I Just Don't Believe It!

[mr_hippo]

Seven days ago on a different forum, I posed what I thought was a simple question. Seven days and thirty pages later, it has been viewed 7182 times and generated 446 replies to date. There is only one possible answer to the question and I have explained many times how I arrived at that answer. What was the question that caused all the fuss? There were two ducks in front of a duck, two ducks behind a duck and a duck in the middle. How many ducks were there?

Edited for typo

Edited June 16, 2007 by mr_hippo

[Paulbangkok]

3??? innit?

Edited June 16, 2007 by Paulbangkok

[mr_hippo]

3??? innit?

That is the only answer that it can be!

[Paulbangkok]

3??? innit?

That is the only answer that it can be!

Exellantavooo

[issanpaul]

3??? innit?

That is the only answer that it can be!

Exellantavooo

????? please explain, cant work it out? or is i just too thick and is obvious?i come up up with many answers but 3 is not one of them? mmmmmmm

[Paulbangkok]

look at the three dummy suckers there in a vertical line

the on at the top has two behind him

the one at the bottom has two in front and

theres one in the middle

TYPO EDIT

Edited June 16, 2007 by Paulbangkok

[Soju]

There is only one possible answer

If there are five ducks in a row, then from the middle duck, there are two ducks in front of that duck, two ducks behind that duck, and that duck is in the middle.

Likewise, if there are seven ducks in a row, then there are two ducks in front of the third duck, two ducks behind the fifth duck, and the fourth duck is in the middle.

There are an infinite number of solutions to this puzzle as it is worded. Perhaps wording it would have been better, such as:

There were two and only two ducks in front of a particular duck, and no ducks behind that duck.

There were two and only two ducks behind a particular duck, and no ducks in front of that duck.

There was one duck in the middle.

How many ducks were there?

In that case, assuming the ducks are all in a row, the correct answer is 3.

Perhaps I'm missing something here and your "only possible solution" is based on something more than the obvious?

[mr_hippo]

Paulbangkok has illustrated vertically and it can also be done horizontally. The '@' will represent 'a duck'

There were two ducks in front of Duck1 who is a duck behind two ducks @@1

two ducks behind Duck2 who is a duck in front of two ducks 2@1

and Duck3 in the middle. 231

[Soju]

Sorry, but this is just silly. I did a search for your post on the other forum you mentioned and in my opinion the people telling you you're wrong are right. You're too caught up with what "a" means to you, whereas it's obvious that to a majority of the people "a" means something different. To you, "a" means "one", using your own words, but in actually, via your explanation, it really means "one and only one" to you. But to the majority of people, "a" does not mean "one and only one", it means "one, but possibly more than one".

If I go with you to lunch and I'm short one dollar and ask you, "do you have a spare dollar?" You look in your wallet and see you have three dollars, will you respond, "no" because you have three spare dollars? Of course not! You'll respond, "yes."

Edited to add:

Furthermore, your original question is not even legitimate, based on your definition of "a". If there is "a duck", meaning "one duck", then there can't be any more. So there cannot be any ducks in front, behind, on top, below, or wherever. There is one and only one duck, period. If you broaden your definition of "a" to what the general population define it as, then your question is valid, but your reasoning behind there being only one answer then fails based on your broader definition. You can't have it both ways.

Edited June 16, 2007 by Soju

[Paulbangkok]

OY Enough of all This...... I solved it and thats all that matter's :D :D :bah:

[mr_hippo]

Sorry, but this is just silly. I did a search for your post on the other forum you mentioned and in my opinion the people telling you you're wrong are right. You're too caught up with what "a" means to you, whereas it's obvious that to a majority of the people "a" means something different. To you, "a" means "one", using your own words, but in actually, via your explanation, it really means "one and only one" to you. But to the majority of people, "a" does not mean "one and only one", it means "one, but possibly more than one".

If I go with you to lunch and I'm short one dollar and ask you, "do you have a spare dollar?" You look in your wallet and see you have three dollars, will you respond, "no" because you have three spare dollars? Of course not! You'll respond, "yes."

