# Boards

## Guys can you solve this problem?

let's not argue though!

http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/apr/13/can-you-solve-the-singapore-primary-maths-question-that-went-viral

=======

"Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

May 15 May 16 May 19

June 17 June 18

July 14. July 16

August 14. August 15. August 17

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

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

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

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

When is Cheryl's birthday?"

=====

## I can narrow it down to three dates

beat that

## trick question

Cheryl was never born.

## Albert and Bernard created her

in their minds

## yeah

## As much as I love viral maths questions,

I can't really be bothered if I'm honest.

## If theres one thing we'll always remember about you

Its your love of viral maths

## Cheryl's a fucking prick

## She's quirky!

## Chryl is a cannibal

and her birthday is an axe made from ice?

## Google translate sometimes struggles with Rammstein lyrics

i worked this out earlier when i first saw it and was very pleased with myself

## got it down to three dates, you mean?

## I'm very confused by this

Am I focusing too much on the spoken lines?

Can any of you nerds explain it for the cool kids?

## Your three dates being

July 16th, August 15th and August 17th.

So you're nearly there. Just one final push.

## Albert's first statement narrows the month down to July or August

Bernard's statement then narrows it down to July 16th, August 15th or August 17th.

Albert's last statement then nails it to July 16th.

## oh I'm so stupid

got it now, ta

## Albert's last statement is unnecessary for Bernard to know

## Ah I see what you're getting at.

My statements refer to how much the reader knows at each stage, not what Albert and Bernard know. Obviously since Bernard has already stated that he knows the right answer Albert's last statement isn't required by him. (Note also that Bernard's statement that he didn't originally know the answer is unnecessary since Albert had already deduced that).

## you have to think about how they know what the other knows

you'll soon have three possible dates in mind.

## There's a comment that sort of does but I don't still really get it.

May 15 May 16 May 19

June 17 June 18

July 14. July 16

August 14. August 15. August 17

If the date was 19 or 18 then Bernard would already know, so it's neither of those and that also means that it's neither of those months, since it's Albert's assumption that Bernard can't know and he only knows the month:

July 14. July 16

August 14. August 15. August 17

So Bernard now knows it must be either July or August. At that point the only date that could be sure for Bernard (in possession of the day) is 16th July.

And because Bernard is sure, Albert knows that also.

## Oh, I guess I did get it as I worked through it

:D

## That's not quite correct though.

At the point when he speaks Bernard could know for sure if the correct date were 16th July, 15th August or 17th of August, not just 16th July. Albert then deduces the correct answer only because it happens to be July 16th. If the answer were either of the other two then he wouldn't be able to say that he knew the answer.

## Hmm, okay

yeah I see what you mean. It only works if we are to accept that Albert is correct.

So it's actually impossible?

## the whole thing assumes that Albert and Bernard are correct

that doesn't make it impossible

## Well it means it's not watertight, though.

Albert is only guessing, he can't be sure. There isn't a final line stating they are both correct.

## Just seen your comment down below. Cheers.

## No it's not impossible.

The logic of the conversation does lead to the unique answer of July 16th.

The thing that bends the head is that the conversation itself can only go that way IF the correct date is July 16th.

A more mundane way to approach the problem is just to test each date in turn and establish in each case why the conversation wouldn't go that way for all except July 16th.

## But that isn't a problem with the problem.

There is only one date and you presume Cheryl specifically picked the other dates so that the two of them could determine the correct date without explicitly stating their half of the problem.

## Doesn't sound like someone I'd want to be friends with

bit devious

## No, you don't quite get it

## Yeah I did get it.

Then ColinFilth came up with a batshit issue around the correct answer. I mean a lot of problems would be hard to solve if the answer was different.

## ColinFilth isn't quite right either

## Pretty sure my logic is spot on

but my writing might well be careless cock.

Do elaborate.

## well itss16th July obvs

## or one of the other two dates?

## the clue to narrow it down to one date

is that Albert (who knows the month) has narrowed it down to 1 date

## I'm so close

## you're so close

## just solved it again

For kicks.

## not thinking about it to much it would seem the answer is 16th july

or 17th june, based on fuck all

## I like the fact that in Asian textbooks,

they use foreign names as well.

## wut

## is this Cheryl Cole?

## Kenneth Kong can go to hell

## july 16th

## july 16th

## narrow it down to ONE date

## july16th?

## this is pretty much how it feels

when I try and work out whether I have missed Mrs Meat's birthday or not

Albert knows month: May, June, July or August

Bernard knows day: 14, 15, 16, 17, 18 or 19

Albert knowing that bernard doesn't know means that it's a month that doesn't have a unique number in it. So not May (19) or June (18).

If Albert knows it must be because it's a unique remaining number - 16 (July), 15 (August) or 17 (August)

Dunno how you can narrow it from that tho

## I was once like you

## See my post.

## (don't)

## Yes do, because we discuss why it's dubious.

## it's not though

## It is because we have to assume Albert is right.

Bernard would be sure if the date was the 17th, but Albert doesn't know which month and can't. Unless you'd like to offer another way out?

## Albert gets told the month at the start

## Oh right. :D

## You mean

If Bernard knows it must be because it's a unique remaining number - 16 (July), 15 (August) or 17 (August)

## i do mean this, and had noticed i was wrong

## ok right so bernard DOES know, he just does

albert knows what i know, and also which month. if he's sure of the answer than it must be cos it's july 16th

## Has anyone checked out my lawnmower riddle?

Too difficult for you? Thought so.

## Flying Motus?

## the man fucked a lawnmower on a desert island?

## What a bunch of midnight punks!

## they might be good at maths in singapore but their syntax is horrible

dicks

## August 15

## is what some one who was trying to throw everyone else off the scent

would say

## plane on a treadmill v2.0

## can't stand this sort of thing

## OK i shall explain it

although the language/wording, is not good, we will make the most likely assumptions.

Albert, the month knower (and a bit of a git) says he knows Bernard does not know the date, which means that the birthday is not in a month that has a unique number....i.e. may or june

which means that the birthday must be in July or August.

Bernard then says that he knows now....which must mean that it is a number that is unique in the subset of July and August.....which discounts the 14th.

