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divisionst06
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 Re: Pop Quiz Riddle   « Reply #225 on: May 30th, 2007, 6:47am » Quote Modify

THIS MAY BE IT:

Looking more at the definition of surprise:

"a coming upon unexpectedly; detecting in the act; taking unawares."

The only way to defeat the quiz (so to speak) and to eliminate the indefinite "surprise" from the equation is to BE PREPARED.

If the students prepare and are ready for the quiz to be any day than the quiz is no longer a "surprise quiz" but rather just a "quiz."

The teacher is simply telling them to be ready for a quiz. If they are ready for a quiz, there is no quiz. The error in their logic has been listed several times differently and no doubt there are different errors to their logic. The only answer without a counter example is be ready for the quiz everyday making it no longer a surprise.
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divisionst06
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 Re: Pop Quiz Riddle   « Reply #226 on: May 30th, 2007, 6:54am » Quote Modify

on May 30th, 2007, 6:42am, towr wrote:
 I'm not sure what you mean. If there is any test at all (tuesday or otherwise), it's a countermodel to their logic, because that told them there wouldn't be a test.

I was merely speculating that there could be a mathematical equation in which Tuesday was the sole counter-example to the students logic.
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rmsgrey
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 Re: Pop Quiz Riddle   « Reply #227 on: May 31st, 2007, 5:39pm » Quote Modify

The sharpest form of the paradox comes when the professor says:

"There will be a test tomorrow if and only if you don't expect one"

The bright student reasons thusly: "I am not expecting there to be a test tomorrow, therefore, by his statement there will in fact be a test. However, I now expect there to be a test tomorrow, therefore there won't be a test..."
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srn437
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 Re: Pop Quiz Riddle   « Reply #228 on: Aug 28th, 2007, 12:12pm » Quote Modify

It can't be friday because by thursday you'll know. It can be thursday though because by wednsday if you think it's thursday, you could be wrong. You know on thursday it's on friday, but you'll have already used your guess.
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mahesh
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 Re: Pop Quiz Riddle   « Reply #229 on: Oct 27th, 2007, 10:15am » Quote Modify

Since there was a contradiction the assumption that "there will definitely be a test this week and it will be a surprise" was wrong. The assumption led to the conclusion that there can be no test that week. Since the conclusion contradicts the assumption, the assumption has to be wrong.

If the assumption was relaxed to either "there will definitely be a test this week" or "there may be a surprise test this week" then it wouldn't lead to any contradictions.

The teacher went with the latter assumption and so should have the students. The teacher's logic would have been to pick any day at random and if the test day happened to be a Friday then he would simply not hold the test that week. If it happened to be on any other day he would proceed as planned.

Simple.
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Hippo
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 Re: Pop Quiz Riddle   « Reply #230 on: Oct 27th, 2007, 10:24am » Quote Modify

Friday is OK as well.
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spazdor
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 Re: Pop Quiz Riddle   « Reply #231 on: Nov 7th, 2007, 5:25am » Quote Modify

The professor's statement resembles part of a Godel sentence. Since the students are expected to be good, epistemically skeptical sorts, he is asserting "X is true iff there is no proof(in the students' decision schema) of X."

So indirectly, he's asserting that the students' decision schema is either incomplete or inconsistent.
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Farmer John
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 Re: Pop Quiz Riddle   « Reply #232 on: Jun 30th, 2008, 2:27pm » Quote Modify

If we assume the professor and students to both be completely rational the problem breaks down in an interesting way which I think points to the heart of the paradox:

That a test cannot be a complete surprise unless it was predicted with absolute certainty to be on another day.  If both the professor and the students use the same assumptions and logic processes it is impossible for the professor to completely surprise the students as they would at least be aware of the possibility of the actual day under the assumed rule set.

So the only way to surprise the students is to rely on them making an incorrect assumption or to intentionally mislead / lie so as to confuse them into believing that they had predicted the test.  Interestingly all a logic professor would have to do to achieve this effect would be to lead them to the assumption that they actually could predict the day of the test.

If we assume that the students were mislead into predicting that the test would be on Monday, then we have to wonder what they were thinking on Monday night for it to remain a complete surprise.
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DMR
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 Re: Pop Quiz Riddle   « Reply #233 on: Nov 13th, 2008, 2:57pm » Quote Modify

Everyone is over complicating this.

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

The flaw was in the conclusion that the quiz couldn't happen.  They should have come to the conclusion that their reasoning contradicted a stated fact "We're going to have a surprise quiz next week".  In doing so they made an illogical conclusion.  They should have concluded that they didn't have enough information and that the exact day can't be figured out.   They never even considered (from the text of the riddle) that they had a conflict and thus couldn't resolve the answer with the given information.