Edited to add:

Furthermore, your original question is not even legitimate, based on your definition of "a". If there is "a duck", meaning "one duck", then there can't be any more. So there cannot be any ducks in front, behind, on top, below, or wherever. There is one and only one duck, period. If you broaden your definition of "a" to what the general population define it as, then your question is valid, but your reasoning behind there being only one answer then fails based on your broader definition. You can't have it both ways.

Let's examine 'a duck', can it mean more than one duck? The short answer is that it can't. 'A' is the indefinite article and cannot be applied to plurals, 'Duck' is a singular noun. Do we say 'A ducks'?

If I say to you 'I have a pen in my hand.' How many pens do I have in my hand? According to you, it means that I have one pen in my hand and possibly more. Looking at your dollar 'explanation', how many did you get? One or one and possibly more?

[Paulbangkok]

There were two ducks in front of a duck, two ducks behind a duck and a duck in the middle. How many ducks were there?

A Duck can only mean one thing, 1 Duck, IMHO he's right, and therefore so was I

[PhilHarries]

I think Mr H would be correct if he used the word "only" to classify the two ducks.

As it is, if you have a line of 149 ducks then there are two ducks ahead of duck #3 to Duck #149 and two ducks behind duck #1 to duck #147. The fact that for the majority of cases there are more than two ducks is made irrelevant by the absence of the word "only".

But in common parlance the indefinite article 'a' has come to signify one unit and by inference the 'a duck' in the question is one and the same duck so Mr H is correct.

So I think he is correct and there are three ducks but are they Peking or Bombay ducks?

[mr_hippo]

As paulbangkok and I have said the answer is three, we have both given you illustrations - vertically and horizontally.

[Soju]

Let's examine 'a duck', can it mean more than one duck? The short answer is that it can't. 'A' is the indefinite article and cannot be applied to plurals, 'Duck' is a singular noun. Do we say 'A ducks'?

If I say to you 'I have a pen in my hand.' How many pens do I have in my hand? According to you, it means that I have one pen in my hand and possibly more. Looking at your dollar 'explanation', how many did you get? One or one and possibly more?

As per my dollar example, I might have received more than one single dollar. It depends on the giver and whether he thinks I just needed one dollar or maybe I might need more.

As to do we say "A ducks"? No, we do not. But that doesn't mean that "a duck" is strictly singular. If you order a dinner for a large group of people, and for the main course a huge platter of roast duck is served, representing multiple ducks, would you say you ordered "roast ducks"? Of course not, you'd say "roast duck" even though the number of ducks was plural. Thus the absence of an 's' on the end of a word doesn't necessarily denote the absoluteness of singularity. You have to judge that based on the context.

The word "a", likewise, must be judged on the context in which it is used. It can mean "one and only one" when used in a certain context. It is up to the reader to judge whether it means "one and possibly more than one" or if it means "one and only one". In fact, many times the reader cannot judge which is the case based on the information contained in a single sentence but needs more information before such a determination can be made. In the absence of enough information to determine it's exact meaning, it has to be assumed to mean "one but possibly more than one". That is simply the way the English language is understood by the majority of people. Perhaps you think that the word "a" in your example means "one and only one", but the language is defined based upon how the majority of people interpret it, not based on one single person's interpretation. In this case you are clearly outnumbered and so the majority rules. Your puzzle was not really a mathematical puzzle, but a linguistic puzzle based on your own private interpretation of the language that doesn't hold true to the general population, thus you cannot state that your answer is correct and that others are incorrect because your correctness is based totally on your own interpretation of the language and not on undeniable mathematical principles.

Here's a question for you:

There is a duck. How many ducks are in front of the duck?

Based on your interpretation of "a", your answer must be zero, because if you solve for x, where 1 + x = 1, x must be zero. Am I correct?

Now, take this one step further, and make the question:

There is a duck in the middle. How many ducks are there?