Albert then says that he also knows.....if the month were august, then he would be unable to say this as he would not know whether it were 15th or 17th, however since he does know then it must be because he has been told July....and it must be the 16th or else Bernard would not know the date.

Simples

## Not bad.

Applauds.

## I have two grown up sons

had many birthday parties, a lot of their freinds parents are awkward and difficult like this, with their cryptic invitations, so its a doddle to me

## OK then...

Take ten random coins of any denomination you choose. Lay them in a straight line. You (who has first go) and an opponent take it in turns to take one of the two coins at either end of the line until there are no coins left. If at that point you have at least as much money as your opponent you win.

Is there a winning strategy for either player?

## without thikning too much

surely the answer is "take the big value coins, and don't take the coins currently covering the big value coins"

## Given that at each turn you have a choice between two coins

if your strategy is to always take the largest of the two coins then that isn't the correct answer.

A simple counterexample to that is

1p 1p 1p 1p 1p 1p 1p 1p £1 2p

where you would end up with 6p versus your opponent's £1.04.

## yes....alcxxk said as much when he said, don't take the coins currently covering the big value coins

and i just re-iterated that you need a mix and match between the two techniques that alc**k mentioned.

## but when do you choose which strategy?

## you chose which strategy based upon the order and the denomination of the coins

Im not going to compile an algorithm right now for you, unless Im guarenteed a percentage

## but the algorithm is what's being asked for

## here it is

..take the 1st, 3rd, 5th, 7th and 9th and add these. compare it with the sum of the 2nd 4th 6th 8th and 10th coin

which ever set has the most, start with a coin in that series.....you can always ensure that you can take from your own series that you started on then and you will always not loose

## Have you worked it out john?

## as Alc**k says \/

although it depends on the random order of the different denomination coins...so you will have to use a mixture of taking highest value coins vs revealing even higher value coins

## Whoops...I mean up there ^

## Think about it a bit more. The answer is more definitive than you might think.

## make sure you only go first?

## Well that was stated in the original post.

So are you saying that the person who goes first has a guaranteed winning strategy?

## if they persue the correct course then they can prevent themselves from

loosing, certainly.

## OK but I need to know what the strategy is.

Not just some handwaving about taking big coins. A proper algorithm for winning/not losing. (Not losing is winning by the way, there are no draws in this game).

## you want an algorithm?

....i to take into account all denomination possibilities and all possible moves by opponant, is a bit of a chore....its much easier for you to become practiced at it

## Well obviously I know the right answer

and you're not there yet.

## oh I have it....just not translated it form that is transmitable to other humans at the

moment

## OK got the algorithm..

..take the 1st, 3rd, 5th, 7th and 9th and add these. compare it with the sum of the 2nd 4th 6th 8th and 10th coin

which ever set has the most, start with a coin in that series.....you can always ensure that you can take from your own series that you started on then and you will always not loose

## you will need to do a bit of adding up, dependant upon the order

and denomination of the coins, but then, by applying the best course of 'taking the largest coin available, tempered with, do not take a coin covering a large denomination' then the person who goes first, can always guarentee to not lose (of course it can be a draw)

## This example might help

50p 5p 20p 1p £2 £1 5p £2 50p 20p

I'm assuming in this case your first move is the 50p since it's the larger of the two choices and is also covering the lower of the two "next" choices. If your opponent then takes the 20p then you're left with a dilemma: pick the 50p and uncover the £2 or pick the 5p and leave the 50p.

## cool well let's play

LEFT

a: 50

c:0

5p 20p 1p £2 £1 5p £2 50p 20p

## I take the 20p

I assume you then go for the 5p to avoid uncovering the £2. I then take the 20p. You now uncover a £2 whichever way you play it so you might as well take the bigger (50p). I then take the £2. Leaving us with 1p £2 £1 5p. You get the 5p and the £2, I get the £1 and the 1p. End result: I have £3.41 and you have £3.10. I WIN!

## well the thing is that you have to let the other player make their own

moves....If you were playing me. I would take the 20p on the right first.

so that 50p, 5p, 20p, 1p, £2, £1, 5p, £2, 50p remain.....your go

## Fine, but you have to give me a reason why you take the 20p first.

Your choice appears to contradict both your "sort of" rules. The 20p is the smaller of your two choices and it uncovers the bigger of the two possible revealed coins.

It is the right answer though.

OK I'll simplify things a bit:

There is a 100% winning strategy for the player who goes first.

Nobody has come close to it so far.

You can express it without knowing the values of any of the coins and it will always work regardless of what those coins are. You do need to know the coins and their order to actually put the strategy into practice though.

I'll post the answer tomorrow unless everyone's bored and wants me to put them out of their misery now.

## no its ok I can translate it to human now

..take the 1st, 3rd, 5th, 7th and 9th and add these. compare it with the sum of the 2nd 4th 6th 8th and 10th coin

which ever set has the most, start with a coin in that series.....you can always ensure that you can take from your own series that you started on then and you will always not loose

## Bingo!

The only disappointment about this neat trick is that after the first move player one always ends up taking the coin next to the one the opponent picks. So if you did it in practice you'd wow your opponent the first time, but they'd soon spot what you were doing if you played more than a couple of times.

Nice work though. Took you about as long to crack it as it did me originally.

## grrr my arrogance is dented

;D

## I must admit I didnt think it was going to be as simple

as that....I was sighing to mysef and resigning myself to having to notate a big algorithm, but in the process the shortcut revealed itself.

Hey are you a mathmo?

## Very much so

## :( wish I was

I had disagreements with the way they taught me maths though

## creaky takes 5p

20p 1p £2 £1 5p £2 50p 20p

## It is better if you start, to go for the 20p on the right

of course

## I've already had the 20p on the right.

Now I take the 20p on the left.

So you have 55p, I have 40p

and we're left with 1p £2 £1 5p £2 50p

## play me, i'll win

RIGHT

a:50

c:20

5p 20p 1p £2 £1 5p £2 50p

LEFT

a:55

c:20

20p 1p £2 £1 5p £2 50p

## 20p

## do you subtract the one you'll be exposing from the coin you take

so if you did that for both sides you'd choose (5p-20p) over (50p-£2)?

