Main content

## Math for fun and glory

### Course: Math for fun and glory > Unit 2

Lesson 1: Brain teasers- Cheryl's birthday
- Heavier ball
- Liar truth-teller brain teaser
- Toggler brain teaser
- Alien abduction brain teaser
- Blue forehead room brain teaser
- Blue forehead room solution
- Forehead numbers brain teaser
- Light bulb switching brain teaser
- Path counting brain teaser
- 3D path counting brain teaser

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Cheryl's birthday

Deductive reasoning problem from Singapore.

## Want to join the conversation?

- Can you please make it more clear because I didn't understand how it became July 16?(2 votes)
- Sorry, but June 16th was not even in the question. The answer is June 18th.(0 votes)

- Why doesn't Cheryl just tell them her birthday instead of making them have a hard time guessing. Or why don't Albert and Bernard just share their information to figure out the month and day of her birthday. Isn't it simpler that way?(5 votes)
- Cheryl wants to give Albert and Bernard a challenge. What would be the point of giving them a problem if she is just going to give them the answer?(4 votes)

- In the top left corner, there is a 24.

Are there any other Deductive reasoning problems that Sal was given?(3 votes)- The 24 represents that it was problem number 24 on a math test. The other questions were not based in pure logic.(4 votes)

- How do you know when you do the teaser that Albert knows that its not May or June?(3 votes)
- Since Cheryl only gave just one number of the day for May, and just one for June, if Bernard was given the month, he would already know her birtday, but Albert says that Bernard doesn't know when her birtday is(0 votes)

- At the end of the video, Bernard's list still has months to cross off, and did not reach a conclusion. How then does Bernard know Cheryl's birthday(2 votes)
- If Albert & Bernard are trying to determine the solution without giving each other any clues, why would they respond the way they did above and give each other the answer? If they were trying to determine the answer together, why didn't they just share what they knew?(2 votes)
- They were able to share what they knew, just indirectly. Since we know they're good logicians, and as friends they know they're both good logicians, they would probably know that the other would be capable of figuring out the answer based off of the indirect hints they give. Who says they can't challenge each other? =)(1 vote)

- How can Albert find out that the birthday is not on May 15th or 16th? I don't see how "i know that he does not know" implies that the month is not May. The fact that he only knows the date and not the month means that the day numbers that only exist once (i.e 19 May and 18 June ) are not her birthday days. I can't see how this fact correlates with her birthday not being in May. There are two more days in May for which Bernard has no information whatsoever.

My train of thought was the following :

-Albert knows that Bernard knows only the day.

-They both know all the possible birthdays.

-So Albert can take out all the day numbers that exist once because he knows that Bernard does not know.

-Then he can take out June because he knows the month and it has only 1 date, therefore if it was June he would know the birthday date.

-? ? ?(1 vote)- Albert can eliminate the months of May and June because he was told what month it was, and that month is not May or June. The reason
*we*can eliminate May is because Albert says that he knows Bernard does not know. Albert knows that Bernard doesn't know because Albert must have been given a month that doesn't include a day number that exists only once.(2 votes)

- I try to solve it myself but I don't know what to do and I don't know how you guess the numbers....(2 votes)
- Brain teaser based on Korean drama show My Daughter Geum Sa Wol:

So Kook-Ja (Grandma Emiko) baked 2 batches of Bum Bum Emiko Cookies.

They were both for her granddaughters. There was a batch of rainbow sprinkled cookies and a batch of chocolate chip cookies. Which batch was for Dalleh? Which batch was for Jjilleh?

Hints:

Both granddaughters love the colors of the rainbow.

The girls both have sweet tooths.

Be sure to watch My Daughter Geum Sa Wol TODAY from6:30PM to9:00PM!(1 vote)- I think that you could've added more information. Personally, Jjileh had sprinkles.(2 votes)

- This problem is an example of how simple statements which apparently have no information can solve a problem using astoundingly simple logic. Are there any more complex versions of such problems?(3 votes)
- I at least deduced that X and Y's values are both 2-49. The exchange between S and P is not that clear.(0 votes)