Again, based on your interpretation of "a", the answer must be one. Correct?

So back to your original question:

There were two ducks in front of a duck, two ducks behind a duck and a duck in the middle. How many ducks were there?

It contains the statement:

[There was/were] a duck in the middle

to which we have already determined it means there is a total of one duck, based on your interpretation and thus there cannot be any more ducks so your entire question is nonsense since you contradicted yourself within your own question.

[mr_hippo]

Soju, do you really want me to reply to your post?

[PhilHarries]

Just realised that my last arguement comes up with five ducks........................doh!

Can't even offer a hangover as an excuse and, quite frankly, I don't care as next stop is Finnegans for a pint. But if I have two pints in front of my pint and two pints after my pint how many pinntttssscccchhh have I had!

Good day and have a good weekend all of you.

[Soju]

Just have to add this:

If you have one large father duck on the right, and one large mother duck on the left, and three baby ducks lined up between the mother and father duck, as per the following configuration:

M Baby 1 D

o Baby 2 a

m Baby 3 d

Is there not two ducks in front of baby 3? Are there not two ducks behind baby 1? Is not Baby 2 in the middle? Are there not five ducks total? Why is this not a solution to your puzzle?

Edit to add, someone will say that Baby 1 and Baby 3 are also in the middle, so that makes three ducks, not one duck in the middle. In this case, consider that they are flying in this formation but that Mom, Dad, and Baby 2 are all level with each other, while Baby 1 and Baby 3 are flying above and below the plane of the others, thus they are no longer technically in the middle, but Baby 2 would still be in the middle.

Edited June 16, 2007 by Soju

[Soju]

Soju, do you really want me to reply to your post?

ABSOLUTELY! I wouldn't have posted it if I didn't want a reply!

[mr_hippo]

OK, I will humour you -

Baby1

Front

Mum Baby2 Dad

Baby3

I have just tidied your illustration up, there are three ducks in the middle

Edited June 16, 2007 by mr_hippo

[mr_hippo]

'A duck' is one nondescript duck. There is nothing to distinguish that 'a duck' from millions. We know nothing about 'a duck' but wait - what do do we know about the first 'a duck'?

'Two ducks in front of a duck', do we know anything about this duck, can we define it? 'It is a duck that has two ducks behind it.' The second one is 'A duck behind two ducks' so that is 'that has two ducks in front of it' and we know where the third one goes.

We have three ducks who have been described and only three. I have not suggested that there are any more, have I?

Let the symbol '@' represent 'a duck'

Front @@@ Rear

My statement describes the position of three ducks and only three ducks.

Can you see two ducks in front of a duck? If you point to the duck on the right, it does have two in front of it. Point to the left duck and it does have two ducks behind it. Now describe the only duck that you have not pointed to, could this be described as 'a duck in the middle'?

[Soju]

OK, I will humour you -

Baby1

Front

Mum Baby2 Dad

Baby3

I have just tidied your illustration up, there are three ducks in the middle

No, I made my illustration the way I did because the mother and father ducks are large and their bodies the length of the three baby ducks put together. The beaks of Mom, Dad, and Baby 1 are all at the furtherest forward point. The tails of Mom, Dad, and Baby 3 are all at the furthest rear point. Thus Mom and Dad are not in the middle, they are on the sides. Also Mom and Dad are not in front of or behind any of the other ducks because their bodies extend the entire length of their babies. They are merely beside their babies.

[Paulbangkok]

Just realised that my last arguement comes up with five ducks........................doh!

Can't even offer a hangover as an excuse and, quite frankly, I don't care as next stop is Finnegans for a pint. But if I have two pints in front of my pint and two pints after my pint how many pinntttssscccchhh have I had!

Good day and have a good weekend all of you.

ave one extra! for me pls

[mr_hippo]

We have already proved that there are only three and no more, learn to live with that fact.

[Soju]

'A duck' is one nondescript duck. There is nothing to distinguish that 'a duck' from millions. We know nothing about 'a duck' but wait - what do do we know about the first 'a duck'?

