sense.

My reasoning:
1. Albert knows Bernard doesn't know - means its not the 18th or 19th as those were unique dates.
2. Albert doesn't know despite knowing Bernard doesn't know - after striking the 18th and 19th, Albert doesn't know - so that eliminates June 17th as that is the only remaining day in June. Albert knows the month so if it were June he'd know it was teh 17th after eliminating the 18th in #1.
3. After hearing Albert's assertions in 1 and 2, Bernard now knows the date - this told me there was a unique date remaining, one date in only one month. The only date that met that criteria was August 17th.

I'll give it more thought later and see where I went wrong.

My brain must be deteriorating in old age. I got August 17.

...neither knows the date after Cheryl tells them information AND both guys know the other guy doesn't know the other doesn't know the date after Cheryl gives the information. (That's what I initially assumed)

However, IF Albert doesn't know one way or the other what Brendan knows, when Albert isn't told May or June then he knows Brendan can't know the date. In other words, if Albert was told "May", as far as he knows Albert might have been told "19" which would mean that Albert knows the birthday. But since Albert wasn't told "May" or "June" then Albert knows that Bendan can't know the date.

In comment 12235447 WideRight said:

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If Bernard was told August 15 th or 17th, his statement would still be true, and Albert wouldn't know. So there really isn't anyway Albert actually knew, but since he says he does, and he doesn't lie, I guess it makes sense.

This part seems to be tripping up a lot of people. Keep in mind that both Albert and Bernard have more information than we do. Think of it this way: Bernard could NOT have been told August 15 or 17 (specifically, Bernard would only be told "15" or "17"). Here is why:

Bernard was able to eliminate May and June because of Albert's comment (see above posts for explanation as to that if that doesn't make sense).

While we as readers are then left with five choices (July 14, July 16, August 14, August 15, August 17), Bernard is only left with AT MOST two choices because remember, Bernard has known the date the entire time/.

So if Bernard says that he knows Cheryl's birthday, it means that the number he was told, is not in both July and August, thereby eliminating July 14 and August 14.

This leaves July 16, August 15, August 17 as possibilities for us readers. We as readers do not know Cheryl's birthday yet, but Bernard does because he was either told 16 (=July 16), 15 (=August 15) or 17 (=August 17).

We still don't know. But Bernard knows.


From Albert's perspective: He knew the month the entire time. So Albert was either told May, June, July or August, meaning that no matter what, he only had two or three dates to have to figure out.

Albert's first comment that Bernard can't know meant that we (and Bernard) now know that Albert was not told May or June. So we (and Bernard) know that Albert was told July or August. We (and Bernard) don't yet know which month Albert was told, but Albert has always known this.

If Albert were told July, then he would have had to decide between the 14th and the 16th. If Albert were told August, he would have had to decide between the 14th, 15th and 17th.

To Albert (and to us) Bernard's exact knowledge meant that it can't be the 14th (otherwise Bernard wouldn't know whether 14 meant July 14 or August 14).

So now, if Albert had been told July, the birthday is July 16. If Albert had been told August, the birthday would either be August 15 or August 17. But it's not like Albert could have been told either one of these months. Cheryl has one specific birthday and she told him exactly the month it was in.

Albert has known the exact month the entire team. He doesn't have to choose between July and August. He knows for a fact that it is either July or August.

So, when he makes the comment that he now knows Cheryl's birthday, the only possible way for him to know that is if he were told from the outset that the birthmonth is July.

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it's the 16th. That also happens to be my birthday. But, because the 16th is the only date that doesn't show up in other answer choices, it's got to be correct. Every other date and every month show up more than once, but once the date is revealed, both boys know the answer.

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Based on Albert’s first statement, you can rule out May 19, June 17 and June 18. You can’t rule out all of May.
Based on Bernard’s first statement, the day has to be the 17th and the only day left with the 17th is August 17th. If it was another day, he wouldn’t know.
Based on Albert’s second statement, he knows Bernard can only be sure of the birthday if it’s on the 17th, since that’s the only day left.

I’m not sure you can look at the three statements purely sequentially. I found myself looping back and forth between them to arrive at the answer.

In comment 12236034 RB^2 said:

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You can’t rule out all of May.

That's where I seemed to stray from Paul and others. I ruled out the one day in May, all of June, but not the other 2 days in May. When I have a bit more time to think through it, I will see where I got off track.

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lies about her age

In comment 12236034 RB^2 said:

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Based on Albert’s first statement, you can rule out May 19, June 17 and June 18. You can’t rule out all of May. Based on Bernard’s first statement, the day has to be the 17th and the only day left with the 17th is August 17th. If it was another day, he wouldn’t know. Based on Albert’s second statement, he knows Bernard can only be sure of the birthday if it’s on the 17th, since that’s the only day left. I’m not sure you can look at the three statements purely sequentially. I found myself looping back and forth between them to arrive at the answer.

Of course the statements are sequential. It's a conversation.


Albert is told ONLY the month. He is told, May, June, July, or August. he is told only one month and no other information.

Bernard is told ONLY the day. He is told 14, 15, 16, 17, 18, or 19 and no other information.

Albert thinks about the month he was given and says "I don't know when Cheryl's birthday is, but I know that Bernard does not too"

The first part of the sentence is obvious. From only knowing the month, Albert does not know Cheryl's birthday. The second part is the clue. The only way Albert can know with certainty that Bernard doesn't know the exact birthday (rather, the month) with only a number, is because Albert looked as possible dates in the month Cheryl told him, and saw that they all appeared in other months as well. Again, in the month Cheryl told him, Albert does not know which date she then told to Bernard. Thus, we now know that Cheryl either told Albert July or told Albert August because for either of these months, no matter what day Cheryl told Bernard, Albert know it wouldn't be sufficient information to reveal the entire birthday.

Albert couldn't make that claim if she told him May because Albert can't rule out that Cheryl told Bernard 19 which would immediately alert him to the exact birthday.

The same logic applies to why Albert could not have been told June, because he couldn't rule out "18" and therefore could not guarantee that Bernard didn't know the answer immediately.

Bernard confirms that it wasn't May 19 or June 18 when he says "At first I don't know when Cheryl's birthday is..."

Here, Bernard only has a date. He has a 14, a 15, a 16, or a 17. He knows the number, but we don't. But he also doens't know the birthday because all of these numbers appear in other months.

However, thanks to Albert's first statement that he knows Bernard can't know, Bernard is also able to eliminate May and June the same way that we (readers) are able to eliminate May and June.

Now, Bernard knows the exact birthday and is able to finish his statement (after Albert's) with "but now I know).

In order for Bernard's statment to be true, it means that he could not have been told a number that appears in both July and August, which means that Bernard was NOT told 14.

So Bernard knows the birthday because 15 only appears in August, 16 only appears in July, and 17, only appears in August. So he knows the birthday. It's just that we the readers don't yet know.

AFTER HEARING BERNARD SAY HE KNOWS THE BIRTHDAY, Albert says "Then I also know when Cheryl's birthday is."

Albert has known this whole time whether it was July or August because Cheryl either told him July or August.
We, the readers, don't know whether Albert was told August and is debating between August 14/15/17 or was told July and is debating between July 14/16.

But now, because Bernard knows, Albert (and we) can eliminate the 14th since it is in both months.

So, Albert was either told July at the beginning and knows it is July 16, or was told August at the beginning and narrowed it down to August 15/17. But Albert JUST said that he knows the exact birthday, which means that he must have been told July. Otherwise, he couldn't make that statement.

and explained, paul

are given.

And Cheryl should have just told us when her fucking birthday is.

is a tease