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Difficult Riddle!

Posted on 2003-03-03
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A man comes up to you and says, "Everything I tell you is a lie!". Is this man telling the truth or is he lieing?
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Question by:Tutalian
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by:billious
ID: 8060667
Yes.

...Bill
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by:TheBeaver
ID: 8060693
He is lieing.

Because if he was telling the truth, then the statement he makes about "everything" being lies is a lie.

And if he was lieing that everything he says is a lie then he is telling a lie in that statement.

So he is lieing.
 
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by:TheBeaver
ID: 8060702
Just to clarify my previous rambilings :)

If his statement is true then he would be lieing right now.

Therefore his statement MUST be a lie. Because if he always lied, then he would not make that statement.
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by:halfcent50
ID: 8061236
Neither - it's a paradox - similar to:

"Assume that God can do anything.  Therefore can He create a rock that he cannot lift?"

Much like division by zero, no acceptable answer.
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by:TheBeaver
ID: 8061266
Only the "everything" part is a lie. Its like he is saying "I only lie sometimes"
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by:MacRae
ID: 8062118
No, I don't think there's a paradox.

Say this is a guy who mixes truth with lies.

This time he has told us that ALL his statements are lies. This is clearly a lie, but no paradox - it just happens to be one of the times he lies.

In a minute he may well truthfully say "A minute has gone by since I last spoke".
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by:halfcent50
ID: 8062294
<TheBeaver>
IMHO, if any part of a statement is false, then the entire statement is false.

<MacRae>
If I understand the question correctly, Tutalian is asking whether the statement is true or false - not whether the man is truthful person or a liar.
The statement itself can neither be the truth, nor a lie.  Both choices become their own contradictions, so there is no answer.
Whether the man is a truthful person or a liar is irrelevant to the question.  With no more information available, only that single statement itself can be analyzed for its honesty.

<Tutalian>
Is the statement itself the only focus of your question, or is the honesty of the man himself the question?
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by:Wise_guy
ID: 8062420
The statement that he lies about everything, is not plausible. It is impossible to lie about everything. There for his statement is in fact a lie.
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by:jpkemp
ID: 8062451
I would have posted this riddle as:

"A man comes up to you and says something. You know immediately that he is lying. What did he say?"

Jeff
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by:billious
ID: 8062570
"With the latest version of Windows, your applications will run faster and better than ever before!"

Hey, jpkemp - you're right! I even know WHO the man is!

...Bill
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by:JerMe
ID: 8062912
"Everything I tell you is a lie."

If "Everything" includes the man's statement, then the man's statement is a lie in itself.

If the statement is a lie, then the man is telling the truth.

But... If the man is telling the truth, then the truth is a lie.

It's a paradox...
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by:andyalder
ID: 8063066
The paradox is "this is a lie"...

"Everything I say is a lie" is not a paradox but a lie by the same reasoning as TheBeaver, the truth of the matter is that sometimes he lies and sometimes tells the truth.
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keneso earned 100 total points
ID: 8064757
as posted the question could be this is the first and only statement from him, being so, the man is telling the truth.

the premise:
at least one time in one's life we tell a lie or a truth.

the conclusion:
Being the only statement from the man, we can say he is lying when he says everything he tells is a lie, therefor he is telling the truth, since his everything has to be applied to that sentence only, being that sentence a lie, he is telling the truth about "everything being a lie" his "everything is his only sentence.

of course I agree too with who says this is a paradox!
here is another lie paradox:
"All Athenienses (spelling?) are liars, I am an atheniense"

<billious>
LOL a great one!
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by:ozo
ID: 8070088
That's not a paradox as long as there exists at least one truthful Athenian
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by:keneso
ID: 8070604
yes it is, bc the one who says that, is an athenian, therefore if he is telling the truth he must be a liar, do you see it?
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by:Sanker
ID: 8071234
[quote] "Assume that God can do anything.  Therefore can He create a rock that he cannot lift?" [/quote]

He can create the rock, and then he can lift it.  :-)  Because, by that statement, he can do anything... And contadiction is part of everything...  This takes me back to quantum maths, I'm gonna stop now before I get a headache :-)
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by:Mennovdh
ID: 8072877
He's not lying, and neither is he speaking the truth,...he's just drunk.
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by:Linzer
ID: 8073145
andy and those who agree with him : I agree with you!

And everybody who said there is a paradox : read the sentence again...