## Video transcript

- [Voiceover] So, this is a
fun deductive reasoning problem that's being forwarded
around the Internet. Several people have
actually forwarded it to me, and so, I thought it would be
a fun thing to work through. The grammar isn't perfect,
but the problem is a fun one. So, it says Albert and Bernard just, it should say became friends with Cheryl and they wanted to know
when her birthday is. Cheryl gives them a list
of 10 possible dates and we have our 10 dates here. Cheryl then tells Albert and
Bernard separately the month and the day of her birthday, respectively. So, just to make sure we're
parsing that sentence correctly, she gives Albert, she tells Albert the
month of her birthday. And she gives Bernard, she gives Bernard, the day of her birthday. And, I think we, it's fair
to assume that Albert knows, he's been given the month and he knows that Bernard's been given the day. And Bernard's been given the
day and he knows that Albert has been given the month. And we should also assume
that they are good logicians. That they are going to
do very logical things. And then, we have this dialogue. Albert says, I don't know
when Cheryl's birthday is, but I know that Bernard does not know too. That's fascinating. And then, Bernard says, at first I didn't know
when Cheryl's birthday is, but now I know, but now I know. Fascinating, and then Albert says, then I also know when
Cheryl's birthday is. So, when is Cheryl's birthday? So like always, pause the video. See if you can work
through this on your own. It's a fun problem to tackle, and I'll give you a little bit of a hint. Diagram out, write the
information that each, that Albert knows and
how does the world look from Albert's point of view. And then, write out how the world looks from Bernard's point of
view and then tell us, and then think about what these, what you can deduce from these sentences. So, I'm assuming you've had a go at it, so let's just do what I just said. Let's diagram out the world from each of their points of view. First, from Albert's point
of view, A for Albert. So, he's been given the month. so he's been given either
May, and if it's May, he says, well then if
it's May it's gonna be, the actual day is gonna be 15, 16, or 7, the 15th, 16th or 19th,
15th, 16th or 19th. He was told, or he was
told the month June. And if he was told the
month of June, then he says, well I don't know if the
date is 17 or 18, 17 or 18. If he was told the month of
July, if he was told July, he'd say, well I don't
know whether the date is the 14th or the 16th. And if he was told the month August, if he was told the month August, he'd be thinking to himself, well, the date's either gonna be the 14th, the 15th, or the 17th. Now, let's think about the world from Bernard's point of view. >From Bernard's point of view,
he's been given the date. So, if he's been given the date the 14th, if he was told the
14th, then he would say, all right, let's see, May's not an option. June wouldn't be an option,
July would be an option and August would be an option,
'cause there's a July 14. and an August 14. There's no May 14th or June 14th. So he would say, well, I'm not sure. If he was told it was the 14th, then it's either gonna be July or August. If he was told the 15th,
then it would be, let's see, May would be an option,
there's a May 15th here, or August would be an
option, there's no June 15th or July 15th here. So, May, May or August. If he was told the 16th, let's
see what are the options? It could be May, there's a May 16th as one of the options. There's no June 16th,
there is a July 16th. So he'd say maybe it's July. And there's no August 16th either. If he was told, it's a 17th, if he was told it's the 17th, he could say, well it's
not gonna be in May, there's no May 17th. There is a June 17th. There is a June 17th. There's no July 17th, but
there is an August 17th. So, there is an August, there is, I'll just write Aug for short. There is an August 17th. And then, if he was told an
18th, he would say, let's see, there's no May 18th, there is a June 18th, and I think that's the only
18th that we have here. So, if he was told that
the day is the 18th, then he would know, he would
know that the month is June. And, if he was told that
the day is the 19th, then up here, the only
19th here is May 19th, May, May 19th. So, if Bernard, Bernard's interesting. If he was told the 18th or the 19th, then he would know what the month is. So, with this out of the way, and if you're getting
inspired, I encourage you to pause the video again and see if you could work
through these statements, but now let's work through the statements. So, Albert says, I don't know
when Cheryl's birthday is, which makes sense 'cause no matter what month he's been given here, there's multiple options
for each of those months, so it makes sense that he doesn't know when Cheryl's birthday is. But, I know, I know that
Bernard does not know too. So how could he be so confident that Bernard does not know too? Well, Albert has the same information that we have right over here
and Albert says well look, if the date, if Bernard
was given an 18 or a 19, then he would know for sure
that Bernard does know the date. So, the only way that
he can feel confident, the only way that he can
feel confident that Bernard, the only way he could say, I know that Bernard does not know too, means that Albert knows that Bernard did not get an 18th or 19th. So, another way to
translate this statement is, Bernard did not get an 18th or 19th. Bernard not get 18th or 19th. Now how can Albert be so confident that Bernard did not get an 18th or 19th? Well, Albert knows,
Albert knows the month, Albert knows the month. And if he's so confident that Bernard did not get an 18th or 19th, that's because he knows
it's not May or June. If the month that Albert got
was May, then he would say, oh maybe he did get an 19th here, in which I can't, couldn't
make the statement. Or, if the month was June, well then 18th would've been a possibility
for what Bernard got. And so, he wouldn't have been able to make this statement here. But because he says, I know that Bernard does not know too, the reason why he can say that is because he knows it's not May or June. So we can rule out, we can rule out May or June. So we can rule out, we can rule out the 18th, the 19th here, and we can also rule out May
or June now from Bernard. Now from Bernard's point
of view, we can say look, Albert was, the only
reason why he was able to make that statement
is because Albert knows that the month is not May or June. So, let me rule out all
of the Mays and Junes. So, let me rule out June here. Let me rule out, let me
rule out May over here. Now I think you see where this is going. Now Bernard, and once again, at any point, if you get so inspired,
please pause the video and continue on with
the deductive reasoning that we have started. All right, now Bernard says, At first, I didn't know
when Cheryl's birthday is. Which is fair because it
wasn't the 18th or 19th which Albert already knew. But now I know. So, now I know. So before he didn't
know, but now he knows. So, if now he knows, what
are the possibilities? What are the possibilities going on here? So he knows if the date
he was given is the 17th, we've been able to, then
he could deduce that, hey, the month is now August. If the date he was given was the 16th, the month that he could
now deduce is July. If the date he was given was the 15th, he could deduce August. But if the date he was given was 14th, he still wouldn't know what the month is. It could still be July or August. So we could rule out the 14th, 'cause if the date he
was given was the 14th he still wouldn't know. But he says, now I do know. So we could rule out the 14th. And once again, we're assuming
Albert is hearing everything. Albert and Bernard,
they both could kind of draw these diagrams out. And so Albert could now say, okay, look, if he now knows, then the date
couldn't have been the 14th. So then he rules out the 14th. He rules out the 14th. So the stuff in orange that I just did I got from this statement there. And then Albert says, then I also know when
Cheryl's birthday is. So, from Albert's point of view, the only way that he now
knows what the birthday is if the month he was given was August he still has two options there. But he says he now knows
when Cheryl's birthday is. So it can't be August because
all the deductive reasoning we've just now done,
if he was given August then he would still not know whether it was the 15th or 16th. But now that he knows, it must be July. Because if he was given the month July, there's only one option now for the date. So therefore, the date must be July 16th. Albert must have been given July, Albert must have been given July. And Bernard must have been given, must have been given the 16th. So Cheryl was born on July 16th. Lots of fun.