Continuing the discussion from A Tough Logic Puzzle:
So no one has an answer to the Surprise Quiz Paradox?
Should I re-post it in a separate thread, did it get buried here?
I am honestly hoping some one here can explain the logical resolution to the paradox.
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Seeing that I aced my 11+ earned my Mensa certificate and was given such puzzles as this to do in Junior School, I’ll pass… as I’ve earned that luxury. ; )
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I definitely need to stimulate my brain, but with much more than that!
Well feel free to give us a clue or a hint then, since you are Mensa-certified and this little logic puzzle that no one here can solve, including me, must be child’s play to you.
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A continual process of a conveyor-belt of elimination, until you get to the end… so also, what Einstein said 
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[I would advise to only use AI as a thesaurus or encyclopaedia/research tool, but nothing else, in order to maintain brain plasticity and mental acuity]
A sketch of a thought on resolving the paradox:
There is still the possibility of surprise if the quiz is on Friday. For one thing, the students might be surprised at the end of class on Thursday that the quiz would be on Friday. For another, a logical proof that the quiz can’t be given on Friday would make it even more surprising if the quiz were given on Friday. This seems like an objection that “it will be a surprise” is a bit ambiguous. It doesn’t seem clear exactly how to reason from nested surprise conditions.
It does seem like the conclusion that the quiz can’t be given at all is faulty, since if not giving the quiz at all is a possible, then on Friday the students don’t know whether the quiz will be given on Friday or not given at all, so the outcome is a surprise on Friday and the whole chain of reasoning falls apart.
I’m trying to come up with a more rigorous expression of what it means logically to be surprised, but I’m struggling. Best I’ve come up with is something like uncertainty, in which case the uncertainty seems to collapse only at the end of class on Thursday, not a moment sooner.
I’ll give it some more thought.
Notes of Sleeping Beauty Paradox
Well the rules of the situation are clear:
“There will be a surprise quiz next week (next week Monday-Friday).”
And,
“It will be a surprise (means: you won’t know ahead of time which day it will be; or, you won’t be able to know which day the quiz will be until the moment it is announced).”
Let’s add another defining feature here, perhaps: after next week the class is finished. So clearly if there is to be a surprise quiz it must occur before the class is over, i.e. some time next week Monday-Friday.
Given these parameters, I see no logical resolution to the supposed paradox. Which is all the more funny because clearly there is no real paradox at all. No one knows which day the quiz will be, and if we pick a random day like let’s say Tuesday, no one knew it before hand. It was a surprise.
And yet, the logic involved seems to invalidate each day in retroactive order from Friday to Thursday to… Monday, for the same reason we already know for certain that it can’t be on Friday.
The ambiguity comes in with the word “surprise”.
Say it’s Friday, and the following exchange takes place:
Clever Student says: “Well Professor, now you’re in a bind. Either you don’t give us the quiz, in which case you violate premise #1, or you give us the quiz on the only day left to give it, in which case you violate premise #2.”
Professor, looking dejected: “You’re absolutely right. I have failed you, made a liar of myself, and shamed my family… PSYCH, it’s quiz o’clock”
Clever Student: *surprised Pikachu face*
Is the student not surprised?
Now that I think of it, this paradox is similar to the liar paradox: if the Clever Student’s syllogism works, i.e. if it truly proves that the quiz cannot be given on Friday, then giving the quiz on Friday would have to be ‘surprising’, because someone doing something they cannot do is nothing if not surprising. But if giving the test on Friday is still surprising, the syllogism doesn’t work, and so giving the test on Friday isn’t surprising … in which case the syllogism does work.
Another way of getting to the same place is to conclude that we never truly believe that “or I’m lying” is not an option, and that lets us be ‘surprised’ even when the syllogism says we shouldn’t be. We basically don’t fully accept the premises. But if the syllogism works when we do accept the premises, i.e. if the premises are inherently contradictory, then we should be ‘surprised’ by any scenario in which the quiz still takes place … in which case the premises are not contradictory.
One interesting thought in trying to restate the puzzle without the concept of ‘surprise’: we could state it in terms of ‘knowledge’, e.g. the student’s won’t know the day of the quiz before the day of the quiz. I think this still creates the paradox. I thought at first it was just a problem of ‘knowing’ the future, but that doesn’t seem so: consider the case where the quiz has taken place, we don’t know what day, and we’re watching recordings of each class.
That suggests that the paradox may be rooted in the problem of knowledge: we can’t really ever truly 100% know anything, so any syllogism that has ‘know(x) \implies y ’ as a premise doesn’t work.
If it comes to Thursday and the class finished, and there has been no quiz so far this week then every student will know “oh shit, the quiz is gonna be tomorrow” because they already know the quiz MUST occur Monday-Friday this week. Hence on Friday morning when class begins they know for certain they will have the quiz today, which means they could cram study Thursday night, which was part of the reason of having a surprise quiz i.e. to make sure they can’t just cram the night before.
So no, if the quiz is on Friday then it does indeed violate the condition of being a surprise.
There is no absolute logic when it comes to human thinking.
Wow, truly amazing contribution here, thank you!
So if it doesn’t happen by Thursday, it’s not happening? Knowing that, I would cram on Sunday & Wednesday.
I only read your comment in the entire thread.
Why do people spend hours on this kind of thing?
This logic doesn’t work. If they knew for certain that there would be a quiz on Friday, then the second premise would be false. But instead, the first premise could be false: there’s no quiz at all this week. Falsifying either premise works.
Which premise will prove false? It’s a surprise!
That’s the moral of your paradox
What does it mean though? What’s the difference between there being absolute logic vs not being absolute logic?