## I *think* that's the way I've worked it through in the post above.

## but is that the general strategy?

## No because in the above example it loses.

## this sounds like a good rule

50p 5p 20p 1p £2 £1 5p £2 50p 20p

1: Left, 50 (50)

5p 20p 1p £2 £1 5p £2 50p 20p

2: Left, 5 (5)

20p 1p £2 £1 5p £2 50p 20p

1: Right, 20 (70)

20p 1p £2 £1 5p £2 50p

2: Left, 20 (25)

1p £2 £1 5p £2 50p

1: Right, 50 (120)

1p £2 £1 5p £2

2: Right, 200 (225)

1p £2 £1 5p

1: Right, 5 (125)

1p £2 £1

2: Right, 100 (325)

1p £2

1: Right, 200 (325)

1p

2: n/a, 1 (326)

TWO WINS

## Guys this thread is about birthdays

## Well that's a game alright

but I don't see a strategy.

However it's not a coincidence that in that game the two players end up 1p apart at the end...

## ok

translated it for others now

## oh, that's good

bloody minded but good

## cool SO if creaky method played j0hn method:

50p 5p 20p 1p £2 £1 5p £2 50p 20p

odds: 325

evens: 326

creaky chooses evens

c: right, 20 (20)

50p 5p 20p 1p £2 £1 5p £2 50p

j: left, 50 (50)

5p 20p 1p £2 £1 5p £2 50p

c: left, 5 (25)

20p 1p £2 £1 5p £2 50p

j: left, 20 (70)

1p £2 £1 5p £2 50p

c: left, 1 (26)

£2 £1 5p £2 50p

j: left, 200 (270)

£1 5p £2 50p

c: left, 100, (126)

5p £2 50p

j: right, 50 (320)

5p £2

c: right, 200 (326)

5p

j: n/a, 5 (325)

creaky wins

## I peak too early

with my 270 - 26 lead

## it was a pain, because although I was calculating

out all the possibilities to the 10th turn, i was then having to recalculate every time just to ensure I was still on track, until I tried to algorithmise what I was going on in my head and spotted the short cut.

## hmm what if there were 11 coins?

;)

## same system, but with even more premium on going first

## nah

if evens beat odds with 11 coins, then the person going second can utilise the creaky method and win even with the first person having an extra coin

## unless that first coin is ENORMOUS

e.g. £2 1p 1p 1p 1p 1p 1p 1p 1p 1p 1p

or other subtler set ups

## yeah i think it's only if evens beat odds?

## Pretty much the opposite

Since after move one the problem reverts to the ten coin problem. So if anyone can guarantee a win then then it's player two.

However in that case it won't always be possible. It could be that the value of the first coin picked is sufficiently large that even creaky's algorithm couldn't make up the difference for player two.

## In fact take any coin bigger than 1p

and add it to either end of our example and you've got a case where neither player can guarantee a win from the start.

However there may be a point in the game when as a result of previous moves player two can then ensure a win using creaky's method from that point on.

## yup, you just have to work out the sum difference between the two series

## aha!

## that strategy is j0hns:

if we label them

L1, L2, L3....R3, R2, R1

IF (L1-L2>R1-R2)

CHOOSE LEFT

## literally can't believe that creaky has come along with the most concise answer to this

literally

## haha

## hrmmpphh!

I do have an exceedingly high iq you know.....of course those iq testy things are a load of old bollocks, so that doesn't mean much.

## nobody is challenging the fact that you are obviously SUPER CLEVER creaks

It's just that you can be a bit, you know, wordy sometimes and what you have done here is an amazingly clear and concise explanation of something that is actually quite hard to iterate. which is really sweet because concise is not what you're known best for < 3

## yeah the emphasis was on concise

## concise in calculation of a single answer where there IS a single answer

is OK, when there should not be a single answer, then it not a bad thing to be inconcise, otherwise people might think it IS, the done thing, to search for certainty when they should not be.

## ^ I should have been more precise and put a full stop after OK

and my 'when' should be a 'When'

:) sorry

## Emailed this to a work colleague

He sent me back a concise reply, including tables and everything.

But I can't upload it to the internet, as my work blocks images.

Help?

## Hate these threads

## go buy some new clothes then, grandpa

## It was 17 August all along!

http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/apr/15/why-the-cheryl-birthday-problem-turned-into-the-maths-version-of-thatdress

## ===THREAD RE-OPENED===

## i got august 17th when I did it

All of this july 16th bullshit is embarrassing, guys

## there are a coupe of variables

one of which is how A reaches the conclusion that B does not know. Most people are presuming that he deduces this rather than is told, which takes you to july 16th.

## it's hardly presumptuous to approach a logic puzzle as a closed world

and not one in which various bullshit secret pacts have been arranged

## although i did just read a comment on the guardian

which pointed out we're not explicitly told that Albert knows that Bernard knows the date

it is nonsensical without that though

## this is amazingly stupid

of course albert doesn't know (that bernard doesn't know) due to a deus exmachina, cos that'd be a completely ridiculous thing to happen in a logic puzzle. may as well argue that it's 25th December and that they've all been told to lie at all stages

## I knew it wouldn't be long before the 16 July sheeple started getting aggressive!

## nah

1st step: Removes June 18th and May 19th cause they're unique. Also removes June 17th cause then Albert would know.

2nd step: Its obviously August 17th cause this is now the only unique date

There was more to this in my initial workings, but its very clearly, almost incandescently the 17th August

YeaH?

## not following you in the slightest

## Faultless logic:

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

Albert knows bernard doesn’t know, so it can’t be a unique number, meaning its not May 19th or June 18th. It therefore also can’t be June 17th as Albert would then know.

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

Having discounted these three dates this leaves only one unique number left, meaning Bernard, in possession of the number 17, now knows that it must be the 17th august.

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

Albert now deduces that it must be the 17th too, since Bernard would still not know the correct date if it was a shared number, like July/August 14th.

When is Cheryl's birthday?"

17th august m8

## so are you going with reading albert as having been told

"bernard doesn't know"

as opposed to the sane thing of reading it as him having deduced it from what he knows?

