
A maths question for Singapore schoolkids - jeremynixon
http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/apr/13/can-you-solve-the-singapore-primary-maths-question-that-went-viral
======
rr56
Because A knows the month and says B doesn't know the birthday, it cannot be
May or June since they have unique days (Which would allow B to know the
birthday). So far so good.

After this statement B know it's one of the remaining two months, July or
August and that's enough for him to know the correct date hence they day he
was told cannot be the 14th. leaving only July 16th, Aug 15 and Aug 17.

Since this information is enough for B to know the exact date, it clearly
cannot be August, leaving only July the 16th.

~~~
gcb0
only 19 is a unique day.

~~~
mynegation
No, 18 is also a unique day

------
guard-of-terra
This is a recurring but stupid theme. Look people in the past/in other
country/in other school know how to solve problems which are unfamiliar to us!
We have no clue and they do it pretty easy. They must be very smart and
learned?

Take aways:

\- You never learned to solve problems, just apply familiar patterns. This is
sad, you wasted youth.

\- Those people probably didn't either, but they were given a different set of
patterns. Doesn't make them smarter.

\- Anyone with actual solving skill looks at all of you with amusement.

~~~
mwfunk
What is "solving skill"? Where can I get some of that? Why do the people who
have it look at the people who don't with amusement, are they jerks? Should
those of us without "solving skill" rise up against them? This changes
EVERYTHING people!

~~~
guard-of-terra
I don't know where. Where do you get some of foreign language knowledge? I
don't have such place ready for you, yet here I am writing to you in a
language that is foreign to me.

"Why do the people who have it look at the people who don't with amusement?"

Because people who don't have it consistently praise the wrong thing.

~~~
imgabe
You get foreign language learning by looking at examples of the patterns used
in a language and learning how to apply them. By your logic there should be a
general "language skill" that anyone could use to immediately apprehend any
language. No such thing exists.

~~~
guard-of-terra
You also learn how to infer new patterns.

When I started to learn English any non-normal form like 'ye olde' or 'lotsa'
threw me into stupor. Now I can derive meaning from context while gaining
better understanding.

------
ironrabbit
Others have described the solution in this thread, but I thought I would
express it more visually since I still see some confusion:

[https://docs.google.com/presentation/d/1YVe2WymBiu_zBwZ9Dnqu...](https://docs.google.com/presentation/d/1YVe2WymBiu_zBwZ9DnquSmedQEfM5rqFBS0ivl84vyo/edit?usp=sharing)

~~~
swavaldez
I'm still confused by this "If Albert can tell from just the month that
Bernard does not know, then we can rule out all of May and June"

~~~
ironrabbit
I shouldn't have tried to fit that on one slide :)

Consider the case if the birthday is May 19th:

\- Bernard knows the date, and he knows that May 19th is the only possible
"19th", so he knows the answer immediately.

\- Albert would know it's in May, and that May 19th is _possible_. So, he
knows there's a _chance_ that Bernard knows the birthday immediately.

Since in the question, Albert is confident that Bernard doesn't know the
birthday immediately, we can conclude that the month cannot be May. The exact
same logic applies for June and the 18th.

The only possible months are July and August, because every possible date in
July and August also appears in another month.

Hope that makes more sense!

------
Aradalf
This is interestingly very similar to the Computer Science specific questions
on the Oxford Mathematics Admissions Test (MAT).

For examples, look at page 16 of the 2013 exam:
[https://www.maths.ox.ac.uk/system/files/attachments/test13.p...](https://www.maths.ox.ac.uk/system/files/attachments/test13.pdf)

and page 16 of the 2014 exam:
[https://www.maths.ox.ac.uk/system/files/attachments/test14.p...](https://www.maths.ox.ac.uk/system/files/attachments/test14.pdf)

~~~
ballpoint
I've taken those before and I thought this was harder.

------
dlu
More of a logic question, though at its core math is logic and pattern
recognition.

I'm certainly going to need a lot more practice if I want to place in
Singapore's top 40% of 14/15 year olds

~~~
ricree
I don't know the context around which this was presented to students, but it's
much easier if you think of it as a set operations problem than a pure logic
one.

Also nice to see that the age old act of providing irrelevant distracting
information in word problems is still alive and well.

A neat problem, though. I'm curious whether I would have gotten it at that
age.

------
croon
I was great at this and would have solved it before that age (not actually a
brag). I would never be in that olympiad. I was not good at maths when it
turned from numbers to letters.

When solving this I didn't apply any form of maths, but non-articulated
abstract reasoning I would have no idea how I'd put on paper.

What I'm saying is: Is this really math? I'm great with puzzles, not math.
They are not translatable for me.

~~~
guard-of-terra
Of course it is math.

Is it abstract (can be retold about other unrelated objects without changing
solution)? Yes.

Does it have a definite answer? Yes.

Do you use reason to get from A to B in simple concrete steps? Yes.

It's math then.

~~~
croon
Fair enough then. I guess I got hung up on not being able to model it on
paper, or relate it to any maths I've studied, but I can't deny your
definition.

------
fsk
These actually are standard problem types once you get used to them. They sell
books with logic puzzles like this.

One example is "Sherlock" by Everett Kaser.

[http://www.kaser.com/](http://www.kaser.com/)

It's like giving someone a Sudoku problem on a Math test. If you'd never seen
it before, you'd probably fail, but if you'd seen it before, it's easy.

