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Topic: Pop Quiz Riddle (Read 78452 times) |
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MikePeuser
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Re: anyone know the answer to the pop quiz riddle?
« Reply #75 on: Oct 6th, 2002, 11:20am » |
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Lets apply formal logic to this problem:
A = write test
B = is surprise
The students conclude:
A and B -> not B,
thus not A
This however is basically wrong!
Because A -> B is identical to not A or B, we can re-write the students conclusion
not (A and B) or not B
which is
not A or not B or not B
or just
not (A and B)
which means: the test can be no surprise!
This however is all that can logically be derived. That means the teacher has "lied", or has stated something contradictical.
Setting themselves in a state of "surprise" is by no means backed up by "logic". But because they do it the teacher is proved right in the end.
Lets fill the logical structure with another content:
"You are very clever but you will not pass the exam".
Student might derive from the fact of beeing clever that he/she will pass the exam. (He/She might as well have argued the other way round...) Becaus of his/her behavior he/she fails the exam and the teacher is proved right.
No logic problem in it......
Mike
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wingyen LAU
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Re: anyone know the answer to the pop quiz riddle?
« Reply #76 on: Nov 26th, 2002, 12:38pm » |
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Hi ALL;
The problem with this riddle is the logic is in time.
If the teacher lets the students make a guess everyday, then it can't be on Friday, since when u come in on Friday, u either had the test or u didn't. If u didn't that means, coming in on Friday u know u'll have a time, and since u can say to the teacher u know it's today(friday) so it's not a surprise. But M-TH can't be ruled out. BUT one funny thing about this one is that the forward process works. If the students can guess everyday then the students can get away by saying they know there's a test on Monday, so it can't be on M. Then they say on tuesday that they know it's on tuesday and on tuesday the teache can't give a test, and the students do this till friday. =)
If the teacher lets the student make one guess on Monday ONLY, then it could be on any day.
Wing
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Gowtham Goli
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Re: anyone know the answer to the pop quiz riddle?
« Reply #78 on: Nov 27th, 2002, 9:50pm » |
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Finally every single day the students are expecting the prof to give a quiz and the prof never gives the quiz.
So as long as everyone studies really hard everyday the prof doesn't give the quiz, he cannot due to his statement, unless the students don't study wherein he can give his quiz because they are not expecting it.
solved?
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Dylan parrish
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Re: anyone know the answer to the pop quiz riddle?
« Reply #79 on: Nov 28th, 2002, 7:32pm » |
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You are all over looking the fact that he can be totally random. The students can have all there damn logic. If they told him that they didnt think there was a test at all during the week, then whats to stop him from giving one on tusday. Logic cannot account for randomness.
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Joe Pellino
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Re: anyone know the answer to the pop quiz riddle?
« Reply #80 on: Dec 12th, 2002, 3:06pm » |
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Ok I think you are stupid if you haven't thought of this: The test isn't planned for a specific day. The teacher can change the day if he wants to. If the kids say it is on Tuesday, he can change it to any other day. This will make the kids think, which is what any good teacher wants. 
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fenomas
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Re: anyone know the answer to the pop quiz riddle?
« Reply #81 on: Dec 15th, 2002, 9:46am » |
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Seems fairly simple to me... People seem to assume that the professor will set the quiz attempting to prevent the students from figuring out when the quiz will be, but the puzzle says nothing to contradict the idea that he may have chosen a day at random. He doesn't stipulate whether the students must (or can) use logic to figure out the date, or even if figuring out the date of the quiz is possible! Since the problem doesn't stipulate those things either, the students may not rely on them. Thus, they cannot assume that the professor would not put a quiz on Friday since people would realize the date after Thursday's class.
In general, the puzzle is simply too vague-- it gives no information about whether the students must guess before the week of the quiz, or if they can guess anytime, or how many times they may guess, or if a correct guess must be accompanied by a logical explanation of why it is correct. It's just a vague puzzle-- that's why it doesn't have a pat, satisfying answer.
If there's a problem with the above, please let me know....
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Joe Pellino
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Re: anyone know the answer to the pop quiz riddle?
« Reply #82 on: Jan 9th, 2003, 6:16pm » |
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Thank you for agreeing.
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Jiterbug
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Re: anyone know the answer to the pop quiz riddle?
« Reply #83 on: Jan 10th, 2003, 2:33am » |
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A given fact in this riddle is that there will be a test next week!