## what difference does it make, he knows either way

They just met her and they want to know what her birthday is

Therefore neither of them know

## he knows bernard doesn't know cause they just met her

and albert would be able to tell by bernard's smug expression if he knew, since they're boys from way back

## unless we're being horrifically pedantic

A knows that his boy B knows the day of the month C was born.

and if it was 19th or 18th, B would know

so A couldn't say that B didn't know, based only on the fact that they'd just met

## this is doing my nut in

this is.

right in

## do you literally not understand why the answer is 16th July?

like, ignoring the fact that you can make up nonsense about Albert being informed that Bernard doesn't know, when he could well know, do you not understand why the answer arrived at by thousands of people and the setters of the question is 16th July?

## im not sure if I do

cause Bernard tells Albert that 'at first he didn't know'

So Albert knows that Bernard didn't know, it doesnt require an assumption

## 1. Albert knows that Bernard doesn’t know. (Maybe Cheryl told him as much).

2. Albert deduces Bernard can’t have a unique date such as 18 or 19.

3. Albert, smugly taunts Bernard, announcing Bernard doesn’t know. This is the first statement of the problem.

4. Bernard realises what Albert has realised, which is that Bernard does not have 18 or 19. Now if Albert was holding June he would know the answer, because there is only one remaining date in June, namely June 17. So Bernard deduces it is not June.

5. Bernard announces he knows the answer. This is the second statement of the problem.

6. If Bernard is so confident, he must have a unique date. We know it’s not 18 or 19. What other unique date can it be? There are two 14s, two 15s, two 16s and two 17s - but Bernard has eliminated June 17 - leaving him with August 17 only. That’s how he worked it out.

7. Albert is furious Bernard beat him to the answer. Albert puts himself in Bernard’s shoes, running through the six steps above. Finally Albert reaches the same conclusion we have, Bernard must have 17. Albert announces he knows the answer too.

So August 17 is a valid answer.

## Yeah

In fact the only real correct answer is:

It's either August the 17th or July 16th depending on how Albert arrived at the knowledge that Bernard did not initially know the correct date.

Fucking brilliant stuff. I love maths.

## no it isn't

cos you're bringing in bullshit about C telling A that B doesn't know. whereas, in the actual scenario, C has told B the day of the month, and not told A the day of the month. Therefore if C had told B "19", A would be incorrect in stating that B doesn't know. so A couldnt say that

## No it's more subtle than that.

Nobody's saying "C told A that B doesn't know". What is being said is that you can't assume how A found that out. It's no more valid to say that B deduced it than to say that C told B, because neither statement has been asserted as true. Therefore you have to consider that either could be.

## C told B what?

## Sorry C told A

## then yes, obviously it is more valid

in a logic puzzle, that A deduced it, rather than having been told something off page. like i say, if we can assume people have just been telling eachother stuff that's not on the page we can just assume that every word is a lie and cheryl's birthday is 25th December and she is also jesus

## it doesnt strictly mention an albatross

but we can't rule it out

That's the gist of it, right?

## the gist of what i'm saying you're saying, yes

## so we agree!

Tbh tbf I think were both right

## 16 July & 17 August: both right in different ways

Glad we're all agreed!

## He knows!

## but bernard says:

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

Thats how WE know that Albert knows that Bernard didn't originally know. Its not down to the assumption that Chezza told him, its because Bernard tells him

## NO......

1) this guardian logic is very flawed.......I will annotate it in my next post

2) it is a logic problem....the convention and expectation is that they give the minimal clues necessary to answer......oh_good entreated us to come up with ONE answer.....I already caveated that it is not the best wording as it does not insulate the logic problem fully from peoples 'imagination' and 'blue sky thinking' and 'wish to be rebels'

3) its as if, since I have come into 'conciseland' others have left to enter my previous world of inconcision.

4) Invent away, if you want to, and ignore one of the given clues......but if you are free to do that, then I am somewhat dissappointed by the limit to the imagination on show, that it can only create a scenario with august the 17th as an alternative.....aim higher, see what scenarios you can imagine where each one of the other dates can be valid. (I can do a couple so far, it gets embarrising to go further, but It can be done)

## No the logic is fine and correct.

The reason for the ambiguity is that a logic problem has been taken from the realms of formal logical notation (which has painstakingly been developed to avoid ambiguity) and put into English, at which point the potential to write an ambiguous statement is introduced (and indeed it has been).

If the puzzle were intended to produce the unique answer July 16th Albert's first statement should have been:

I do not know the answer. The fact that I know the month implies that Bernard did not know the answer before I spoke.

## YES, I know this, I was busy writing my rationale below

I understand perfectly that the wording of the puzzle is not exact enough.........even what you say does not fully suffice, because some may feel it needs to be stated that albert and bernards logical deduction is correct...it is very common for people to deduce things incorrectly......you may think that this need not be stated, because of convention of such logic puzzles...but if this were so, then why is it ok to ignore the relevance of the third statement clue, surely the convention should be that it is there for a purpose?

(I don't really know, I don't often do these sort of things.....Im a bit annoyed because i was trying to give 'One Answer' as ohGood kept saying to do)

## A deduction has to be correct

otherwise it is not a deduction.

It's also reasonable to draw a line at the point where you say that every statement made in the problem must be true.

That covers most of the "yeah but what if" answers. The basic fact is that if you express the problem in any format other than formal logic you'll most likely introduce an ambiguity. That's no biggie, and in this case one interpretation seems to be generally far more acceptable than any of the others.

What is truly beautiful though (from a mathematical standpoint) is that changing one word can have such a profound change in the possible reasoning to an answer. That's fun. Not significant, just fun.

## you are right.....its good to have had the aug 17th rationale mentioned

it is fun (I would have found it more fun I suppose, were I not permanently scarred by THEOS IMPOSSIBLE RUNWAY, many years ago.

Did you ever see THEOS IMPOSSIBLE RUNWAY?

maybe it needs your rigour to clear it up once and for all.....not another discussion.....it just needs to be exhumed so it can be buried properly.....you could be like Sam and Dean maybe.

## Even if we allowed for unmentioned bits of information passed on by Cheryl

the guardian article logic still has flaws, as detailed below somewhere

## or substitute the word 'know' for 'deduce'

my objection to the defence of aug17th is based on 'the spirit of'

If we are allowed to imagine other methods of Albert 'knowing' that bernard didnt know, other than process of deduction,

then there is nothing to stop us from imagining that in Bernards statement

"At first I don't know when cheryls birthday is but I know now"

was also not down to deduction.....what is there to sop our imagination from assuming that cheryl told bernard, or albert telling bernard, or bernard just suddenly getting an overwhelming feeling?

