Most of you (except the guys holding onto the "prof prick theory") have got parts of it, although to be fair, there is no clear answer to this problem in mathematics yet.
What is clear though is that parts of the problem are a paradox (well done to those people who figured that out). There is also a big error in the students conclusion, caused in part by the paradox.
Firstly, the paradox:
The professor told the students that there would be a surprise test the next week, so it could either be on Monday, Tuesday, Wednesday, Thursday, or Friday. It can't be on Friday because on Thursday evening the students would know the test had to be on Friday (the only day left), and therefore wouldn't be a surprise. It can't be on Thursday for the same reason, since on Wednesday evening the students would know it had to be on Thursday (since it can't be on Friday). This argument applies for each preceding day, until we reach the conclusion that the test cannot be on any day.
Of course, the paradox is that the test seemingly can't be on any day without being a surprise test, and yet this is clearly untrue, since the professor can surprise the test on his students on any day.
The error in the students reasoning lies in their conclusion; because of the paradox, they conclude that the test cannot happen on any day. However, this is in stark contradiction to what the professor told them (that there would be a test at some point next week). Also, the professor told them that he would cancel the test if the students were able to guess what day it would be on; however, they did not do this. They deduced that the test could not be on any day, and as such, did not expect it on any day. The professor could then easily schedule the test for any day (even Friday) and it would be a surprise.
It should be noted that there are many objections to the whole problem in the first place, hence why it is currently "unsolved". My explanation is but one of many possibilities (others are listed here).
What is clear though is that parts of the problem are a paradox (well done to those people who figured that out). There is also a big error in the students conclusion, caused in part by the paradox.
Firstly, the paradox:
The professor told the students that there would be a surprise test the next week, so it could either be on Monday, Tuesday, Wednesday, Thursday, or Friday. It can't be on Friday because on Thursday evening the students would know the test had to be on Friday (the only day left), and therefore wouldn't be a surprise. It can't be on Thursday for the same reason, since on Wednesday evening the students would know it had to be on Thursday (since it can't be on Friday). This argument applies for each preceding day, until we reach the conclusion that the test cannot be on any day.
Of course, the paradox is that the test seemingly can't be on any day without being a surprise test, and yet this is clearly untrue, since the professor can surprise the test on his students on any day.
The error in the students reasoning lies in their conclusion; because of the paradox, they conclude that the test cannot happen on any day. However, this is in stark contradiction to what the professor told them (that there would be a test at some point next week). Also, the professor told them that he would cancel the test if the students were able to guess what day it would be on; however, they did not do this. They deduced that the test could not be on any day, and as such, did not expect it on any day. The professor could then easily schedule the test for any day (even Friday) and it would be a surprise.
It should be noted that there are many objections to the whole problem in the first place, hence why it is currently "unsolved". My explanation is but one of many possibilities (others are listed here).