If it is Thursday night of course the test will be on Friday, but how did the students manage to refrain from guessing a day until Thursday night?
The deductive reasoning behind Wednsday, that also set a precedence for the other days, states that the test MUST BE on Thursday, as otherwise it would be on Friday which is no surprise. The problem with this statement is that Friday is not a surprise if and only if it is Thursday evening! Since the students must guess prior to the test they have to guess on Wednsday night if they believe that Thursday would be the day. However if they are forced to submit a guess on that evening then Friday has just as much likelihood of happening as does Thursday.
Another way of looking at this problem is to consider a hat with the #s 1,2,3,4,5 in it (each number represents a day in the week), and an envelope with one of these numbers written on it (as the day is a surprise, you can consider the number as random). You can choose to do one of 2 things:
1) Guess up front which number is in the envelope, in which case the envelope is openend and your guess is verified.
Or
2) Let the numbers be drawn from the hat, and at any point in time you can stop the drawer of numbers and submit your guess (provided that the number in the envelope hasn't been drawn yet, if it would have been drawn, then the drawer would stop, as they themselves know the number, and prove to you that it was drawn by opening the envelope).
Would you deduce that there is no number in the envelope?
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Icarus
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Re: anyone know the answer to the pop quiz riddle?
« Reply #84 on: Jan 10th, 2003, 3:36pm » |
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Okay, consider the following variation:
The teacher announces that he will give a test next week, but the students will not be able to determine which day it will be until he walks in with the test. In deed, if before the test occurs they can show him with solid logic that his announcement is false (either by determining which day the test is on, or by showing that he cannot give the test under those conditions), the test will be canceled and everyone will get 100%.
The students all reason as before, and tell him that his announcement is false and why. Everyone is surprised when he walks in on Tuesday with the test.
Did the teacher lie?
This version avoids some of the things people have argued about, such as the meaning of the word "surprise", or that the teacher chooses his day only after they pick one (if the logic was solid before he picks his day it is also solid after).
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Joe Pellino
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Re: anyone know the answer to the pop quiz riddle?
« Reply #85 on: Jan 13th, 2003, 2:51pm » |
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I have thought of yet another brilliant conclusion. Say that the test really cant be on friday. Well then using that resoning, the test cant be on thursday either because since it cant be on friday, if it hasnt been given by wednessday, they will know it will be a surprise. so with friday and thursday eliminated, that leaves 3 days. Now, since it cant be on thursday or friday, it obviously cant be on wednessday. So that leaves monday and tuesday. Now this goes until monday right. I aggree with the students on their thinking no test. But because they told the teacher that there was no test, that must be what they really thought. The teacher though knew they werent expecting a test so he let one day pass, to make them think they were right. On tuesday SURPRISE he pulls a test out totally unexpected. It is a surprise test. The students didnt expect it at all. It is basicly a trick question.  There you have it. Case closed
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redPEPPER
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Re: anyone know the answer to the pop quiz riddle?
« Reply #86 on: Jan 13th, 2003, 4:28pm » |
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If the teacher can surprise the students with a test on tuesday, that means there's a mistake in their logic (and yours).
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grrarrgh
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Re: anyone know the answer to the pop quiz riddle?
« Reply #87 on: Feb 4th, 2003, 9:34am » |
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Well, having read through the majority of this thread, I feel as if Nicodemus and Archon, among others, have already addressed the question sufficiently--at least the original, core issue, since there are additional interesting tidbits along the way that do not directly impact the question. It seems that most of the continuing discussion is about improving the method used to explain the riddle/the psychology of
decision-making/problem solving, or meaning, such as the
"surprise definition" debate, which is also interesting in its own right.
Here are my 2 incremental attempt at improvement and one bonus question, the first of which I believe covers little new logical ground, but might be more convincing for certain people; my third point might actually be mildly original:
Firstly, the (correct) claims are properly stated as "IF it is wednesday (or later), AND there is no test yet, THEN it must be later in the week;" "IF
it is already thursday (or later) AND the students are definitely untested, THEN there can be no test on friday." However, they do not actually allow the logic used by the
students to be valid. I think problem-solvers tend to overlook the first part of each conditional's antecedent -- it has to be a given day (or later). In other words, the glossing over of logic by saying, as the students do, that "the quiz can't be on Thursday, because we know it won't be on Friday," forgets that the "base case" of sorts actually gives us: IF it is fridayAND there has been no test, THEN it cannot be given on fridaysuccessfully. This seems trivial, but to link it back to the problem, the logic of the studentsinitially is fine: "if the quiz doesn't happen by Thursday, it'll be obvious the quiz
is on Friday." So, it can't be Friday. BUT, in each ensuing step, the antecedent aspect of each claim is forgotten, and we just end up lumping the statements together.