JerMe :
>> If the statement is a lie, then the man is telling the truth.
This is an incorrect conclusion.
Negation of "I always lie" is not "I always tell the truth"...
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by:Tutalian
ID: 8075614
Maybe some of you are confused. What I am trying to ask is: Is the statement 'Everything I tell you is a lie' the truth or a lie?
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by:Wise_guy
ID: 8075696
I answered that question. It is not plausible to lie about everything. The literal definition of a lie is a delibrate intent to deceive. It is not possible for someone to deliberately deceive on a consistent basis. He has to be lying.
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by:andyalder
ID: 8075837
>Maybe some of you are confused. What I am trying to ask is: Is the statement 'Everything I tell you is a lie' the truth or a lie?

It is a lie. Always truthful and always lying are not mutually exclusive. The sets intersect where the current statement is untrue but some previous and future statements willhavebeen be true. What part of that do you not understand?
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by:halfcent50
ID: 8076864
Statement:  "Everything I tell you is a lie"

OK, I've flipped my opinion on this one.  As stated previously, in several of the above posts, the only valid answer to this is that the statement is a lie.

If we test this statement by assuming that the statement is true, then (by the statement's own admission) everything the person says IS a lie, therefore making this statement a lie also.  It can't be both the truth and a lie.  This contradiction demonstrates a classic paradox here, so the statement simply cannot be true.  So "truth" would be an invalid answer.

But, if we test this statement by assuming that the statement is a lie, then we'll find that we really know two things:
First, the person DOES lie sometimes (this statement proves that).  Secondly, he CANNOT lie in EVERY statement that he makes.  If he DID lie in every statement that he makes, then the above statement would be true, causing the paradox explained in the first test.  But we are not asked whether the person actually lies in every statement that he makes.  We are only asked if THIS statement alone is the truth, or a lie.

So, as shown by the tests above,  the only possible answer is that the statement must actually be a lie, since it CANNOT be the truth.
I know that I'm just repeating the same answer given in some previous posts.  I'm just stating it a little differently.  Just using the same reasoning that I was taught in school to use on True/False questions on tests.  That is that if any part of a question is false, the entire question is false.
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by:ecims
ID: 8079374
Ah yes, the Liar's paradox, aka Epiminedes paradox.
I believe this question was answered 2600 years ago.  

Without a contextual false this is an undecidable proposition, aka "meaningless statement".

You must understand grasshopper, "without an inside there can be no outside..."

For further discovery;
http://www.uwm.edu/~britton/newsletter/news2-4.html
http://www.geocities.com/galois_e/page/paradox.html
http://www.redding.com/columnist/dsoccio/stories/20030224colds035.shtml

Honestly Tutalian, the truth is I am lying.
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by:Squajbob
ID: 8082074
He is lying.

Lets look at it this way.....

If he were telling the trust, then the statement "Everything I tell you is a lie" is the truth, which then turns the statement false.  This means that statement of his is a lie.

If we say that the statement "Everything I tell you is a lie" is a lie, that means that what he says is the truth, meaning that he cannot always give lies to you.  

So my answer is that this man is lying.  
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by:kohashi
ID: 8087928
I believe this was more well known as the Cretan Paradox (because Epiminedes was from Crete :)  )
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by:kohashi
ID: 8087954
he is also lying.  Everything he tells you isn't a lie but some of it is.  :)
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by:sagacity
ID: 8090368
HE IS LYING.  THE SENTENCE IS NOT A PARADOX.

This is an extremely simple proof by contradiction:

1)
Assume he is telling the truth.
If he is telling the truth, then he is lying.
This is A PARADOX.
--> He cannot be telling the truth.

OR

2)
Assume he is lying.
--> SOMETHING he says is the truth.  Not necessarily that statement.

Looking at the above proof, we can see that if he's telling the truth, then he's lying.  This is the liar's paradox.  It is NOT UNANSWERABLE.

If he is telling the truth -- paradox.
If he is lying, NO PARADOX.

Ergo - he is lying.


ecims,
The UMW article is wrong in regards to Epiminedes.  It was written by a linguist, not a logician.  According to the linguist:

"Let's look at the phrase again: ``All Cretans are liars." Now, knowing that Epimenides was a Cretan, the problem becomes clearer (while at the same time the sentence becomes less clear).
[A]Epimenides is a Cretan, so he must be a liar, but if he is a liar, then what he says would be a lie. If this were the case, then the original statement would be a lie.
[B]Following this through would then mean that Cretans are not liars, and Epimenides, being a Cretan, would then be uttering the truth, and that is where this whole paradoxical mess began!"

