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Archon
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #50 on: Aug 16th, 2002, 1:05am » Quote Modify

I have read the whole thread, which is why I mentioned that I was surprised by the commentary on the semantics of "surprise".

I was not trying to say that the logic results in a contradiction and is therefore invalid, certainly you can have a logical argument resulting in a contradiction.
The problem is that the recursive application of the logic results in a condradiction with the initial assumption on which the logic is based. The recursive application still relies on the initial assumption of "no test by end of thursday" but then continuing the logic places it on thursday. Can't do that. You can see a similar thing happening in the Universal Truth Machine puzzle, where people are assuming that it works in order to prove that it doesn't.
I think things have gotten far too abstract on the path of what a "surprise" is, and has missed this fundamental point, which is the answer to the question posed.
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anshil
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #51 on: Aug 16th, 2002, 7:24am » Quote Modify

I say recursivness has not much to do with the paradoxon, see the "there is a surprise test tomorrow" variation, there is no recursivness in there, and still holds true for all other traits of the puzzle.
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George Wright
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #52 on: Aug 16th, 2002, 7:19pm » Quote Modify Remove

Archon,

Although its a tad confusing given the way some people
have written the students proof I don't think that's at fault.
Here is another way of writing it that might make it clearer.

Since from the professors statement we assume there exists at least one quiz, on Monday through Friday

Either 1) the only quiz is on Friday,
or
2)there exists a Quiz on Monday through Thursday.
these are the only 2 possibilities

If case (1) were true the students would come in Friday morning knowing that there had been no previous Quiz.
And therfore be able to deduce that the quiz had to be on Friday. So under the assumptions that case 1) is true we
reach a contradiction.  Therefor case 2 must be true.

Now we know that there exists a Quiz on Monday through Thursday.  There are 2 cases

Either 1) the only quiz is on Thursday,
or
2)there exists a Quiz on Monday through Wednesday.
these are the only 2 possibilities

We repeat this procedure until we get to

There exists a Quiz on Monday.

Now there are no two possibilities, the only possibility
is itself a contridiction, and we are left to conclude that
the axioms that were used to formulate the problem
were inconsistent.

-George
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Archon
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #53 on: Aug 16th, 2002, 8:20pm » Quote Modify

Quote:
 Now there are no two possibilities, the only possibility   is itself a contridiction, and we are left to conclude that   the axioms that were used to formulate the problem   were inconsistent.

Which axioms are those?
As far as I can see, there is nothing wrong with saying "assume no quiz by thursday, then quiz is predictably on friday".
And there's certainly nothing wrong with "there will be a quiz next week".

Quote:
 Either 1) the only quiz is on Friday,   or   2)there exists a Quiz on Monday through Thursday.   these are the only 2 possibilities       If case (1) were true the students would come in Friday morning knowing that there had been no previous Quiz.   (...)   Now we know that there exists a Quiz on Monday through Thursday.

No we don't. We were only able to eliminate Friday by assuming that there had been no test mon-thu. We cannot now "know" that the test must be on mon-thu, having just assumed that it wouldn't be in order to make our case.
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Ryan Lawrence
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #54 on: Aug 17th, 2002, 6:46pm » Quote Modify Remove

George, the logic used still relies on, as Archon said, the semantics of a "surprise." The logic being used to discount Friday as being the quiz day is as such:

If the quiz does not happen by Thursday, the students would know it was Friday and as a result it would no longer be a surprise, therefore the surprise quiz cannot be on Friday.

Personally, that is not too convincing to me, especially since it relies on a *huge* assumption that the author of the riddle intended for there to be an inherent catch-22 (that you can stop the quiz if you find out what day it is on, but you can't find out when the quiz would be or else it wouldn't be a surprise).

"Sometimes a cigar is just a cigar," and in this case sometimes a pop quiz just means that the students aren't told what day the quiz is on. Therefore, to me the obvious answer is that the entire logical chain is based on the quiz not occuring on Monday through Thursday, so when the quiz occured on Tuesday, the students were surprised.

Maybe there are toe answers, the simple one and the long, drawn-out, complex answer that you folks are tryin to get to, but personally, I am quite content with the obvious.
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George Wright
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #55 on: Aug 17th, 2002, 9:49pm » Quote Modify Remove

Archon,
I should probably just let this drop, but I have far too much of a stuborn streak.

The 2 cases I presented in my argument are mutually exclusive, and cover all possible conditions.  If you
disagree with this statement, then please either show me
how they can both be true at the same time, or show
me how they can both be false, given that there exists
a test.

Next I chose to take each case one at a time.

