Do you know Cheryl's birthday? Math problem stumps Internet

Ok, I clicked on the picture one. Unless I'm missing something (entirely possible), that's not a math problem; it's a logic problem. I'd think it was me, but I took the SATs, which featured mostly logic problems they called math problems, though none this Marilyn Vos Savant dippy. I feel like I've got her name wrong somehow.

I'm also going with that 'respectively' means told the one guy the month and the second the day, though the translation is a bit iffy but if that's not it, I have no clue wtf to do.

Ok so... I'll white out so as not to spoil in case I'm right?

If A knows B doesn't know, then he knows it's not June, because that month is the only one with an 18 date, so if she'd said 18, that'd have to be it, or May, because see 19.

So it has to be July or August. So then B says he knows - if he realizes that A knows he, B, didn't know because of the above, then he can only immediately know if it's July 16, because that's the outlier of the remaining dates. Is that right?

May 15. She's obviously so Taurus, you guys!

Logically, Albert and Bernard should just communicate with each other more directly.

It's not a math problem, it's a grammar problem.

I don't trust Cheryl, if that's even her real name.

July 16th

It's a logic problem, and you solve it by eliminating the unique answers, then the ambiguous ones.

Albert knows the Month
Bernard knows the Day

It cannot be June 18 or May 19 because these are the only 18 or 19 and so Bernard could not have been given that DAY or he would know. Albert knows Bernard doesn't know, so we cross off the 18th and 19th.

Bernard knows it's not June, because the 18th is eliminated and Albert still doesn't know. Albert would know because he knows the month. Albert knows it's not May, so it must be July or August.

Since the 14th could be in either month, it's out.

The 15th and the 17th would mean Albert doesn't know - cause he knows the month - so eliminate those.

Leaves only July 16th

Dude. Spoiler.

It's logic - and I get the same answer as cornflake. All three statements are essential.

I understand the solution and the why behind it, but the problem is wrong. It allows that Bernard knows Cheryl's birthday because Albert does not know, first and foremost. Forget the third statement. Bernard's certainty comes before that. And that's logically impossible. His certainty is predicated on the assumption that Albert will also know once he knows.

There's probably a way to structure the problem correctly, though.

Of course Albert and Bernard take a woman's birthday and make it all about the men.

Notice how Cheryl declines to give them the year? Typical woman...

Maybe if Albert and Bernard weren't such ageist bastards, Cheryl would have given them the year.

It's not like they're going to remember her birthday, anyway...

robeiae said:

I understand the solution and the why behind it, but the problem is wrong. It allows that Bernard knows Cheryl's birthday because Albert does not know, first and foremost. Forget the third statement. Bernard's certainty comes before that. And that's logically impossible. His certainty is predicated on the assumption that Albert will also know once he knows.

There's probably a way to structure the problem correctly, though.

Click to expand...

Yes, Bernard knows the birthday after the first statement. Albert knows after the second statement. The reader only knows after the third statement.

The problem (good catch) is not with Bernard's certainty; it's with Albert's. Bernard's statement doesn't narrow down his options at all. But if we accept that Albert does end up knowing, we can solve.

poetinahat said:

Yes, Bernard knows the birthday after the first statement. Albert knows after the second statement. The reader only knows after the third statement.

The problem (good catch) is not with Bernard's certainty; it's with Albert's. Bernard's statement doesn't narrow down his options at all. But if we accept that Albert does end up knowing, we can solve.

Click to expand...

But Bernard's statement does narrow down Albert's options, because Albert knows the birthday is in July.

Albert knows July. Bernard knows 16th. Once Albert lets on that the month is not one with a unique day in it, Bernard knows the 16th must be in July because it can no longer be in May. And once Bernard knows that the month is July, Albert knows that the date has to be the 16th. Because there are only two dates in July--the 14th and the 16th. If Bernard had been given the 14th, he wouldn't know whether the month was July or August. Since Bernard knows it's July, then the date must be the 16th.

Agreed. After step 1, I'd overlooked Albert's knowing the month. Nice work.

I get how it's solved, but I've never been a fan of such illogical logic questions. It doesn't make sense that she would make a game out of it like this. It's like the question maker has never seen how people actually interact before.

Also, it doesn't say if Cheryl specifically told them what thing she told the other person. For all they know, she could have said anything to the other guy.

And finally the question assumes that Cheryl didn't purposefully make it confusing and try to trip them up.