All of the what if's go beyond the original question "Where was the flaw".  Once that Flaw was made the rest of any further discussion is moot.  If you mess up step 2 of 200 the last 198 don't matter.
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sippan
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 Re: Pop Quiz Riddle   « Reply #234 on: Dec 11th, 2008, 9:58am » Quote Modify

Now I don't have time to page through this entire thread, so maybe this has been said before...

In my humble opinion, if you're following a logic chain that ends up contradicting the whole premise of the problem, then the chain is irrelevant to the case and invalid.
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Mickey1
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 Re: Pop Quiz Riddle   « Reply #235 on: Oct 20th, 2009, 7:31am » Quote Modify

(I apologize if somebody said this before)

It seems to me that
- the student's first reasoning is ok
- the second part "So it can't be on ANY day, so there's no quiz next week!" is in error.

The professor promised to cancel the quiz if the students could find out which day it was,
"if you can figure out what day it will be on, I'll cancel the quiz".

The student failed to do that, (they did something else, pointing out that the professors statement was meaningless) and therefore deserved to have the quiz.
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ThinkerzBlok
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 Re: Pop Quiz Riddle   « Reply #236 on: Jun 7th, 2010, 8:07am » Quote Modify

The biggest flaw is that the quiz CAN be on Friday. No matter what happens the quiz can only be on one day and the students have a 1/5 chance of guessing it.

It is true that the students will know that the quiz is on Friday after Thursday is over, but that's because the students already gambled on the fact that the test was on Friday.

It is very possible that the students would use up their guess before then.

Anyone get what i'm saying?
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Grimbal
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 Re: Pop Quiz Riddle   « Reply #237 on: Jun 8th, 2010, 2:20am » Quote Modify

Good point.

The professor's remark that the test might be canceled actually removes the paradox.

The professor can select Friday.  If the students say it is on Friday the test is canceled.  If they select another day, they won't know on Friday if the test was scheduled on the other day and was canceled or if it was scheduled on Friday.
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towr
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 Re: Pop Quiz Riddle   « Reply #238 on: Jun 8th, 2010, 3:17am » Quote Modify

You can easily enough rephrase the problem in such a way that the paradox remains.
The problem is that being told a true fact can lead to inconsistent knowledge if you were to accept it as true.
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Wikipedia, Google, Mathworld, Integer sequence DB
RrjH
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 Re: Pop Quiz Riddle   « Reply #239 on: Jun 9th, 2010, 4:39pm » Quote Modify

This is actually a riddle based off of an old paradox, the paradox was similar, but it was an execution instead of a quiz, and a prisoner instead of students.

The idea is that since the students figured out that it wouldn't be on Friday, and therefore couldn't be on Thursday, and Wedensday, and so on, that by giving them the quiz on one of those days, they would not see it coming.

In a sense it was their own logic that surprised them when he ave out the test.

There is no math to this riddle, ignore the people that say there should be. It's a plain and simple paradox with one answer.
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Mickey1
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 Re: Pop Quiz Riddle   « Reply #240 on: Jun 10th, 2010, 12:48pm » Quote Modify

Let’s have another look at the teacher’s statement:
“We're going to have a surprise quiz next week, but I'm not telling you what day... if you can figure out what day it will be on, I'll cancel the quiz."

There is no contradiction here – the teacher could have said:
“We're going to have a surprise quiz next week. You will not know what day it is...”. This is what I originally and erroneously read into the statement. These two latter statements are contradictory, but not the teacher’s.

“I am not telling you” does not amount to a statement that can be used to deduce anything at all. Therefore the students cannot avoid the quiz based on anything the teacher has said. The teacher’s promise is worthless in terms of avoiding the quiz but valuable in misleading the students and myself to the Friday to Monday induction.

A related issue: if stated as my alternative above - or as  rmsgrey - would the students' Friday-to-Monday reasoning be logically valid. I think it would.
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rmsgrey
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 Re: Pop Quiz Riddle   « Reply #241 on: Jun 11th, 2010, 7:14am » Quote Modify

An interesting variation on the puzzle is the one where the students, by cramming the night before a test, can significantly improve their marks in the test - but if the test isn't the next day, the effect is lost (though they can always have another cramming session).

With this variation, it becomes clear that the students can successfully improve their grades by "predicting" the test by cramming for up to five nights (they can stop once the test happens) - or they can fail to improve their grades by not cramming at all. In the former case, their successful prediction relies on them being allowed to take as many guesses as they need, which is altogether unsurprising...
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Bobzor
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 Re: Pop Quiz Riddle   « Reply #242 on: Apr 28th, 2012, 1:30pm » Quote Modify

Because of the student's certainty of the tests incapability of being a surprise having the test at any day would be a surprise even when they have somehow deduced the date of the test.
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