Secondly, it is not the case that it cannot be on Friday; it would just mean that if it got to such a point, it would be cancellable by the students (to read the problem strictly). In other words, by reserving the ability to "give" a predictable and hence, cancellable exam, the professor preserves the ability to keep the students in the dark. Let me be clear -- I think problem-solvers confuse "cannot give" with "gives a cancellable exam," since the latter often seems equivalent from the perspective of a student 
Thirdly (this is partially an expansion on the earlier
poor definition point made by others), what exactly do the students have to do? Say, before class every day, the students guess that today is the test -- they'll always be wrong (or get to cancel the test), but they'll never end
up having a test that counts. Isn't this ability the equivalent of being able to apply the student's "logic," and if so, doesn't that make the problem sort of silly, rather than mind-boggling? I'd try to explain in more detail, but I have to run to a Business Chinese class, and isn't part of the fun of discussing puzzles generating new ones?
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poseur
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Re: anyone know the answer to the pop quiz riddle?
« Reply #88 on: Feb 4th, 2003, 10:39am » |
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The answer is simple. The teacher may say "The test is going to be a surprise," if and only if he knows he's smarter than the students. If he knows exactly where their logic will stop, then he can always take it one step farther and surprise them. Let's say his students were so stupid that Friday rolled around and they still couldn't figure out the test would be today. Then Friday would be an acceptable surprising day even though logic rules Friday out. If they're just a little smarter, they could rule out Friday but not look that far ahead on Thursday. Then he could surprise them on Thursday, even though logic rules Thursday out. And if they rule out every day of the week, then he may go one step farther than their logic and place the test on any day and surprise them even though logic would rule that day out.
Now if his students were even smarter, then they'd have figured this out and they would have ruled Friday out a second time because, even though Friday has already been ruled out, if Friday comes along and they haven't had a quiz yet, then they should say it's going to be today, not because they think it is but because it can't hurt to say it. And they could go on to rule out Thursday a second time if they know the teacher might think that way. But as long as the teacher is always one step ahead of their logic, he can always make the quiz a surprise.
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poseur
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Re: anyone know the answer to the pop quiz riddle?
« Reply #89 on: Feb 4th, 2003, 11:20am » |
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And one other thing that makes it simple is, I would assume that they'll only be allowed to guess once. They can't come in Monday and say It's going to be today, and then come in Tuesday and say It's going to be today, and so on. Therefore, even though if Friday rolls around and they haven't had the quiz yet and they haven't guessed yet, then they can definitely cancel the quiz, the fact is that they don't dare wait that long before making their guess or the quiz will probably come while they're waiting. So Friday makes a very good day to put the quiz. It's true, when it comes it won't be a surprise, but by then they will have used up their one guess so it won't matter. Besides, he doesn't say exactly what the surprise will be. Maybe they won't be sitting there saying, "What? A quiz today?" But they will be surprised in the sense that they still can't believe he scheduled it for Friday.
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nietisne_
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Re: anyone know the answer to the pop quiz riddle?
« Reply #90 on: Apr 21st, 2003, 5:52pm » |
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what i say has been already said.i just think that people didn't payed the right attention to it.I think that the logic of the students disagrees with it self.if there was only one possible day that the quiz would be a surprise quiz(impossible) then this would be the day that we r looking for.this day appears for a moment to be monday(just the moment before we decide that it can't also be monday  ).But by the time we conclude the day is not monday we close a circle.Our conclusion now is that we should not expect the quiz on any day.in other words whenever he gives us the quiz the quiz will be unexpected.
and just a comment to a previous post :when u r setting the rules, then the only thing u have to do to be ahead of the logic of the players is to have no logic in what u do. 
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jackper
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Re: anyone know the answer to the pop quiz riddle?
« Reply #91 on: Jun 4th, 2003, 12:53pm » |
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Ok, I've read the entire thread, so I think (& hope) I'm adding a bit here:
I think the problem with the students argument is that it rests on two assumptions (at least), the truth of which can't be determined until after Friday, and therefore relate to the student's ability to 'know' the day of the test.