Since case 1 and 2 were mutally exclusive, when I consider
the possibility that case 1 is true, I am allowed to assume that case 2 is false.  But only for this portion of the argument.
What I found, was that by assuming that case 1 was true I reached a contradiction.

According the the laws of sentential logic, If I know
that one of A or B is true, and then I find that assuming A leads to a contradiction, then B must be true.

There for when I show that not having a test Monday
claim that there must be a test Monday through Thursday

Also the Axioms I was refering to , were those outlined
in my message on this topic dated August 10th.

Cheers,

George
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Archon
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #56 on: Aug 18th, 2002, 1:48am » Quote Modify

OK, assuming your use of "sentiential logic" is correct, then the eventual conclusion is that there is no test, which is obviously false, and therefore clearly *something* is wrong. Agreed?

The problem is that each case is a self-contained unit. You cant start with one assumption in one case, and then rely on the assumption in a completely different case in order to complete the logic:

Case 1
Assumption: No test before Fri
Conclusion: Test must be on Fri.
OK.

Case 2
Assumption: No test before Thu
Conclusion: Test must be on Thu.

This is clearly NOT OK. The correct conclusion should obviously be "Test must be on Thu OR Fri."
We were only able to eliminate Fri in case 1. This is not case 1. You must IGNORE case 1 when you start case 2.

Continuing, the correct conclusions are obvious...

Assume no test before Thu. Then test must be on Thu OR Fri. OK.

Assume no test before Wed. Then test can be on Wed, Thu, or Fri. OK

etc.
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anshil
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #57 on: Aug 18th, 2002, 3:28am » Quote Modify

Archon:
No we know on wensday already that there can never be a suprise test on Friday.

Again think about the "there is a surprise test tomorrow or the day after tomorrow" version. This still has the same problematic, and this thinking does definitly not work here.

Ryan Lawrance:
Of course as I've written above there are two variants you can look this upon, the easy one just meaing surprise by any time, and the interesting one meaning suprise-all-the-way.  Of course from practical view it isn't too interesting going after case 2, however from a scientific view it is a very interesting "gedankenexperiment" in the science of logic, you can't just render this case invalid just because you can find another view to look upon this.
 « Last Edit: Aug 18th, 2002, 3:39am by anshil » IP Logged
Archon
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #58 on: Aug 18th, 2002, 7:39am » Quote Modify

on Aug 18th, 2002, 3:28am, anshil wrote:
 Archon: No we know on wensday already that there can never be a suprise test on Friday.

That doesn't matter.
As soon as a "surprise" (read, time unpredictable) quiz is announced for next week, we know it can't be on Friday and also remain unpredictable, because that would make it predictable *by the end of thu*. As I have said twice now, there is nothing wrong with this part of the logic. It doesn't mean the quiz can't be on Fri, it simply means that we will KNOW it is on Fri *by end of Thu*.

That means that yes, on Wed, we still know that there cannot be an unpredictable quiz on Fri. But we still do not know whether it will be on Thu or Fri. If Thu goes by without it, THEN we know it's on Fri, and is predictable. But we do NOT know on Wed that the quiz is on Fri, only that IF it is on Fri, we will be able to predict it at the end of Thu.

Let me put the riddle to you another way. I am thinking of a number between 1 and 5. I am going to count from 1 to 5. If you can tell me which number I am thinking of before I say it, you win, otherwise I win.
Are you going to tell me that I cannot actually be thinking of a number between 1 and 5? (analogous to the reasoning that results in: "there cannot be a surprise quiz next week").
 « Last Edit: Aug 18th, 2002, 7:42am by Archon » IP Logged
anshil
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #59 on: Aug 18th, 2002, 9:21am » Quote Modify

<i>Let me put the riddle to you another way. I am thinking of a number between 1 and 5. I am going to count from 1 to 5. If you can tell me which number I am thinking of before I say it, you win, otherwise I win.
Are you going to tell me that I cannot actually be thinking of a number between 1 and 5? (analogous to the reasoning that results in: "there cannot be a surprise quiz next week").</i>

Thas there is there cannot be a _mmm_ quiz next week, without surprise all the way. The analogous would be you think of a number, count from 1 to 5, and you tell me additionally , it's a number I can never predict (thats the surprise fact). This argument has something wrong in itself. Since it may never be a 5, since it would be a number I can predict at four, rendering your arument false and you would have lied. So if we're at 3 I know it may not be a 5, since you said it's a number I cannot predict, so it must be a 4, (or you would lie), but then again I can predict a 4 again, so it can't be that either, or you would have lied, about the predict (=surprise) part. It can also not a 3, 2 or 1 then. Got it now?
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Archon
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #60 on: Aug 18th, 2002, 3:32pm » Quote Modify