[A] - logically sound and true
[B] - logically unsound and false


Peace,
Drew
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by:ecims
ID: 8093369
<<sagacity:  This is an extremely simple proof by contradiction:>>

I must respectfully disagree with you.  If you are going to split hairs, in fact, the paradox stated is more appropriately known as "Eubulides Paradox".  It was one of a series of puzzles attributed to the Megarian logician Eubulides of Miletus and is part of the Sorites paradox, which is a class of paradoxical arguments also known as little-by-little arguments.  The "original" Epiminedes Paradox, which was solvable is "All Cretans are liars...One of their own poets has said so.".  But the statement made by Tutalian was "Everything I tell you is a lie!".  This version is known as the strengthened liar's paradox, which is in fact a paradox.  

The only reason a linguist got involved is because in order to form a "solution" one must infer or assume context.  Without context and some linguistic inferences and assumptions this is a paradox.

This is a declarative sentence without context.  It is not solvable through contradication, but unsolvable by contradiction.  It is most certainly unanswerable the way it was stated using "modern" logic.  Halfcent50 summed it up when stating "Much like division by zero, no acceptable answer."

You have already unwittingly shown that it is in fact unanswerable.  Because there is an equally possible chance he is lying or thruthful this question can not be solved.  Your argument fell apart the second you typed OR.  The OR creates an equally probable situation without context.

You simply have no way to prove he is truthful or lying from that one statement.  

Ergo - it's unanswerable.

http://www.classroomtools.com/logic.htm
http://mathworld.wolfram.com/LiarsParadox.html
http://www.utm.edu/research/iep/p/par-liar.htm
http://www.cs.cornell.edu/Info/Projects/NuPrl/Intro/TypeSetDomain/typesetd.html
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by:ecims
ID: 8093376
Oops, sorry, my diatribe about the paradox name was directed towards kohashi.
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by:sagacity
ID: 8094597
ecims,

While I appreciate your conviction, this is not a matter of opinion.  The above scenario (A man says, "Everything I tell you is a lie.") has only one result.  He is lying.

If you read a bit closer on your links (http://mathworld.wolfram.com/EpimenidesParadox.html), you'll find I'm right:
"A version of the liar's paradox, attributed to the philosopher Epimenides in the sixth century BC.  "All Cretans are liars...One of their own poets has said so." This is not a true paradox since the poet may have knowledge that at least one Cretan is, in fact, honest, and so be lying when he says that all Cretans are liars. There therefore need be no self-contradiction in what could simply be a false statement by a person who is himself a liar.

A sharper version of the paradox (which has no such loophole) is the Eubulides paradox, "This statement is false.""

Just because it looks like a duck does not mean it's a duck.  In essence, you're comparing apples to crabapples.  Similar, but not the same.

If you really find it necessary to back your case up wtih links, then here's one:
http://linas.org/mirrors/www.ltn.lv/2001.03.27/~podnieks/gt5.html
"a) If Epimenides' statement is true, then Epimenides also is a liar, i.e. he is lying permanently, hence, his statement about all Cretans is false (and there is a Cretan who is not a liar). We have come to a contradiction.

b) If Epimenides' statement is false, then there is a Cretan, who is not a liar. Is Epimenides himself a liar? No contradiction here.

Hence, there is no direct paradox here"


Now as a follow up to your invalid statement of:
"You have already unwittingly shown that it is in fact unanswerable.  Because there is an equally possible chance he is lying or thruthful this question can not be solved.  Your argument fell apart the second you typed OR.  The OR creates an equally probable situation without context."

There is NOT an equally possible chance he is telling the truth vs. lying.  Especially not because I used the word OR.  To be more accurate, I should have used XOR.

As in:
He is lying or telling the truth, but not both (hence the exclusive or).

If you take a multiple choice test with the question "What integer is between 4 and 6" and you are presented with the possible answers of "5, 20, 50, 1000" -> that does not mean 50 is equally as likely to be an integer between 4 and 6.

So back to square one:
He is either lying XOR telling the truth.
If he is telling the truth, there is a paradox.
If he is lying, there is no paradox.
Ergo - he's lying.

Now in all fairness - there ARE self-referencing sentences that can create a paradox.  The above example, as well as Epiminedes ARE NOT PARADOXES.  Hence, they are both solvable.