The assumption is that they are deducing.....that is the context

that is the scenario.

You are given a set of what appear to be, sparse clues, that do not seem to initially indicate what the answer could be, but because the protagonists can deduce then we are meant to use what we can deduce is their reasoning to deduce the answer......if you allow for other deus ex machinas that have not been specifically excluded from the initial problem then it becomes open ended.

## No it isn't sufficient to substitute know for deduce.

He could "deduce" it from anything, including that he'd been told it by Cheryl. The use of the X implies Y format I chose was deliberate since it mirrors the propositional logic formulation.

## fair enough

I was trying to appeal to a wider audience as well I guess.....and addressing the terminology that the guardian article used (deduce vs statement of fact) ....but OK, even if Im not nailing it down airtight, can you not see my objection to taking something not in the spirit of the question, where there is enough to interpret the spirit of the question

## Ordinarily yes

and as mentioned in various places I think the problem does lend itself pretty strongly towards the July 16th interpretation. It's just that it's very attractive that a slight difference in interpretation can lead not only to a completely different valid deductive chain, but also to one unique alternative answer.

## I agree that the result is entertainingly different and should be mentioned

for this reason.....but im just wearing my one concise hat today, so require that anyone saying aug17th acknowledges first that it is an interesting aside.

## Nah, the article falls at the very first step

August 17th is not a valid answer in any way.

## It really doesn't

## creaky's first step comment

is that Cheryl might have lied, or that either Albert or Bernard might have made an incorrect deduction. If you're going to accept that as valid then there's no point in trying to solve any problem like this.

As I said it is reasonable to assume that every statement written in the problem is true. This includes statements where a person says they know something, and also the part where Cheryl passes them both information.

The whole point of the alternative interpretation is that it ISN'T necessary to invent further information to arrive at the new answer. If anything the August 17th answer is logically more attractive since it relies ONLY on the fact that Albert knows that Bernard doesn't know, not that he has worked it out (which he doesn't say incidentally).

## It really does

"1. Albert knows that Bernard doesn’t know. (Maybe Cheryl told him as much)."

The possibility of Cheryl telling him is not valid as there is nothing in the question to suggest that is the case, and it is entirely unnecessary for Albert to be told this in order to realise that Bernard doesn't know.

From point 4:

"4. Bernard realises what Albert has realised, which is that Bernard does not have 18 or 19. Now if Albert was holding June he would know the answer, because there is only one remaining date in June, namely June 17. So Bernard deduces it is not June. "

This is not correct because it wrongly determines how Albert realises that Bernard does not have 18 or 19. The only way for Albert to realise this is that he has been told a month other than May or June. We know at the very first step that Albert has been told July or August, and Bernard would also realise this once Albert has indicated that Bernard does not know the correct answer. Bernard has therefore eliminated both May and June at this stage.

"6. If Bernard is so confident, he must have a unique date. We know it’s not 18 or 19. What other unique date can it be? There are two 14s, two 15s, two 16s and two 17s - but Bernard has eliminated June 17 - leaving him with August 17 only. That’s how he worked it out. "

Nonsense - Bernard has already eliminated May so there are not two 16s to choose between.

## Well I've already answered point 1

It is not necessary to state that Cheryl has told him. What we KNOW from the statement is that Albert knows that Bernard doesn't know. We don't know how he knows it, specifically we don't know he's deduced it. The one thing we do know is that he knows, and we proceed with the logic from that fact and that fact alone.

## On point 4

This is not correct because it wrongly determines how Albert realises that Bernard does not have 18 or 19. The only way for Albert to realise this is that he has been told a month other than May or June. We know at the very first step that Albert has been told July or August,

No we don't. As set out in the alternative solution we know at the very step that Albert has been told July or August... or May.

As I said both proposed solutions rely on Albert and Bernard both making the same interpretation of Albert's first statement.

## And point 6 falls because of the fallacey in creaky's argument about point 4

## "We don't know how he knows it, specifically we don't know he's deduced it."

Wrong - we know he can only deduce it if he had been told either July or August. As we know that he has deduced it we therefore know that he has been told one of those months. We can conclude at this very first step that May and June have been eliminated.

## Read what I wrote carefully

I didn't say "we don't know how he's deduced it", I said "we don't know he's deduced it".

And we don't, because it's not written in the problem that he did.

## Both answers are slightly unsatisfactory

July 16th because there is an assumption that Albert made a deduction in stating that Bernard didn't know.

August 17th because this involves a passing of information to one of the protagonists that isn't documented.

Both are equally irksome, but neither dents the logic that flows from them.

## No

August 17th requires an entirely fabricated passing of information.

## And July 16th

Requires an assumption that Albert is making a deduction when he states only that he knows Bernard doesn't know. There's no evidence of that in the text either.

## It doesn't require an assumption without evidence

We are explicitly told what Cheryl said to each of them - the month and day respectively only. Of course Albert makes a deduction that Bernard doesn't know - the whole point of the question is in working out how Albert and Bernard deduce the answer.

## No, you are wrong

The only facts known by the first step are:

- Albert has been told the month

- Bernard has been told the day

- Albert knows that Bernard does not know the answer

That is all we know. From this we can determine that since the 18th and 19th are the only unique numbers that Albert must realise that Bernard was not told either of those numbers. The only way Albert could know that is if he had been told either July or August. We therefore know at this stage that May and June have been eliminated.

The alternative solution falls at the very statement by Albert because it incorrectly does not eliminate both May and June at this stage. The rest of the reasoning in rest of the alternative solution is therefore irrelevant.

## Please stop telling me I'm wrong.

It's pretty rude and I'm trying as hard as I can to avoid doing you the same discourtesy.

With respect to your comment:

"The only way Albert could know that is if he had been told either July or August. "

This is not true. We don't know anything about "ways" that Albert knows things. ALL we know is that he DOES know that Bernard doesn't know the answer. As the reader you do not know that he's deduced this from information in the question or whether that information was supplied to him as a direct statement.

The argument in the article is fine. If it weren't he probably wouldn't have published it and it would have been torn apart by better minds than both of ours.

## Sorry about being rude in calling you wrong

"The only way Albert could know that is if he had been told either July or August."