The assumptions: 1/ that the teacher isn't a liar, and 2/that the teacher isn't an idiot. (mighty risky assumption, judging from my experience).
Consider:
Thursday morning comes. The students say, 'well, he can't give the test tomorrow, so he has to have scheduled it for today.' They go to the teacher and say, 'Ok, you're giving the test today, because you can't give it tomorrow.' The teacher says, 'Ooops, I'm an idiot. Hadn't thought of that. I scheduled it for tomorrow.'
[So, if the students allow for the possibility the teacher is an idiot, then, on Thurday morning, they can't be sure the test will be Thursday, and so they can't eliminate Thursday]
You see, the students (on Thursday) can only know the test is on Thursday if they know the teacher's not an idiot (or a liar). How can they be sure he isn't an idiot They cant!...They have to wait till Friday to find out if he's an idiot.
The riddle involves the students 'knowing' something... and this means that the 'assumptions' they make are part of the essential riddle and cant just be assumed to be true by us.
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Icarus
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Re: anyone know the answer to the pop quiz riddle?
« Reply #92 on: Jun 4th, 2003, 4:17pm » |
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Okay - now how does that fit with the variant form I gave in my previous post? Would you say in the situation I described that the teacher was lying? Yet the students failed to predict when he would give his test, just as he said. The fundamental thing here is that the teacher is correct in his statement. How is he then a liar or an idiot?
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jackper
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Re: anyone know the answer to the pop quiz riddle?
« Reply #93 on: Jun 5th, 2003, 1:21pm » |
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on Jun 4th, 2003, 4:17pm, Icarus wrote:| Would you say in the situation I described that the teacher was lying? |
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No, I would not say the teacher was lying.
on Jun 4th, 2003, 4:17pm, Icarus wrote:| The fundamental thing here is that the teacher is correct in his statement. How is he then a liar or an idiot? |
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No, the question isn't whether the teacher actually IS an idiot.
What's critical is that the students can't know whether or not he is an idiot. Even if we stipulate in the riddle that the teacher is not an idiot, the students still can't know this. The only way they can know if he is an idiot is to wait and see what day he picks for the test.
About the teacher being 'correct' in his statement, I'm not sure... suppose the teacher walked in on the last day of the week with the test, would you say his statement was correct then?
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Icarus
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Re: anyone know the answer to the pop quiz riddle?
« Reply #94 on: Jun 5th, 2003, 6:30pm » |
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Yes, I would say that the teacher was correct - because the students did not predict he would give the test on friday.
When friday morning comes, the students are not expecting the test because they predicted there would not be a test at all.
(I suppose that at the start teacher should inform the students he will not tell them if they are right. They will only found out when test happens, or doesn't happen. And he should allow them only one chance - to avoid the "predict it every day" strategy.)
My point is that the flaw here is not that the students don't know if he is a liar or an idiot. Because he acts contrary to their prediction without being either. If the students had told him, "You are either lying, or mistaken, or you cannot give a test next week", and the teacher gives the test on any day, he will have shown their claim to be false. The teacher's statement was true. They failed to predict when he would give the test. So he wasn't lying, or mistaken.
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jackper
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Re: anyone know the answer to the pop quiz riddle?
« Reply #95 on: Jun 6th, 2003, 8:23am » |
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on Jun 5th, 2003, 6:30pm, Icarus wrote:
When friday morning comes, the students are not expecting the test because they predicted there would not be a test at all. |
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Yes, I suppose the students can't know, on Friday, that there will be a test (or that the teacher will be trying to give them a test...they need to raise their logical argument before he pulls out the test) on Friday.... but, again, I say this is only because they cant know if the teacher is a liar, an idiot, or maybe he's just senile and forgot.
We both seem to be repeating ourselves without much convincing going on. Hopefully, someone else can step in here and help. 
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Icarus
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Re: anyone know the answer to the pop quiz riddle?
« Reply #96 on: Jun 6th, 2003, 5:38pm » |
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Alright - try it this way: The teacher has a locked case with two keys. When he gives his proposal to the students, he tells them that he has written down when (if ever) he is giving the test on a sheet of paper. He then puts the paper in the case (a simple case - no magic tricks!) and locks it. He keeps one key, and gives one to the students. He tells them that when he gives the test, if they do not predict it, they will open the chest and see that this was his plan all along, or the test is canceled.