Shadow Dragon said:

Also, it doesn't say if Cheryl specifically told them what thing she told the other person. For all they know, she could have said anything to the other guy.

And finally the question assumes that Cheryl didn't purposefully make it confusing and try to trip them up.

Click to expand...

Oh, sure, because all women are deceitful and malicious. The misogyny in this thread appalls me.

Cheryl was dealing as best she could with those two sexist, ageist bastards, and yet she gets nothing but abuse from you people.

Celia Cyanide said:

It's not a math problem, it's a grammar problem.

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My grammar says she didn't do it.

That's not math. It's a logic problem, like the door where one guard lies and the other tells the truth.

And I'm going to go with July 16 as the answer.

Myrealana said:

That's not math. It's a logic problem, like the door where one guard lies and the other tells the truth.

Click to expand...

Yes. The difference is that the above problem makes it clear who has what knowledge.

Again, this problem proceeds from an assumption with regard to Albert's initial claim on the part of Bernard. The certainty is assumed, not stipulated. So the problem remains wrong, imo.

Certainly, if the assumption is taken as a given, a symbolic representation of the problem has a valid solution (the one given). But the matter-of-fact-ness of the solution remains incorrect, with regard to the word problem.

/pointless nitpicking

robeiae said:

Yes. The difference is that the above problem makes it clear who has what knowledge.

Again, this problem proceeds from an assumption with regard to Albert's initial claim on the part of Bernard. The certainty is assumed, not stipulated. So the problem remains wrong, imo.

Certainly, if the assumption is taken as a given, a symbolic representation of the problem has a valid solution (the one given). But the matter-of-fact-ness of the solution remains incorrect, with regard to the word problem.

/pointless nitpicking

Click to expand...

Nah, take another look. There are no assumptions.

Albert and Bernard have only two possibilities each:

Albert knows the month is July. There are only two dates given for July, so he knows Cheryl's birthday is either July 14th or July 16th.

Bernard knows the date is the 16th, so the only two possibilities for him are May 16th or July 16th.

Albert knows the month is July, so he knows Bernard must have been given either the date of the 14th or the 16th. Therefore, he knows Bernard cannot know Cheryl's birthday for certain, because both of those dates appear in more than one month. He says, with absolute knowledge that although he doesn't know Cheryl's birthday, neither does Bernard.

Bernard's only choices had been May 16th or July 16th. When Albert is certain that Bernard cannot know Cheryl's birthday, Bernard now knows that the month cannot be May. Albert just told him it cannot be May. It cannot be May because May includes a date that does not appear in any other choice for month. With May excluded, Bernard now knows that Cheryl's birthday is July 16th. He tells Albert he knows when Cheryl's birthday is.

Albert's only choices had been July 14th or July 16th. If Bernard had been given the 14th, Bernard still wouldn't know Cheryl's birthday, because there's also a 14th given for August. The fact that Bernard knows for certain when Cheryl's birthday is means that the date has to be the 16th. So now they both know Cheryl's birthday.

Does that help?

Marlys said:

Does that help?

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No. I understand it perfectly. My issue is with the way the problem is set up. Again, Bernard's certainty is taken as a given.

But it's okay. The problem is still a fair test of logic. One just has to know what is being assumed, as in all things.

robeiae said:

No. I understand it perfectly. My issue is with the way the problem is set up. Again, Bernard's certainty is taken as a given.

But it's okay. The problem is still a fair test of logic. One just has to know what is being assumed, as in all things.

Click to expand...

I guess I'm just not seeing your problem with the set up. What assumptions? Everything Albert, Bernard, and the reader need to know to solve the puzzle is stated in black and white right in the problem.

On what basis does Bernard assume Albert's statement is a consequence of analysis beyond what is given?

Albert is told the month. He knows that. And (frankly, we assume here, too) he knows Bernard has been told the day. Albert can proceed to the statement that he makes on this basis alone: he knows he does not know Cheryl's birthday (because he only knows the month) and he knows Bernard does not know the birthday (because Bernard only knows the day). No matter what the actual birthday is, the above is correct as an initial postulation.

In order to solve the problem, that postulation has to be ignored in favor of one wherein Albert has considered the consequences of what Bernard knows before making his statement. Bernard's statement assumes a level of certainty in Albert's statement that is not a given--is not necessary--for Albert to have.