This is true based on the information provided in the question.

"As the reader you do not know that he's deduced this from information in the question or whether that information was supplied to him as a direct statement."

Yes we do know - we are told that they have been separately told the month and day. There is nothing else said to them - to suggest that he could have received a direct statement that Bernard does not know is an entire fabrication on the part of the author of that article.

## Aug 17th still requires Bernard to know that Albert did not deduce

but as told......the article misses that out has anyone mentioned that yet ;P

;D Im being rude now.

ALthough to be the criticism about my argument you are arguing with confrontedwithbears, is probably correct.....I was not fully onside with the aug 17 when originally criticising it.....I am now merely criticising the spirit of it, whilst acknowledging its interest and funfactness......i still think its far less of an assumption to assume that in a problem with few seeming facts that we are to deduce from a few facts.....since part of this deduction requires that Bernard does some deduction, to 'know', then it is also most reasonabe to assume that when Albert 'knows' it is also by deduction, rather than an off stage unseen method....we have a limited set of tools on front of us and we are told to work out a problem....i have used the tools laid in sight of us, and assumed that the methods that Albert has had to 'know' are the same methods as Bernard had to 'know'.....i.e. deduction.

I was unaware of the whispered prompt to first Albert "Pssst Al, Bernie doesnt know the date so it cant be a unique number" and that Al therefore did not even attempt to deduce that by the fact that he had either July or August as a month and therefore he would have been able to deduce that Bernard could not have known the full date anyway....irrespective of whether he was told or not.........thus leaving the next act to be the most crucial, the bit where someone offstage whispers to Bernie that Al was told that Bernie didnt know, and that Al didnt do any deduction at all because he is lazy......iF noone whispered this to Bernie, then Bernie might assume that Al had deducted after all why should Al be the one getting the secret prompts and not him?

Perhaps the better way for the guardian article, aug17th fans to put it woud have been to forget mentioning Albert being told, but to say what Bernard does not know how albert knows that bernard does not know, but he can assume two methods 1) Albert has been told 2) Albert has correctly deduced from the month that he knows.

## "Aug 17th still requires Bernard to know that Albert did not deduce"

Yes, and how could that be the case without making ridiculous additions to what each person was told initially?

## here is my other objection to the explanation

even if i try to go along with their thinking (on another day in a less concise mood i would happily zoom through the rings of saturn to come up with other dates)

in the guardian articles explanation, then for Bernard to be able to make the assumption in 4, then Bernard would ALSO need to know that Cheryl has told Albert that Bernard did not know the date..........so thats a second non mentioned factor that is required for an august 17th date.......if cheryl is giving extra different clues to albert AND Bernard, that we are not told about in the problem, then really what the point of this exercise?

I would find it easier to accept if they had said, the answer should be july 16th....but here is an interesting thing, if we assumed......blah blah blah, then it would be a different date.

## This is actually a really good point

and one that occurred to me whilst thinking about this. Basically both "strands" of reasoning assume that Albert and Bernard both have the same understanding of what Albert means when he says he "knows" that Bernard doesn't know.

That of course doesn't need to be a problem, since the facts are laid out in the statements in the problem and if the situation where the two had different interpretations meant that the series of statements couldn't truthfully occur then you can infer that they must share (one of the two) interpretations.

Don't know if that's the case though. What happens if Albert "knows" because he's been told, but Bernard thinks Albert "knows" because he's deduced it?

## i've got another solution, for January 27th

But it involves the assumption that Cheryl is a time travelling ghost, and that Albert and Bernard are in fact the same person from alternate, but almost identical dimensions - the only difference between the dimensions being that the names Albert and Bernard are the same name spelt differently - like Ewan and Eoghan, or something

## NO.....that guardian piece involves several things that are flawed.

This problem was set as a question.

The problem gave you few clues, from which it was testing if you could come up with an answer from.

It was not testing your imagination to see if you could a) provide an alternative addenda to one of the clues and using this invented extra clue you could then come up with an answer by imagining that one of the eisting given clues had no relevance (the last one) becaus that was just a bit of colour (albert beeing put out and just saying something throwaway)

5) how do we even know cheryl is not a liar? perhaps she plays bridge with Bernard, or Albert, or even Both, the hussy (that means they may have secret signs, or be able to read each others tells)...you know that sort of thing. or maybe Bernard was born on 15th august and albert knew her birthday was after hers......ys this ignores the relevance of the stated clues, but then again the guardian explanation ignores the relevance of the last stated clues.

## Both?

Ian Botham's in on this too now???

## HE WOULD BE ALL OVER HER

HE TAKES WACKY BACKY DOESN'T HE?

## here is the guardian article explanation with my critique of it

1. Albert: I don’t know when the birthday is, but I know Bernard doesn’t know too.

2. Bernard: At first I don’t know when the birthday is, but now I know.

3. Albert: Then I know the birthday too.

THE ABOVE ARE THE CLUES, THE BELOW IS THE GUARDIAN......I AM IN CAPITALS

I’ve broken down the process into seven steps.

1. Albert knows that Bernard doesn’t know. (Maybe Cheryl told him as much). (THE STUFF IN BRACKETS IS INVENTION, IT IS NOT DISCOUNTED, BUT THEN IF INVENTION IS ALLOWED THEN WHY NOT 'THEY WERE BOTH WRONG, BECAUSE CHERYL LIED WHEN SHE TOLD ALBERT THAT BERNARD DIDNT KNOW)

2. Albert deduces Bernard can’t have a unique date such as 18 or 19. (WE MUST ASSUME THAT ALBERT AND BERNARD ARE CORRECT AND AS CLEVER IN DEDUCING THE TRUTH AS US, OTHERWISE WE CAN IMAGINE ALL SORTS OF WRONG CONCLUSIONS THEY DRAW, AND THEN ANY DATE CAN BECOME THE TRUE ANSWER......ALBERT CAN ALSO DISCOUNT THE 15TH MAY 16th May AND 17TH JUNE)