LOL, it's not that I don't "get it". I am pointing out the flaw, which is the object of the riddle. You have done a commendable job of explaining the logic used by the students, but it's still flawed
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anshil
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #61 on: Aug 19th, 2002, 12:40am » Quote Modify

I think we're at the point this discussion with you doesn't bring any fruits, no the logic of the students is not flawed, as pointed out already several times by several authors, the base of problem itself is flawed. And still it seemed you don't get what it means that the quiz itself disables itself for not beeing a surprise quiz.
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Archon
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #62 on: Aug 19th, 2002, 4:45am » Quote Modify

<shrug>

Quote:
 the quiz itself disables itself for not beeing a surprise quiz.

Quote:
 On Tuesday, the professor gives the quiz, totally unexpected!

QED.
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anshil
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #63 on: Aug 19th, 2002, 5:06am » Quote Modify

He could also give the quiz on friday totally unexpected! (Since the studends thought there would be none)
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Onetus
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #64 on: Aug 19th, 2002, 6:10am » Quote Modify

Okay - I'm just going to concentrate on what I believe is the nature of the puzzle - why is the student's logic wrong - not what day the test is, or what the definition of surprise is. I would expect that these questions should be solved without arguing the definition of the question.

Oh and one more thing - I'm not even looking at whether the student's logic is even the correct way to guess the day - I'm solely interested in why their answer was wrong.

The students identify the following pattern. On day n their cannot be a test on a day > n.
Consider this - Numbering Monday to Friday 1..5
On day 4, they identify that 5 cannot be the quiz day.
On day 3, they identify that 4 or 5 cannot be the quiz day.
On day 2, they identify that 3,4 or 5 cannot be the quiz day.
On day 1, they identify that 2,3,4 or 5 cannot be the quiz day.
On day 0, they ... wtf? There is no day 0!

According to their logic if there wasn't a test on the current day then it can't be any day in the future. Which is great until this falls down for Monday. It's the first day of the school week - and according to their logic - they can't prove there will not be a quiz for this day.

So I humbly believe, that the flaw in the student's logic was that they took their "sequence" beyond the bounds of what they could prove and that was their mistake in the logic.

Perhaps I've missed something fundamental or maybe I was hit by the obvious brick, but hey, bring on the lions...
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Florian Pflug
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #65 on: Aug 22nd, 2002, 2:00am » Quote Modify Remove

Hi

IMHO the flaw in the students logic is to assume that THERE WILL BE A TEST UNDER ANY CIRCUMSTANCES.

But this isn't what the teacher stated. His statement was "There wil EITHER be a Test, OR (if you would know when it takes place in advance) there won't be one".

On thursday night, the students know for sure that there won't be a test (unless it has taken place already).

But on wednesday night, there are two possibilities now
1) The Test is on thursday
2) There won't be a test.

Without knowing for sure that there WILL be a test, the students can't rule out (2). This qualifies as being "surprise" I guess.

Greetings, Florian Pflug
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James Fingas
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #66 on: Aug 22nd, 2002, 8:16am » Quote Modify

I think the solution to this problem is in how the students predict the day of the test. In order to predict the test, they have to TELL THE PROFESSOR what day the test will be on. And they have to do this before the test is handed out.

So, if it were Friday morning, and there hadn't been a test yet, then they could say "The test will be today!" thus cancelling the test. Of course this statement would be false but that's beside the point.

However, on Thursday morning, they can't say "The test will be today", because that would preclude them from guessing on Friday. There's no way the professor would let them guess more than once! And by saying that, they would make it possible to put the test on Friday.

So, every day they can either: predict the test, or say nothing. But (except for Friday) either choice could be wrong. Therefore, they have a chance to predict the test, but it's like the Jack of Spades game now, and they must play against the teacher. It's possible that they'll guess right, but more likely that they won't.

Assuming they're not going to guess until they're SURE of the test date, then the professor can schedule the test on any other day than Friday. I'm sure it would still surprise some people!

And convincing themselves that there cannot be a test means that they'll never predict the test, guaranteeing that there is a test, and guaranteeing that it's a surprise.
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Guest

 Re: anyone know the answer to the pop quiz riddle?   « Reply #67 on: Aug 22nd, 2002, 1:34pm » Quote Modify Remove

I just read this and have looked over the thread, and there are couple folks with whom I agree, but I think for the most part that everyone is not answering the question.

The question is "What's the flaw in the students' thinking?"

The flaw is that the question of whether or not the test happens on Friday is mooted if the test occurs prior to Friday.