As before they predict that he cannot give the test. As before, on a certain day (it does not matter which) he walks in with it. They open the chest, and guess what? That day is written on the paper!
He did not forget (he could not forget, since it was written down beforehand). He was not mistaken, nor does he lie. Everything he said was true! They were unable to predict the day of the test.
If the students did not know if their professor was dependable, then the puzzle breaks down, because in that case, the student can't make their prediction. It is only because the students know that he IS dependable that they are able to reason that he cannot give it on any day. But once they have reasoned this, he can give the test whenever he wants completely in accordance with his words! The professor can be sharp as a tack and as honest as the day is long, and the students can know this in their bones, and to whatever other cliches are out there. Yet the puzzle STILL works!
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Leo Broukhis
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Re: anyone know the answer to the pop quiz riddle?
« Reply #97 on: Jun 6th, 2003, 11:10pm » |
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Let's rephrase the problem using a familiar item:
I throw a die. You try to guess the number thrown using the following scenario:
--> I let you make your guess or pass.
If you guess correctly (your guess does not necessarily have to be 1, it is equivalent to waiting until the corresponding round but speeds up the game), you win.
If you guess incorrectly, you lose.
If you pass, and the number thrown was 1, you lose, otherwise I say "It is not 1 ...", and the second round starts (replace "1" with "2" for the second round, go to --> ), and so on up to round 6, if you're patient enough and lucky enough, in which case you win by default.
What is your best strategy and the probability of winning?
No matter what is the answer, moving the problem into the probability domain lifts the paradox (die throws yield "surprizing" results by definition).
The usual train of thought, converted to the die domain, would go like this:
As there is a chance for you to win by default, to prevent that I'll have to use a loaded die that never goes 6 up, but here the similarity stops: you don't know whether I'm using a fair die or a loaded one, and you have to make an explicit guess of 5 -- winning by default does not move to the preceding rounds.
So, going back, the solution to the paradox is: the professor takes a risk. Simple as that.
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| « Last Edit: Jun 6th, 2003, 11:42pm by Leo Broukhis » |
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jackper
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Re: anyone know the answer to the pop quiz riddle?
« Reply #98 on: Jun 7th, 2003, 11:05am » |
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Icarus,
Great! We are SO close to agreement.
In particular, in your last paragraph,
>>>>
If the students did not know if their professor was dependable, then the puzzle breaks down, because in that case, the student can't make their prediction. It is only because the students know that he IS dependable that they are able to reason that he cannot give it on any day. But once they have reasoned this, he can give the test whenever he wants completely in accordance with his words! The professor can be sharp as a tack and as honest as the day is long, and the students can know this in their bones, and to whatever other cliches are out there. Yet the puzzle STILL works!
>>>>
I would completely agree if you would agree to change the word 'know' to the word 'assume'.
Let me try once more to explain why I want this change:
First, the riddle is still a seeming paradox, the teacher can still give the test, unexpectedly on thursday, and the students logical argument is still fallacious if they simply assume the professor is 'dependable'.
Secondly, I still don't think the students can (theoretically as well as practically) 'know' the teacher is dependable. They can know the teacher HAS BEEN dependable in the past, but they cannot know he WILL BE dependable in the future. ('Future' being anything they do not yet have knowledge of, such as which day he picked.)
I suggest saying someone is 'dependable' is a bit like the old line about an 'irresistable' force meeting an 'immovable' object. If we instead ask 'what happens when an "up till now" irresistable force meets an "up to now" immovable object?', the mystery disappears.
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Icarus
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Re: anyone know the answer to the pop quiz riddle?
« Reply #99 on: Jun 7th, 2003, 2:46pm » |
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As the puzzle stands, the students can't "know" that professor is dependable. But you can adjust the situation again (such as with the lockbox) so that the students need not know, because the professor leaves no space for himself to be undependable. Leaving out the question of whether the students can know such a thing, even if they did know it, not just assume but actually KNOW, that the professor is dependable, they still get caught. Knowing the professor is dependable does not lead them away from their conclusion. And the professor can still flout their logic without being undependable in the slightest.
Leonid - I've scanned your post but will need to think on it a bit more before I respond. (I didn't want you to think that I was ignoring your post.)
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