3. Albert, smugly taunts Bernard, announcing Bernard doesn’t know. This is the first statement of the problem.

4. Bernard realises what Albert has realised, which is that Bernard does not have 18 or 19. Now if Albert was holding June he would know the answer, because there is only one remaining date in June, namely June 17. (THIS LAST SENTENCE IS IRRELEVANT LOGIC AND IS THEREFOR NOT LOGICAL THOUGHT, BERNARD WOULD DEDUCE THAT IT IS NOT IN JUNE OR MAY, BECAUSE ALBERT's DEDUCTION MUST HAVE BEEN BECAUSE ALBERT HAD A MONTH THAT HAD NO UNIQUE DATE IN IT) So Bernard deduces it is not June. (AND MAY.....THIS WHOLE 4TH STEP IS COMPLETELY OFF THE TARGET AND IS AN INDICATION THAT THE GUARDIAN ARTICLE WRITER HAS FLAWED LOGICAL THINKING IN THIS PROBLEM)

5. Bernard announces he knows the answer. This is the second statement of the problem.

6. If Bernard is so confident, he must have a unique date (FROM THE REMAINING DATES THAT HAVE NOT ALREADY BEEN DISCOUNTED......NOT, I REPEAT NOT....I'LL SAY IT AGAIN NOT FROM THE ORIGINAL SET). We know it’s not 18 or 19. What other unique date can it be? There are two 14s(YES), two 15s(NO, THERE IS ONLY ONE REMAINING 15TH, THE ONE IN AUGUST.....THE OTHER 15th FROM MAY< WILL HAVE BEEN DEDUCED BY BOTH BERNARD AND ALBERT TO HAVE BEEN DISCARDED (SEE PREVIOUS EXPLANATION) , two 16s(NO ONLY 1 16TH REMAINS POSSIBLE...IN JULY(AS BEFORE) and two 17s(NO, ONLY 1 17TH, IN AUGUST (SEE PREVIOUS EXPLANATIONS) - but Bernard has eliminated June 17 (BERNARD HAS ALSO ELIMINATED MAY15TH and MAY16th)- leaving him with August 17 only(NO...LEAVING HIM WITH AUG17th, JULY15TH and JULY16TH ND HE CTULLY KNOWS THE NUMBER SO HE KNOWS ThE DATE). That’s how he worked it out. (IT IS NOT FINISHED YET, WHICH IS WHY THE FINAL CLUE IS REQUIRED....BERNARD WILL KNOW THE FULL BIRTHDAY DATE NOW....BUT WE DO NOT.)

7. Albert is furious Bernard beat him to the answer. Albert puts himself in Bernard’s shoes, running through the six steps above. Finally Albert reaches the same conclusion we have, Bernard must have 17(NO ALBERT HAS THE SAME DEDUCTIO POWERS AS BERNARD...HE ALSO KNOWS THERE WILL BE 3 REMAINING DATES TO DEDUCE FROM, UNLIKE BERNARD HE DOES NOT KNOW THE NUMBER, BUT BECAUSE HE KNOWS BERNARD KNOWS, HE ALSO KNOWS THAT FROM JUL16, AUG15 and AUG17 BERNARD COULD ONLY KNOW THE DATE IF IT WERE ONE IN A UNIQUE MONTH FROM THIS SUBSET, SO ITS JULY 16th). Albert announces he knows the answer too.

So August 17 is a valid answer. (IT IS A VALID ANSWER IF YOU CARE TO MAKE UP OTHER SCENARIOS AND HAVE OTHER UNMENTIONED CLUES AND IGNORE THE RELEVANCE OF A GIVEN CLUE< BUT AS I'VE SAID< WE CAN GO ON FOREVER LIKE THAT IN CREAKYKNEES IMAGINARIAM OF LIMITLESS BOUNDRYLESS POSSIBILITIES OF BLUE SKY THINKING, AND WE CAN COME UP WITH SCENARIOS WHERE ANY OF THE DATES COULD BE VALID).

But how is it possible to get two different answers to the same question?

It is all about how you interpret the first statement. If Albert has to deduce that Bernard doesn’t know, then we get July 16.

But if Albert knows that Bernard doesn’t know – in other words, that this is a statement of fact, rather than a deduction – then we get August 17. (CORRECT LOGICAL DEDUCTION, IN THIS CASE IS AS GOOD AS 'STATEMENT OF FACT' IF YOU ARE GOING DOWN THE ROOT OF 'MAKING UP OTHER STATEMENTS OF FACT' LIKE CHERYL TELLING ALBERT OTHER THINGS...WHAT IF SHE LIED? WHAT IF ALBERT MISHEARD HER? WHAT IF DEDUCTION CAN BE FLAWED, THEN WHY COULD BERNARD AND ALBERTS DEDUCTIONS NOT BE FLAWED? AND THUS THE ANSWER COULD BE ANY OF THE DATES IF WE DO NOT ASSUME THAT THEY ARE CAPABLE OF MAKING LOGICAL DEDUCTIOSN THEN THE WHOLE HYOPOTHETICAL PROBLEM IMPLODES INTO A MESSY NOTHINGNESS, I.E. ANY DATES COULD BE THE CORRECT ANSWER IF THEY CANT DEDUCE CORRECTLY".

This incredibly subtle change – deduction vs fact - completely changes the nature of the question. Indeed, with fact interpretation the reader can now deduce the answer from just the first two statements of the conversation, whereas the argument for July 16 does require all three statements.

So, can we accept August 17?

Not any more. The originators of the question, Singapore and Asian School Math Olympiads, have rejected this alternative answer.