Peace and Logic,
*Drew
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by:ecims
ID: 8096349
A) You continue to reference the wrong paradox.
Epidemines Paradox
"All Cretans are liars...One of their own poets has said so."

Eubulides Paradox
"This statement is false."  OR in our case "Everything I tell you is a lie"

B)  The examples you keep showing are from Epidemines Paradox.  We are dealing with Eubulides Paradox.

Epidemines Paradox can be solved.  But we are dealing with Eubulides Paradox and in the case of this paradox it states;    "A sharper version of the paradox (which has no such loophole) is the Eubulides paradox."

It says "NO SUCH LOOPHOLE."  That means not solvable.

C) There is absolutely no way of telling if he is lying or truthful from that statement.

D) This is known as the strengthened liar's paradox and is not solvable.

E)  Do yourself a favor and go to dictionary.com and lookup the definitions of the word paradox.  

paradox
n : (in logic) a self-contradiction; "I always lie"


Peace.
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by:ozo
ID: 8096440
"Everything I tell you is a lie" implies "This statement is false." but is not equivalent to it.
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by:sagacity
ID: 8096570
Thank you, ozo.

ecims,

You're the one that brought in the reference to Epedimines, not me.  I was only illustrating that both Tutalian's example as well as your own are solvable.

"This sentence is a lie."  and "This sentance has three erors." -->  These are "self-referencing sentences".  These are classic examples of the paradox we're talking about.

You're lumping Tutalian's example into this group of self referencing sentences.  The negation of "All whales are blue" is not "All whales are not blue" -- it's "There exists a whale that is not blue."  Therefore the nagation of "Everything I say is a lie" is "There exists at least one thing I say that is the truth."  It just so happens this is not that time.

Read your own sites and posts:
"Ah yes, the Liar's paradox, aka Epiminedes paradox.
I believe this question was answered 2600 years ago." was from your original, then you follow up with "Epidemines Paradox can be solved."

I agree that Eubulides Paradox cannot be solved.  I actually read my citation.  But as ozo pointed out (seemingly more clearly than I) - "Everything I tell you is a lie" DOES NOT EQUAL "This statement is false."  This just ain't Eubilides.  Point of fact, it more closely resembles Epeminides.

In summation:
A)  You were the one to reference Epidemines paradox.  Which coincidentally perfectly applies to this example.
B) Eubulides Paradox is not solvable, but that's not what we're dealing with.
C) There is a way of telling if he is lying or truthful from that statement.  I've already proved it.
D) The strengthened liar's paradox has no bearing on this discussion.  (see B)
E) Perhaps you should do your own self a favor and go to dictionary.com and lookup the words "Similar" and "Equal".

I understand that at this point, you may be too emotionally invested in your opinion to "concede", but regardless, I am continuing to try and make my point clear.  Believe me, it was not my intention to begin a flame war, but logic and reasoning is subject near and dear to me.  I was just trying to end the debate and make it clear to the world, that it's just not that complicated:

He's lying.

Honestly,
*Drew
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by:ecims
ID: 8097346
I mentioned Epidemines because that was my first thought when I saw the riddle.  After I researched it a little I realized it was actually Eubulides Paradox.  This is a classic paradox that is taught in college logic courses and mentioned in New Testament teachings.  Many much brighter minds before us have debated this issue and the result is it's unsolvable using classical logic.  

This is the original paradox as written by Eubulides;
"A man says that he is lying. Is what he says true or false?"

This is the Tutalian riddle;
"Everything I tell you is a lie!". Is this man telling the truth or is he lieing.

Tutalian has asked us to solve Eubulides Paradox.  And Eubulides Paradox is unsolvable.  Period.

This form of Epidemines Paradox is known as the strengthened liar's paradox.  The term strengthened refers to the fact that there are no loopholes.  The statement is a strengthened paradox because Eubulides *intentionally* removed information to make the statement unsolvable.

We are obviously all entitled to our opinions and I have enjoyed your retorts.  But concede, to what?  I would no sooner concede that this is not a paradox than to the idea that division by zero is not unanswerable.  I might as well give up on the scientific method while I'm at it.  That's ok, I will stick with the formal education I have received and depended on for years which tells me this is a paradox.   I really thought the definition in the dictionary would help you understand that this "problem" cannot be solved.  In fact, this self referential riddle is the very essence of the definition of paradox.

I simply find it odd that you fail to see that the statement "Everything I tell you is a lie" is a self-contradiction.
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by:sagacity
ID: 8098384
Please don't imply that my argument has no basis in scientific method.  It seems rather petty.  Especially since it's incorrect.