------
logfromblammo
Another question, with the same date set:

    
    
      Albert: I don't know, but Bernard might.
      Bernard: Then your birthday is in May!
      Albert: Ha ha!  I was lying about what I knew.
      Bernard: So was I!
      Cheryl: Then you both know my birthday now.
    

(May 15, 16, 19, June 17, 18, July 14, 16, August 14, 15, 17)

~~~
jahooma
August 17, assuming Bernard would have said something different if he knew
Albert's first comment was impossible.

~~~
itaibn
If Bernard knew that Albert's first comment was impossible, then by the
principle of explosion his first statement is correct according to his
premises. Therefore his seond statement saying that his first statement is a
lie would be incorrect.

------
BukhariH
Great question! Initially, I didn't quite understand the premise of the
question which is why I couldn't get the right answer but after googling
around I found the correct premise and the correct solution in this article:
[http://www.independent.co.uk/news/world/asia/singapore-
maths...](http://www.independent.co.uk/news/world/asia/singapore-maths-
problem-can-you-solve-the-viral-maths-question-that-was-set-to-children-in-
singapore-10173090.html)

But, I think some people still won't understand the solution without
visualisation! So, here it is:

Well, I started of by setting a table like this:
[https://i.imgur.com/VhJ1gSZ.png](https://i.imgur.com/VhJ1gSZ.png)

Next we are told:

 _" Cheryl then tells Albert and Bernard separately the month and the day of
her birthday respectively."_

Great! Now we know:

    
    
        * Albert knows the month
        * Bernard knows the date
    

_" Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard
does not know too._

The only way Albert (he knows the month remember) can say _" but I know that
Bernard does not know too."_ for definite is if the month he knows is a month
that has a date which clashes with other months!

Why? Because if the month he knew had a unique date then there's a
__possibility __that Bernard could know the month hence he couldn 't know for
definite that Bernard didn't know the birthday. For example if Bernard knew
the date was the 19th then obviously the only month with 19th date in it is
May hence we would know the date of birth is the 19th of May.

Because, of the information above we can __completely __disregard both the
months wholly with the unique date in them which are May & June.

So, we now have a new table which we can update the hit, misses and clashes
on: [https://i.imgur.com/LoBJWa1.png](https://i.imgur.com/LoBJWa1.png)

 _" Bernard: At first I don’t know when Cheryl’s birthday is, but I know
now."_

At this point Bernard knows that the choice is either between July or Aug and
he goes ahead and says he now knows what the full date of birth is!

This tell's us that the date is a unique from the updated table because if it
wasn't a unique date then he couldn't have possibly known the month!

So we can update our table again:
[https://i.imgur.com/UUyNQQC.png](https://i.imgur.com/UUyNQQC.png)

 _" Albert: Then I also know when Cheryl’s birthday is."_

So, now because Albert knows the month is July is can say for definite that
the full date of birth is __16 July __because there is no other date in that
month left.

Explanation: Because if it was August then Albert wouldn't know the date of
birth as there two date for him to choose between (the 15th and 17th) but
because Albert does know the date; we know the month is July and the only date
left in July is the 16th!

Hence the correct answer is __16th July __!

Hope that helped!

~~~
jbob2000
And this is why I didn't do well in math. Whenever I got a question like this,
my first thought was always along the lines of "Cheryl is fucking bitch, just
tell them your goddamn birthday so I can solve a real problem".

~~~
edejong
How does your embarrassing comment add to the discussion we are having? I'm
afraid the gentlemen on this forum could not care less for your childhood
struggles. And just in case you're wondering, your math performance was
probably hindered by your flagrant, insulting and imprecise use of language.

~~~
bnjmn
Thanks for taking a swing at this rebuttal, but isn't "gentlemen" a touch, um,
gendered?

~~~
navait
Also an extremely pretentious way to refer to the users of this forum. I have
no reason to believe HN users are more cultured than the rest of society.

------
JohnLen
A challenging but great example of training a young kids to think logically
and out of the box

------
detcader
I would be interested to see this written formally (at least the premise, if
not also the steps) -- is there a Boolean notation for this sort of thing?

~~~
contravariant
Perhaps a combination of boolean logic and set theory? For instance let X be
the set of possible dates and let m, d, be functions which, respectively,
return the month and the day of any date in X.

Now the three statements can be translated to the following logical statements
(this isn't necessarily a good thing to do, but you can):

P(B) = #m^-1(m(B)) > 1 ∧ ∀x∈m^-1(m(B)) : #d^-1(d(x)) > 1

Q(B) = ∃!x∈X: d(x)=d(B) ∧ P(x)

R(B) = ∃!x∈X: m(x)=m(B) ∧ Q(x)

your task is then to find a birthday B in X such that P(B), Q(B), and R(B)
hold. Or equivalently find the unique element of {x∈X : P(x)∧Q(x)∧R(x)}.

Edit: Still not 100% sure if P(B) is correct.

------
sreeajaym
i found the best explanation
here:[http://readknowandshare.blogspot.in/p/solution-for-albert-
be...](http://readknowandshare.blogspot.in/p/solution-for-albert-bernard.html)

------
enedil
June 17.

~~~
venomsnake
June is impossible because June 18 is unique. So B can possibly know.