They say Bernard did not reveal that he did not know the answer at the start of the conversation, so Albert cannot know this as fact. But I don’t think they have settled it, since this ignores the possibility that Albert knows by some other method, for example from Cheryl. (AS I SAID BEFORE, IF YOU DO NOT ASSUME THAT THEY DO IT BY LOGICAL DEDUCTION OR ARE NOT CAPABLE OF IT THEN THERE IS NO POINT IN POSING THIS PROBLEM, ALL ANSWERS BECOME POSSIBLE IF THERE IS THE POSSIBILITY THAT THEIR DEDUCTION IS WRONG, AND THE PROBLEM FAILS TO STATE THAT THEIR DEDUCTION PROCESS IS FLAWLESS, JIUST AS IT FAILS TO MENTION A HUNDRED OTHER THINGS...THE SPIRIT OF THE ASKING OF THE QUESTION SHOULD ACT AS YOUR GUIDELINE AS TO THE BEST ANSWER, WHICH IS JULY 16th........IF YOU ARE GOING TO TRY TO PLAY DEVILS ADVOCATE OR 'THINK OUTSIDE THE BOX, AND ARGUE IT wITH ME...>RECONSIDER, IM IN THE BIG LEAGUE OF IMAGINARIUMS....IF YOU WANT TO STRETCH THE NON ENFORCED BUT IMPLIED BOUNDARIES TO ALLOW AUG 17TH, THEN YOU ARE PUNY IN THAT YOU DO NOT CONSIDER THAT THIS GIVES LARGESSE TO STRETCH THEM EVEN FURTHER TO ALLOW ALL THE DATES TO BE POSSIBLE

## the imaginarium of dr creaknassus

## yep sherlock holmes has a mind palace

I have an mind imaginarium or bizarinarium

## its got lots of those crazy mirrors like what you get at funfairs

## Wrong

The final clue is not required

## not if you make an assumption that is not mentioned in the problem it isn't

otherwise it is.

That is part of my argument......why take an approach which requires an imagined assumption, which then makes one of the given clues redundant, when you can arrive at an answer without any imagined assumptions that fully utilises all the given clues.

## No, it isn't required at all

No imagined assumptions are necessary either.

## oh....sorry I can't see how it works unless you presume that cheryl has told Albert that Bernard

didnt know.

Although for Bernard to make his deduction in point 4 of the guardian article, Bernard would ALSO have to know that Albert had been TOLD that Bernard didnt know.

Not only that, but it not only requires that CHERYL tells Albert, but that ALbert could not deduce (from his month knowledge) that Bernard didnt know) otherwise Bernard might be making his deductions based on the fact that albert had made deduction....so that another little pre-requisite that is necessary for august.....

please explain your logic....I could very well be missing something...i am prone to it

## then how do you know whether it is the 16thjuly or the 15thaug or the 17thaug?

## Sorry Creaky

I had only skimmed over your post and had misread what your point was. I have now read the complete subthread about the supposed validity of Aug 17th as an alternative answer and I am on your side.

## =birthday(cheryl)

## it's a logic question btw guys, not maths

## whilst some of your statement is true, some of it is also false.

## btw

Big Titty Wobblers?

## Decided to take the coin game from up there^

and make a terrible computer game when you always lose (or draw):

http://repl.it/inX and press run

## hello - where is run button?

## should be 'share', 'save', and 'run' at the top of the code bit on the left?

## ah

## low grade responsive design that doesn't show you all options in

certain browser sizes

## Why not randomise who goes first?

(I'm not going to venture into that block of fucking fraction bullshit to try to understand what this 'game' is.)

## if you go first there's a way that you can always win (or draw)

that creakyknees found, so that's what my 'compchoose' function does. If the computer went second, i'd need to create a different strategy.

I basically just wanted to try out coding the creaky method.

## what's the 'block of fucking fraction bullshit'?

## Well there's a whole discussion up there about repeating decimals

and stuff. I just ignored it as it was pretty tedious and I thought the coin thing was embedded in it.

## No that's another thread

I can be boring in two places at once.

## It was only the subject that was tedious to me.

I understand the desire to get the point correct. :D

## Well to be honest

All I wanted was a nerdy ramble with a fellow mathematician. And I got that, so that was a result.

## that's a different thread

the coin discussion is based on this post: http://drownedinsound.com/community/boards/social/4462045#r8543820

## Yeah.

The fact the thread's smashed added to my disinterest to try to unpick things, to be honest.

## talking of which

Im learning Ruby......do you think Sean might want me to have a go when Im up to speed?

## whoops forgot the safety ;D

## Sounds like you're already up to speed to me!

;)

## depends on how much you've got done on a dubstep album, surely

## Ah right, so my job is to foil the computer's strategy?

## Oh right, I see, you can't stop it working, can you?

## nope, you always lose (or occasionally draw)

great game

## You never draw

If the amounts are tied player one wins.

## I didn't implement that rule

just seems unfair

## Has anyone considered he could be eating his dead wife?

## ..

"Smee and Balonz just became friends with Theo, and they want to know when her birthday is. Theo gives them a list of 10 possible dates.

May 15 May 16 May 19

June 17 June 18

July 14. July 16

August 14. August 15. August 17

Theo then tells Smee and Balonz separately the month and the day of her birthday respectively.

Smee: I don't know when Theo's birthday is, but I know that Balonz does not know too.

Balonz: At first I don't know when Theo's birthday is, but I know now.

Smee: Then I also know when Theo's birthday is.

When is Theo's birthday?"

## dean

says he dont give a fuck

## * sean Arghhhh

and I forgot the safety wink ;)

Sorry Theo, this thread going on has brought back memories of ......you know what

## Next in my series of terrible games

here's a 2 player noughts and crosses that doesn't check if anyone's won or if the grid is full:

http://repl.it/inr/23

## great game

Here's the grid:

A B C

1 - | - | -

---------

2 - | - | -

---------

3 - | - | -

Player 1, choose a position: b2

Here's the grid:

A B C

1 - | - | -

---------

2 - | O | -

---------

3 - | - | -

Player 2, choose a position: b2

Not a valid position, choose again: 1a

Traceback (most recent call last):

File "", line 47, in

File "", line 16, in validpostion

ValueError: invalid literal for int() with base 10: 'a'

## ah thanks

fixed: http://repl.it/inr/24

want to make it a working game but it will take a while so I should probably do some actual work

## It's a working 2 player game now:

http://repl.it/inr/26

need to create a computer player next

## You can play against a computer now

or watch a computer play against itself

http://repl.it/inr/33

The computer plays randomly though so it's quite easy to win

## Everybody out of my thread please

## it is a tip

## What's weird is that July 16th is my birthday

or I thought it was, until I read this.

## Your birthday's 17 August, silly!!

## Not really interested in the puzzle itself

but you lot that were talking about the fractions, did you come to any conclusions?

## No we just had an argument

## war*!

what is it good for?

*arguing

## So...

We've finally nailed down two of the correct answers - 16 July and 17 August - but can anyone work out the third??

## She was born on the stroke of midnight

on 29th February and technically has no birthday

## Oooh!

## which cunts are perpetuating this thread?

## dios mio