The reailty is (whether you see it that way or not) that I'm arguing that this is not Eubilides.  THIS is really our point of contention, especially since I have frequently agreed that Eubilides is unsolvable.  So instead of going back and forth skirting around the issue with you repeatedly stating as argument what I have repeatedly agreed with, and since you have yet to argue WHY you think it's Eubilides... Let's examine the issue head on.

"I AM LYING" vs. "EVERYTHING I TELL YOU IS A LIE"
=================================================

I will try and show that Tutalian's proposal is NOT Eubilides.

First off, we'll review the rules of implication.

"A -> B" This means A implies B.  Or from programming perspective: If A, then B.  If A is true, then B is true.

"Everything I tell you" is a set which contains ALL sentences.

We'll say A is "Everything I tell you is a lie", and B  is "That sentence is a lie".

HOWEVER:
Though ~B -> ~A (not B implies not A), it is not the other way around.  Specifically ~A does NOT NECESSARILY IMPLY ~B.  That would be an IFF (If and only if...
Which means ~A could imply B.

The paradox arises when we carry out if the sentence is true:
A -> B -> ~A ... paradox (and I'd be lying if I wasn't a little insulted that my disagreeing whether our not this was a paradox prompted you to think I didn't know what a paradox was.)

However, what if A is false (going back to my proof by contradiction -- which IS a proof by the way)
~A -> B.

I also haven't heard a response to my statement that the negation of the universal is the existential...but I digress.

The problem was his sentence was NOT self-referencing.  It only implied it.

*************************************

Now for a litle puzzle of my own:

I determined yesterday an argument that you could make where there would be no room for discussion.  It would absolutely be Eubilides.  I'm making an assumption that really has not been addressed here yet (either pro or con) that in essence means:
If my assumption is correct, then it's solvable.
If my assumption is incorrect, then it's unsolvable.

(And the assumption is NOT Eubilides vs. Epiminides)

I am hoping that our conflict was driven from these different assumptions (~X vs. X) and not because you're questioning my abilities in "classic" logic, or even more insulting - my understanding of logic.  If you are assuming ~X, then you are correct (assuming ~X is the case).

Using MY formal education (in logic, mind you) which has also suited me well, I can certifiably say...heck, even submit to logic professor's to verify...that based on my assumption, the riddle is NOT A PARADOX.  Just as accurately as I would submit that if my assumption is incorrect, the riddle IS A PARADOX.

I'm hoping that you are assuming the negation of my assumption.  That's why I'm giving you a chance, without hint, to state your assumption.  If I am correct about your assumption, then we are both right.  If you can point out that assumption, there's also some points in it for you.  As a show of appreciation.

I'll even admit that case could be made that it's easier to draw the conclusion of your assumption, than of mine.

Logically yours,
*Drew
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by:jtoopitsin
ID: 8115551
Corrupt statement-there can be no such thing
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by:SunBow
ID: 8121853
1) Yes (concur with 1st comment, billious)

2) Concur with TheBeaver 1st comment, it cannot be truth. So given two choices for answer, it becomes true that the statement is a lie

3) Quite interesting, the paradox history chat. Thank you kindly. What comes to mind is: No wonder the Greeks failed to continue to be in charge of world affairs, leading to rise of Romans (who may have fallen due to emulation of such thoughtful Greeks?)

4) I think part of problems above is lack of proper use of set theory, thinking all mutually exclusive, there being either always lie or always truth, leaving little room for many alternatives, begining with sometimes lie, sometimes truth .... sometimes.... else

5) Concur with jtoopitsin => no such thing, therefor, nonsense/useless due to corruption

6) Because of #2, there's no paradox. It cannot be true, it can be one lie. "Everything I tell you is a truth!". is not only alternative to "Everything I tell you is a lie!".
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by:Squajbob
ID: 8127714
Well, are you going to give the answer Tutalian?

Btw, I said his statement is a lie and I'm sticking to that.
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by:Tutalian
ID: 8131593
keneso,
You have posted the answer exactly how I would have. Great job!

to the rest,
Most of your answers were thorough and very interesting to read which is why I let it go a little longer. Thank you for all your responses.
 
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by:SunBow
ID: 8132325
Many Happy Returns                                   :-)
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by:keneso
ID: 8146624
I enjoyed reading this thread too, very interesting.
tnx Tutalian.

p.s. am I lying or telling the truth? hehe ;)
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