'Two ducks in front of a duck', do we know anything about this duck, can we define it? 'It is a duck that has two ducks behind it.' The second one is 'A duck behind two ducks' so that is 'that has two ducks in front of it' and we know where the third one goes.

We have three ducks who have been described and only three. I have not suggested that there are any more, have I?

Let the symbol '@' represent 'a duck'

Front @@@ Rear

My statement describes the position of three ducks and only three ducks.

Can you see two ducks in front of a duck? If you point to the duck on the right, it does have two in front of it. Point to the left duck and it does have two ducks behind it. Now describe the only duck that you have not pointed to, could this be described as 'a duck in the middle'?

I understand your interpretation, but that does nothing to dispute my arguments against your interpretation. You are merely explaining your interpretation further, which I already understood some time ago. An answer to my post, not a further explanation of your interpretation is in order.

However, I cannot let go what you just said about "nondescript duck", "the first 'a duck'", "the second one", and "the third one". Who says you are referring to one group of ducks by all three of your original statements? In your first statement, "There were two ducks in front of a duck", via your logic, that equals 3 ducks. In your second statement, "two ducks behind a duck", that equals 3 ducks, but not necessarily the same ducks as in the first statement. And in your last statement, "and a duck in the middle", it might also not be any of the same ducks as in your first and second statements. Thus you could have 7 total ducks.

Clearly your puzzle was worded in a way that is extremely ambiguous and in general there is no agreement that you are correct because the majority of people do not interpret your words the way you do. Explain your solution all you want, but you cannot deny that others interpret English differently than you do.

[Soju]

We have already proved that there are only three and no more, learn to live with that fact.

Oh dear. A proven fact? In your mind perhaps but obviously not in the minds of most others. You have yet to prove how my mother/father/baby configuration doesn't offer a different solution, and you have yet to prove that "a" is interpreted as "one and only one" by the majority of English speakers, and you have yet to answer the other points I raised. Nothing proven whatsoever. But keep trying, it's fun watching you.

[mr_hippo]

I have yet to meet any English speaker - native or non-native - who will say that a duck is anything more than one duck. It may be one of many but the fact remains that it is only one duck.

My statement about three ducks is complete. You are in possession of all of the facts you need to solve it. Others may interpret it different and read into it more than there is but they are, like you, wrong.

[Soju]

It may be one of many but the fact remains that it is only one duck.

So it then follows, based on your very own words, that "a duck" may be one of many, so in your original puzzle you can replace the words "a duck" with the words "one duck out of possibly many". Correct?

So rewriting your puzzle results in:

There were two ducks in front of one duck out of possibly many, two ducks behind one duck out of possibly many and one duck out of possibly many in the middle. How many ducks were there?

This is precisely what most of us are trying to tell you is how it is interpreted, and how based on your own words it would be interpreted by simple substitution of your very own definition of "a duck". Got it yet?

And you wonder why your post on this subject on the other forum generated 30 pages of 446 replies? I think the answer is quite obvious. You just keep going on yet don't understand what everyone else is trying to tell you. It is you who is wrong.

BTW, still no disputing my Mom/Dad/Baby solution I see.

[mr_hippo]

One duck out of many is still ONE duck. I made a statement describing three ducks, no more, no less. Your 'solution' of the mum, dad and three babies - words fail me! Did I make any mention of baby ducks? Did I mention the size? Why? It is not relevant to the puzzle, is it?

I have made a statement

You words "There were two ducks in front of one duck out of possibly many", now how many ducks are you talking about? You mention two duck and one duck which is three ducks. In case you did not understand the first time - One duck out of many is still ONE duck.

You are thirsty and you go into your local Mini-Mart and and ask for 'A can of Pepsi' There are many cans of Pepsi in the Mini-Mart, how many will you be given? ONE!

[bino]

A Duck can only mean one thing

Yup.

If it looks like a duck, if it walks like a duck, if it quacks like a duck, it must be a duck!