In other words, the flaw was the unstated assumption that the ONLY reason why the test could not happen on Friday was that it would be obvious.  The test could ALSO be prevented from happening on Friday if it occurs earlier in the week.

The difference of course is that the the test cannot occur other than the day on which it exists.  A simple tautoligism, but I think that it is the basic flaw in the students' otherwise vigorous thinking.

My \$0.02
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Mark Wusinich
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #68 on: Aug 22nd, 2002, 7:12pm » Quote Modify Remove

I do not have time to read every responce. But here is my explanation. The QUIZ can be on FRIDAY.  Because if it is Thursday night and the quiz has not yet happened AND they have not yet guessed then they will know it is the next day and can guess that it is on FRIDAY. If however they have already used their guess on any other day then the quiz will still be on FRIDAY. If they get unlimited guesses then each day they should guess that it is on that day.

Mark
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Patrick
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #69 on: Aug 23rd, 2002, 6:24am » Quote Modify Remove

Maybe I am being silly in my reasoning but what if the professor was to have a test on every single day. Perhaps the reason that he surprised them on Tuesday was that they had already had a test the day before. Nowhere in the question does it state that there is only one test.

This could also mean that the students predict that the test is on Monday. The surprise test for that day is cancelled since it can no longer be a surprise having been predicted, however since the students are sitting back content that they have predicted correctly they are taken by surprise by the quiz the next day. The flaw in the students thinking is that there is only one test.
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Steven Damer
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #70 on: Aug 25th, 2002, 9:36am » Quote Modify Remove

My thoughts on this problem. (Warning: long)
The professors initial statement is:
There will be a quiz on some day next week, and it will be a surprise.
Which can be restated as:
There will be a quiz next week, and you will not be able to deduce the date of the quiz from this statement.
Consider the following similar statement:
The number I am thinking of is 5, and you are unable to deduce what number I am thinking of from this statement.
Interestingly enough, even if the number I am thinking of is in fact 5, simply adding the self-referential addenda makes you unable to deduce that the number I am thinking of is 5.  Consider - if the statement is false, you are unable to deduce anything from it.  If the statement is true, then one of the consequences of the statement is that you are unable to deduce the number I am thinking of from it.
Looking at the surprise quiz, the reasoning is similar.  If the professor's statement is true, you cannot use it to deduce the day of the quiz, and if it is false, then you cannot use it to deduce the day of the quiz.
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Gerard
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #71 on: Aug 27th, 2002, 8:39am » Quote Modify Remove

Hello all,

The riddle asks “what's the flaw in the students' thinking?”  However, I do not see a way to show a convincing flaw in the students thinking without proposing a sounder logic that the students could have used. Logic can be shown flawed if the subject matter were more black and white, but that is not the case here.  The thread has discussed what the professor means by ‘surprise’ and the varying importance of the professor’s willingness to cancel the quiz.

Simply being a critic will not conclusively answer this riddle.  We can pick at how the students answer differed from what actually happened, but I for one will not be convinced until I see a riddle answer that contains a more believable answer to the professors’ challenge.

(Felt the need to defend why some of the others and I keep discussing this surprise and the correct answer that the professor would have canceled the test for)

Given the modified not 100% surprise (thanks anshil   ) I still stand by my Monday answer and belief that the students mistake was not in logic but in the definition of the word ‘surprise.’

Gerard
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Marc Lepage
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #72 on: Aug 27th, 2002, 10:53am » Quote Modify Remove

Apply logic not to the student's reasoning, but to the professor's statements.

Consider these facts:

A There will be a surprise quiz next week.
B I'm telling you what day.
C You can figure out what day.
D I will cancel the quiz.

Then the professor said this:

A
!B
C->D

We also know from the meaning of the sentences themselves that:

A->!B
D->!A

So altogether we have:

A
!B
C->D
A->!B
D->!A

Since C->D->!A which contradicts A, we know !C.

The students will not be able to figure out which day. The test will be given. It will be a surprise.

The student's problem is assuming the truth of C; that is, that they can figure out what day the quiz will be on.
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ron barry
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #73 on: Sep 5th, 2002, 3:15pm » Quote Modify Remove

Wonderful analysis, Marc Lepage.  Now for the real question - would the prof have cancelled the quiz if they'd figured out that he was lying?  i.e., !C?

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James Fingas
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 Re: anyone know the answer to the pop quiz riddle?   « Reply #74 on: Sep 6th, 2002, 6:45am » Quote Modify

The prof didn't actually lie about C, he said "if C, then D", or equivalently, "D or !C". Obviously from the story, !D. The professors overall statement was still true, however, because !C.
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