The paradox to me is even giving a heads up that there will even be a surprise quiz removes the main element of surprise. A full on surprise would be no quiz the entire course. A surprise is something unexpected. Expectations depend on a lot of factors…one of which is being informed.
Being informed of a surprise quiz removes the surprise, regardless what day it actually lands on. Surprise is a total misnomer.
It’s more like an informed quiz, but which day of the week it happens on is not settled.
When the professor says, “Surprise! Quiz time!” the students can rightly say, “This was no surprise. A) we’re taking a class, and b) you told us this was going to happen this week. Hence our being prepared.”
sigh words
What ‘second premise’ do you mean? The fact that the quiz must be a surprise? Yes that is exactly the point. That is why it is a paradox. You both can and cannot have a surprise quiz, both appear to be the case at the same time.
By simple logic you reveal that NO day in the week will suffice to have the quiz be a surprise. You can rule out Friday right away. Then once Friday is ruled out, you can rule out Thursday for the same reason, all the way back to Monday. That is just the logic of it, which seems irrefutable except when you realize that IN REALITY and outside of that logic, the professor can pick any day (other than Friday of course) and it will be a surprise.
But is that really true? Think about being a student in the class: say it’s already Wednesday and the class finishes. Now you know the quiz will be tomorrow, because you know it cannot be on Friday. But extend this same logic back. Imagine it is Tuesday and class finishes. Then you know the quiz will be tomorrow. Same reason.
You always know the quiz will be “tomorrow” because it can’t be any of the other days. Ok, so far so good, this seems to be non-problematic. But in reality no one can predict which day the professor will choose. Because no one knows which days they will be wrong about. If it’s Monday morning and you conclude “Well the quiz has to be today since it can’t be any other day” so you study hard and wait for the quiz in class but it never comes… then you were wrong. You might also be wrong about Tuesday, Wednesday or Thursday. You can’t, however, be wrong about Friday unless the quiz occurs on a day before Friday since, if it doesn’t, then you both know it will be on Friday and it will actually be on Friday. Yet it can’t be on Friday because that violates the surprise condition.
The entire logic of the paradox/puzzle can be seen easily by juxtaposing all of that stuff above with the simple addition: after the students argue with the professor that there cannot be a surprise quiz next week for all of the above reasons, the professor goes to his desk and rolls a 6-sided die. The students as what are you doing? He explains, “If I get a 6 I will re-roll. But if I get a 1-5, that is the day the quiz will be on next week”. He doesn’t show them the result of the roll, but writes it down on a piece of paper and puts the paper in his pocket.
Now, as a student, what are you to conclude? You know each day of the week next week has an equal 20% odds of being the day of the quiz. By definition this means the quiz is going to be a surprise, or said more precisely it means that from the moment right now whichever day next week has the quiz is, right now, a complete surprise (cannot be predicted).
Does this situation change when Monday class starts next week? I don’t see how. It is equally possible the quiz will be on Monday as any other day and you know this going into class on Monday. You can only truly rule out Monday when the class is finished and no quiz occurred. So if the quiz WAS on Monday then it would have been a surprise, satisfying the conditions of the puzzle, because on the one hand you can’t actually rule out Monday until Monday class has passed without a quiz, but on the other hand if the quiz does turn out to be on Monday there was no way for you to predict that in advance, knowing the randomization involved in selecting the day.
So the logic itself of working backward by ruling out Friday, then Thursday etc. all the way back to Monday, seems superfluous. Or at least irrelevant. And yet, where is the flaw in that logic? Even if Friday is randomly picked as the quiz day, by the time Thursday comes around without a quiz the students will KNOW the quiz is tomorrow, thus proving that a surprise quiz is impossible (as long as Monday-Thursday have elapsed without a quiz). So it is true that the quiz cannot both be on Friday AND be a surprise, at least this becomes true after Thursday class has ended with no quiz occurring so far this week.
So you might say: even if the quiz is on Friday, it was still a surprise up until the end of class on Thursday, but after that (from Thurs. evening overnight and into Friday morning and right up until the moment of the quiz) it was no longer a surprise.
How does that affect the conditions? If the quiz happens to be on Friday, then it is the case that for some of the week it is possible to have a surprise quiz, but for the rest of the week (including the actual day of the quiz itself, and immediately before) it is NOT possible to have a surprise quiz. Does the fact that it was possible Monday through middle of class on Thursday somehow invalidate the fact that it is not possible from the end of class Thursday to Friday? If the condition is violated even some of the time that would seem to invalidate that entire premise of the setup. Based on that, we should be able to easily rule out Friday. Which means that, if the random die roll selects Friday, the premises fail. But if the random die roll selects any other day, the premises do not fail.
So maybe the answer to the paradox is simply that: it is possible to have a surprise quiz next week 80% of the time, and impossible 20% of the time.
Yes, I think I solved it. This is remarkably simple. Wish I could still claim the automatic ‘A’ in the epistemology class that our professor offered to anyone who could solve the paradox, lol.
It is possible to have a surprise quiz next week if the professor chooses either Monday, Tuesday, Wednesday or Thursday. In such cases the conditions of “there will be a quiz sometime next week M-F” and “the day of the quiz will be a surprise such that you won’t know which day the quiz will occur on until the quiz happens” are upheld. But it is not possible to have a surprise quiz next week if the professor chooses Friday. If Friday is chosen, this violates the surprise condition.
The reason the students’ logic is wrong is that just because the surprise condition fails if the quiz happens to be on Friday, nonetheless the quiz can still actually occur on Friday. If it does, this simply invalidates the surprise condition. Otherwise, if the quiz is on any other day of the week, the surprise condition is upheld. So the students SHOULD HAVE stopped their logical chain after ruling out Friday, and admitted that if the quiz is not on Friday then it would indeed be a surprise.