A teacher tells the class that there will be an unexpected exam sometime within the next week, but does not say when.
Thinking about this....
The exam can't be given on Friday, because on Friday morning the students will expect it as it had not been given earlier in the week, so it must be given on the Friday.
It cannot be given on Thursday either, as the students know that the exam cannot be on Friday, so if the teacher leaves it until Thursday it will be expected because the students haven't had the exam yet and know it cannot be on Friday.
With the same reasoning, the exam cannot be given on Wednesday because the students know that it can't be on Thursday or Friday, and so will expect it on Wednesday if it had not been given earlier in the week.
But then it cannot be given on Tuesday or Monday either for the same reasons above. This means that no matter when the exam is given, it will be expected.
So, is it really impossible to have an unexpected exam ?
Yes it is possible to have unexpected exams... we usually had it...
the thing is.. when our teacher says.. we will have unexpected exams.. he/she will not give a time frame... like your teacher gave (with in a week)... and when teacher go on and on with the usuall way of teaching... students will just get off the mind set of having exam... and started to mess around and forget about the exam... and that is the time... our teacher says.... "Put everything away but your pen" a good teacher can always screw students... the thing is How able the teacher is...
The exam cannot be unexpected if the teacher tells them it is going to occur at some point, this forces the students to expect it, conciously or unconciously, simply through the knowledge that it exists, and specifically within that time frame.
i think it would be fun, if I were a teacher, just to tell kids there will be unexpected exams. Go through the class and say stuff like this will be on the exam. And then not have the exam. I think it would be fun, espically getting near the end of the class when there would be tons of things that would be on the exam, and watching all the frantic students freak out.
ahh but the teacher could very easily anticipate what day they are going to be expecting it. Also i find that logic is flawed, you cannot say that becuase we expect it this day we will expect it another, as the test can only be on one day.. Logicaly the students would be expecting it on only one day. For example:
On Monday if the students were told this they would not have any clue what day the test could possibly be
On tuesday would be no different.
FRIDAY would be the only day they could without a doubt expect it, and even then perhaps it will be the next monday as a week is in fact 7 days.
In this way the paradox is non-exsistant... the reverse-timeline logic is flawed and too inconcluesive to say that it is impossible to have an unexpected exam. 
But i will ask this.. if you are expecting the unexpected to happen, does that make the unexpected expected? 
SunburnedCactus basically found the flaw in the paradox, but I will spell it out. It is not only that the test cannot be unexpected because people are aware that it is coming, but rather one cannot provide a specific frame in which something will occur and yet make it occur unexpectedly since the frame by definition negates the possibility of unexpectedness.
Although an interesting analysis, I don't think many students would consider that. A teacher of mine usually says "Test next week" and then we just kind of go with a random day, not putting as much thought into it. It's possible if no immediate time-frame is given (like one week).
Here in England, no school I went to had anything as a random quiz, we were always told the days! cool huh? 
It is not a paradox, because the situation would arise only, when the students as well as the teacher conducted the reasoning stated in the initial post.
However, it is sub-forum "philosophy & religion", thus I would state some
paradox regarding both.
We assume that God, as he is perceived in Christianity, Judaism and muslim religions, exists and he is almighty.
Is it possible that God creates the stone that he is not, by himself, capable of lifting that stone.
If he can't create the stone -> he isn't almighty.
If he can create the stone, he is almighty, but he can't lift it, so he isn't almighty - just a contradiction, therefore, paradox.
What do you think about it?
